lagrangian optimization of two description scalar quantizers in this paper we study the problem of optimal design of balanced two description fixed rate scalar quantizer 2dsq under the constraint of convex codecells using a graph based approach to model the problem we show that the minimum expected distortion of the 2dsq is a convex function of the number of codecells in the side quantizers this property allows the problem to be solved by lagrangian minimization for which the optimal lagrangian multiplier exists given a trial multiplier we exploit a monotonicity of the objective function and develop a simple and fast dynamic programming technique to solve the parameterized problem to further improve the algorithm efficiency we propose an rd guided search strategy to find the optimal lagrangian multiplier in our experiments on distributions of interest for signal compression applications the proposed algorithm improves the speed of the fastest algorithm so far by a factor of o k logk where k is the number of codecells in each side quantizer we also assess the impact on the optimality of the convex codecell constraint using a published performance analysis of 2dsq at high rates we show that asymptotically this constraint does not preclude optimality for l 2 distortion measure when channels have a higher than 0 12 loss rate

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

threshold dynamics of a delayed nonlocal reaction diffusion hiv infection model with both cell free and cell to cell transmissions abstract in this paper we derive and analyze an hiv infection model containing a fixed latent period and both cell free and cell to cell transmissions the model is described by a spatially non local reaction diffusion system with the zero flux condition on the boundary we first show that the model admits global solutions and possesses a global attractor following the definition of the next infection operator we obtain the expression of the basic reproduction number 0 which is shown as a threshold parameter for the model dynamics our results indicate that the clearance persistence of hiv is governed by the sign of 0 1 in particular an explicit formula of 0 is given in the homogeneous case

n channel symmetric multiple descriptions part ii an achievable rate distortion region in this part ii of a two part paper we present a new achievable rate distortion region for the symmetric n channel multiple descriptions coding problem n 2 where the rate of every description is the same and the reconstruction distortion depends only on the number of descriptions received using a new approach for the random coding constructions along with a generalization of the technique used in the two channel el gamal and cover region to any n the rate region presented here achieves points that have not been known in the literature previously this rate region is derived from a concatenation of source channel erasure codes developed in part i of this work by deploying the framework of source coding with side information random binning the key idea is that by using the framework of source coding with side information multiple statistically identical realizations representing the coarse version of a source can be simultaneously refined by a single encoding we point out that there is an important conceptual difference in random coding construction for the multiple descriptions coding problem between the case of n 2 and n 2 to illustrate the framework we also present the important case of the gaussian source in detail

coordination capacity we develop elements of a theory of cooperation and coordination in networks rather than considering a communication network as a means of distributing information or of reconstructing random processes at remote nodes we ask what dependence can be established among the nodes given the communication constraints specifically in a network with communication rates ri j between the nodes we ask what is the set of all achievable joint distributions p x1 xm of actions at the nodes of the network several networks are solved including arbitrarily large cascade networks distributed cooperation can be the solution to many problems such as distributed games distributed control and establishing mutual information bounds on the influence of one part of a physical system on another

symmetrical multilevel diversity coding and subset entropy inequalities symmetrical multilevel diversity coding smdc is a classical model for coding over distributed storage in this setting a simple separate encoding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate and the entire admissible rate region of the problem the proofs utilized carefully constructed induction arguments for which the classical subset entropy inequality played a key role this paper consists of two parts in the first part the existing optimality proofs for classical smdc are revisited with a focus on their connections to subset entropy inequalities initially a new sliding window subset entropy inequality is introduced and then used to establish the optimality of superposition coding for achieving the minimum sum rate under a weaker source reconstruction requirement finally a subset entropy inequality recently proved by madiman and tetali is used to develop a new structural understanding of the work of yeung and zhang on the optimality of superposition coding for achieving the entire admissible rate region building on the connections between classical smdc and the subset entropy inequalities developed in the first part in the second part the optimality of superposition coding is extended to the cases where there is either an additional all access encoder or an additional secrecy constraint

analysis of a reaction diffusion host pathogen model with horizontal transmission abstract in this paper a diffusive host pathogen model with horizontal transmission and heterogeneous parameters is proposed and analyzed we first prove the global existence of solution and a global attractor of the model we then give the threshold dynamics for extinction and persistence of the disease our result suggests that by adding horizontal transmission even a homogeneous case the basic reproduction number is larger than the case without horizontal transmission mechanism this may lead to over evaluating the threshold role of the basic reproduction number finally we also carry out the bifurcation analysis of steady state solutions by considering disease induced mortality as the main bifurcation parameter and such results can help us better understanding how it affects the spatial pattern of the pathogen

analysis on a diffusive sis epidemic model with saturated incidence rate and linear source in a heterogeneous environment abstract in this paper we are concerned with a reaction diffusion sis epidemic model with saturated incidence rate and linear source in spatially heterogeneous environments we derive the uniform bounds of parabolic system and study the extinction and persistence of the infectious disease in terms of the basic reproduction number the existence of the endemic equilibrium ee is established when the basic reproduction number is greater than one we further investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium our study shows that the linear source can enhance persistence of infectious disease and large saturation can help speed up the elimination of disease

successive refinement of information characterization of the achievable rates let r spl middot be the rate distortion function assume that we want to describe a source with distortion no larger than spl delta sub 1 from the rate distortion theory we know that we need to do so at a rate r sub 1 no smaller than r spl delta sub 1 spl lsqb bits symbol spl rsqb if it turns out that a more accurate description at distortion spl delta sub 2 spl delta sub 2

positive steady states in an epidemic model with nonlinear incidence rate abstract in this paper we investigate a diffusive epidemic model with nonlinear incidence rate under homogeneous neumann boundary condition the value of this study lies in two aspects mathematically we show the stability of the constant positive steady state solution the existence and nonexistence the local and global structure of nonconstant positive steady states and epidemiologically we find that the system exhibits turing patterns controlled by diffusion

two step semi optimal branch and bound algorithm for feature selection in mixed variable discrimination abstract the paper presents a two step procedure for the selection of the most discriminative discrete as well as continuous features in the location model for mixed variable discriminant analysis the multivariate discriminatory measure t 2 is used as a criterion for subset choice the first step consists in finding stepwisely the most discriminative discrete features the second step enables one to select the subset of continuous variables for the previously chosen discrete feature set the two steps may be reversed when the number of discrete variables is already fixed the selection of continuous features is made efficiently by the branch and bound algorithm

the analysis and design of windowed fourier frame based multiple description source coding schemes in this paper the windowed fourier encoding decoding scheme applied to the multiple description compression problem is analyzed in the general case four window functions are needed to define the encoder and decoder although this number can be reduced to three or two by using time shift or frequency shift division schemes the encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index the distortion on each channel is analyzed using the zak transform for the optimal windows explicit representation formulas are obtained and nonlocalization results are proved asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two

long time dynamics of an sirs reaction diffusion epidemic model abstract in this paper we first deal with a diffusive sirs epidemic system in spatially heterogeneous and time periodic environment with no flux boundary condition we establish the uniform persistence if the basic reproduction number r 0 1 when the diffusion rates are equal and the system parameters are constant we obtain the global stability of the unique endemic equilibrium if r 0 1 and that of the diseases free equilibrium if r 0 1 we also study the sirs epidemic system with spontaneous infection in addition to disease transmission our results show that spontaneous infection enhances the persistence of disease the uniform bounds of solutions which are derived by a feedback argument play a fundamental role in our analysis

an achievable rate region for joint compression and dispersive information routing for networks this paper considers the problem of minimum cost communication of correlated sources over a network with multi ple sinks which consists of distributed source coding followed by routing we introduce a new routing paradigm called dispersive information routing dir wherein the intermediate nodes are allowed to split a packet and forward subsets of the received bits on each of the forward paths this paradigm opens up a rich class of research problems which focus on the interplay between encoding and routing in a network unlike conventional routing methods such as in 1 dir ensures that each sink receives just the information needed to reconstruct the sources it is required to reproduce we demonstrate using simple examples that the proposed approach offers better asymptotic performance than conventional routing techniques we show that under certain assumptions on the cost function the problem of finding the minimum cost under dir essentially reduces to characterizing an achievable rate region for a new multiterminal information theoretic setup while it is possible to derive an achievable region for this setup using prior results from general multiterminal source coding 3 these techniques do not exploit the underlying problem structure and thereby lead to suboptimal regions in this paper we propose a new coding scheme using principles from multiple descriptions encoding 2 and show that it strictly improves upon a corresponding variant of coding scheme in 3 we further show that the new coding scheme achieves the complete rate region for certain special cases of the general setup and thereby achieves the minimum communication cost under this routing paradigm

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

on achievable distortion exponents for a gaussian source transmitted over parallel gaussian channels with correlated fading and asymmetric snrs this paper considers the end to end mean squared error distortion in reconstructing a memoryless proper complex gaussian source transmitted over a set of parallel block fading gaussian noise channels where the fading gains are modeled as correlated rayleigh distributed random variables with different average powers thus resulting in asymmetric average received signal noise ratios snrs the distortion exponent i e how fast the average distortion decays to zero as the average received snr increases of several coding strategies based on separate source and channel coding is characterized the definition of distortion exponent commonly used in the literature for snr symmetric channels is generalized to the case of snr asymmetric channels it is shown that fading correlation degrades the achievable mean squared error distortion but does not affect the distortion exponent in the analyzed achievable schemes the logarithm of the determinant of the fading correlation matrix is found to be a proxy for measuring the performance degradation due to correlation as compared with the case of independent fading the proposed framework allows one to study any number of correlated parallel channels contrary to the most of the literature that restricts attention to two channels only with the same received snr and with independent fading in particular a scheme based on the multiple description coding with more than two descriptions is analyzed it is shown that determining the distortion exponent in this setting reduces to solving a linear program which can be done numerically very efficiently the proposed methodology relies on combining the ideas from linear innovation sequences and properties of determinant of sub matrices interestingly it is found that snr asymmetry is beneficial for multiple description coding when the total average received snr in decibel is held constant even in the snr symmetric case asymmetry in the compression rates is shown to lead to a larger distortion exponent than symmetric rates

the rate distortion region for multiple descriptions without excess rate during recent years there has been strong interest in a certain source coding problem which some authors call the problem of multiple descriptions old and new wringing techniques enable us to establish a single letter characterization of the rate distortion region in the case of no excess rate for the joint description

asymmetric multilevel diversity coding and asymmetric gaussian multiple descriptions we consider the asymmetric multilevel diversity a mld coding problem where a set of 2k 1 information sources ordered in a decreasing level of importance is encoded into k messages or descriptions there are 2k 1 decoders each of which has access to a nonempty subset of the encoded messages each decoder is required to reproduce the information sources up to a certain importance level depending on the combination of descriptions available to it we obtain a single letter characterization of the achievable rate region for the 3 description problem in contrast to symmetric multilevel diversity coding source separation coding is not sufficient in the asymmetric case and ideas akin to network coding need to be used strategically based on the intuitions gained in treating the a mld problem we derive inner and outer bounds for the rate region of the asymmetric gaussian multiple description md problem with three descriptions both the inner and outer bounds have a similar geometric structure to the rate region template of the a mld coding problem and moreover we show that the gap between them is constant which results in an approximate characterization of the asymmetric gaussian three description rate region

on the tradeoff region of secure exact repair regenerating codes we consider the n k d ell secure exact repair regenerating code problem which generalizes the n k d exact repair regenerating code problem with the additional constraint that the stored file needs to be kept information theoretically secure against an eavesdropper who can access the data transmitted to regenerate a total of ell different failed nodes for all known results on this problem the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point achieved by a scheme proposed by shah rashmi and kumar the srk point since the achievable tradeoff regions of the exact repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general these existing results suggest a phase change like behavior i e enforcing a secrecy constraint ell geq 1 immediately reduces the tradeoff region to one with a single corner point in this paper we first show that when the secrecy parameter ell is sufficiently large the srk point is indeed the only corner point of the tradeoff region however when ell is small we show that the tradeoff region can in fact have multiple corner points in particular we establish a precise characterization of the tradeoff region for the 7 6 6 1 problem which has exactly two corner points thus a smooth transition instead of a phase change type of transition should be expected as the secrecy constraint is gradually strengthened

varying total population enhances disease persistence qualitative analysis on a diffusive sis epidemic model abstract this paper performs qualitative analysis on an sis epidemic reaction diffusion system with a linear source in spatially heterogeneous environment the main feature of our model lies in that its total population number varies compared to its counterpart proposed by allen et al 2 the uniform bounds of solutions are derived based on which the threshold dynamics in terms of the basic reproduction number is established and the global stability of the unique endemic equilibrium is discussed when spatial environment is homogeneous in particular the asymptotic profile of endemic equilibria is determined if the diffusion rate of the susceptible or infected population is small or large the theoretical results show that a varying total population can enhance persistence of infectious disease and therefore the disease becomes more threatening and harder to control

minimum breakdown degradation in binary source encoding a memoryless binary equiprobable source produces one letter per second two people each are provided separately with private information about the source data at a rate of 1 2 bit per second suppose that by pooling their information they can produce a long mn reconstruction of the source output that has arbitrarily small error frequency we prove that then the least common asymptotic error frequency d that each can achieve without the other s help is sqrt 2 1 2 0 207 since it had been shown previously that 0 200 leq d leq 0 207 our result closes the so called 007 gap new analytical techniques introduced to effect the proof are of broader significance in multiuser information theory

qualitative analysis for a diffusive predator prey model with a transmissible disease in the prey population in this paper we study a diffusive predator prey model with a transmissible disease in the prey population we offer a complete discussion of the dynamical properties under the homogeneous neumann boundary condition we analyze local and global stabilities of nonnegative constant steady states and long time behaviors of the positive solutions moreover we study the existence nonexistence and bifurcation of nonconstant positive stationary solutions finally some numerical simulations are presented to support and strengthen our analytical analysis

multiple description coding with many channels an achievable region for the l channel multiple description coding problem is presented this region generalizes two channel results of el gamal and cover 1982 and of zhang and berger 1987 it further generalizes three channel results of gray and wyner 1974 and of zhang and berger a source that is successively refinable on chains is shown to be successively refinable on trees a new outer bound on the rate distortion rd region for memoryless gaussian sources with mean squared error distortion is also derived the achievable region meets this outer bound for certain symmetric cases

ldgm based multiple description coding for finite alphabet sources this work presents an ldgm based practical successive coding scheme for the multiple description md problem for finite alphabet sources the scheme which targets the zhang berger zb rate distortion region is shown to be asymptotically optimal with joint typicality encoding while as a practical encoding solution a message passing algorithm is adopted we further discuss in more detail the application of the coding scheme in three cases of the md problem with the hamming distortion measure 1 no excess sum rate for binary sources 2 successive refinement and 3 no excess marginal rate for the uniform binary source in the no excess sum rate case some progress is made in the characterization of fundamental limits by deriving the analytical expression of the distortion region for general binary sources and of the auxiliary variables needed to achieve its boundary the exact expression of the zhang berger upper bound to the central distortion is also provided for the case of no excess marginal rate for the uniform binary source the proposed ldgm based coding scheme is tested in practice for all three aforementioned cases the experimental results show very good performance demonstrating its ability to approach the theoretical rate distortion limits or the available upper bounds

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

asymptotic profile of the positive steady state for an sis epidemic reaction diffusion model effects of epidemic risk and population movement abstract identifying the epidemic risk for infectious disease is crucial in order to effectively perform control measures in a series of our work from an analytical aspect we study the effects of epidemic risk and population movement on the spatiotemporal transmission of infectious disease via an sis epidemic reaction diffusion model proposed by allen et al 2008 in 36 in allen et al 2008 36 peng 2009 37 it was assumed that the habitat of the populations consists of only the low and high risk areas the present paper concerns a more complicated heterogeneous environment where the moderate risk area occurs and deals with two cases i only the moderate and high risk areas exist ii the low moderate and high risk areas coexist in each case we rigorously determine the asymptotic profile of the positive steady state i e the endemic equilibrium as the migration rate of either the susceptible or infected population tends to zero our results show how epidemic risk and population movement affect the spatial distribution of infectious disease and thereby suggest important implications for predicting the patterns of disease occurrence and designing optimal control strategies numerical simulations are carried out to support the theoretical results

new results in binary multiple descriptions an encoder whose input is a binary equiprobable memoryless source produces one output of rate r 1 and another of rate r 2 let d 1 d 2 and d 0 respectively denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rate r l only the encoder output of rate r 2 only and both encoder outputs the two descriptions problem is to determine the region r of all quintuples r 1 r 2 d 1 d 2 d 0 that are achievable in thc usual shannon sense let r d 1 d log 2 d 1 d log 2 1 d denote the error frequency rate distortion function of the source the no excess rate case prevails when r 1 r 2 r d 0 and the excess rate case when r 1 r 2 r d 0 denote the section of r at r 1 r 2 d 0 by d r 1 r 2 d 0 d 1 d 2 r 1 r 2 d 1 d 2 d 0 in r in the no excess rate case we show that a portion of the boundary of d r 1 r 2 d 0 coincides with the curve frac 1 2 d 1 2d 0 frac 1 2 d 2 2d 0 frac 1 2 1 2d 0 2 this curve is an extension of witsenhausen s hyperbola bound to the case d 0 0 it follows that the projection of r onto the d 1 d 2 plane at fixed d 0 consists of all d 1 geq d 0 and d 2 geq d 0 that lie on or above this hyperbola in the excess rate case we show by counterexample that the achievable region of el gamal and cover is not tight

near optimality of composite multiple description source codes in this paper new upper and lower bounds are first presented for the rate loss of multiple description source codes mdscs for a two description mdsc 2dsc the rate loss of description i with distortion di is defined as li ri r di i 1 2 where ri is the rate of the ith description and r d is the rate distortion function for the given source the joint rate loss associated with decoding the two descriptions together to achieve central distortion d0 is measured as l0 r1 r2 r d0 consider an arbitrary memoryless source with variance 2 and let the distortion measure be the mean squared error distortion measure it is shown that for any optimal 2dsc a 0 l0 0 8802 and 0 l1 l2 0 3802 if d0 d1 d2 2 b 0 l1 l2 0 4401 if d0 1 d1 1 d2 1 2 1 c 0 l1 l2 0 3802 and r max d1 d2 1 l0 r max d1 d2 0 3802 for all other d0 a tighter bound on the distance between the el gamal cover inner bound and the achievable region is also presented inspired by these new bounds a low complexity composite 2dsc design first developed by lastras montano and castelli is extended and the resulting code is shown to be near optimal for all memoryless sources and all distortions these results are also extended to mdscs with an arbitrary number of packets finally gaussian sources are analyzed in detail to verify these bounds and examine their tightness

achievable rates for multiple descriptions with feed forward the two channel multiple descriptions problem for an independent and identically distributed i i d source with feed forward to one or both side decoders is considered a single letter achievable rate region is derived it enlarges the best known rate region for multiple descriptions without feed forward the proof of the result uses a block markov superposition source coding strategy in point to point source coding feed forward does not decrease the rate distortion function of an i i d source in contrast an example is provided to show that the derived region can be strictly larger than the optimal multiple description rate distortion region without feed forward

broadcast coded modulation multilevel and bit interleaved construction the capacity of the awgn broadcast channel is achieved by superposition coding but the superposition of individual coded modulations expands the modulation alphabet and distorts its configuration hierarchical modulations which appear in the literature mostly in the context of unequal error protection can approach only a few isolated points on the boundary of the broadcast capacity region this paper studies multilevel coding mlc for constellation constrained broadcast coded modulation the conditions under which multilevel codes can achieve the constellation constrained capacity of the awgn broadcast channel are derived we propose a pragmatic multilevel design technique with near constellation constrained capacity performance where the coupling of the superposition inner and outer codes is localized to each bit level it is shown that this can be further relaxed to a code coupling on only one bit level with a little or no penalty under natural labeling the rate allocation problem between the bit levels of the two users is studied and a pragmatic method is proposed again with near capacity performance in further pursuit of lower complexity a hybrid mlc bit interleaved coded modulation is proposed whose performance is shown to be very close to the boundary of the constellation constrained capacity region simulation results show that good point to point ldpc codes produce excellent performance in the proposed coded modulation framework

selection of variables in mixed variable discriminant analysis a manova log linear formulation of the location model for mixed variable discriminant analysis is considered a strategy for the selection of variables and terms in such a model is based on akaike s criterion to overcome problems caused by noncomparable submodels some modifications to akaike s criterion are proposed an example of discrimination between bad and good melons illustrates the selection procedure

multiuser successive refinement and multiple description coding in this correspondence we consider the multiuser successive refinement msr problem where the users are connected to a central server via links with different noiseless capacities and each user wishes to reconstruct in a successive refinement fashion an achievable region is given for the two user two layer case and it provides the complete rate distortion region for the gaussian source under the mse distortion measure the key observation is that this problem includes the multiple description md problem with two descriptions as a subsystem and the techniques useful in the md problem can be extended to this case it is shown that the coding scheme based on the universality of random binning is suboptimal because multiple gaussian side informations only at the decoders do incur performance loss in contrast to the case of single side information at the decoder it is further shown that unlike the single user case when there are multiple users the loss of performance by a multistage coding approach can be unbounded for the gaussian source the result suggests that in such a setting the benefit of using successive refinement is not likely to justify the accompanying performance loss the msr problem is also related to the source coding problem where each decoder has its individual side information while the encoder has the complete set of the side informations the msr problem further includes several variations of the md problem for which the specialization of the general result is investigated and the implication is discussed

distributed multilevel diversity coding in distributed multilevel diversity coding k correlated sources each with k components are encoded in a distributed manner such that given the outputs from any alpha encoders the decoder can reconstruct the first alpha components of each of the corresponding alpha sources for this problem the optimality of a multilayer slepian wolf coding scheme based on binning and superposition is established when k leq 3 the same conclusion is shown to hold for general k under a certain symmetry condition which generalizes a celebrated result by yeung and zhang

dynamics and profiles of a diffusive host pathogen system with distinct dispersal rates abstract in this paper we investigate a diffusive host pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts we first prove that the solution of the model exists globally and the model system possesses a global attractor we then identify the basic reproduction number r 0 for the model and prove its threshold role if r 0 1 the disease free equilibrium is globally asymptotically stable if r 0 1 the solution of the model is uniformly persistent and there exists a positive pathogen persistent steady state finally we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen s most favoured sites when the mobility of the infected host is limited

vector gaussian multiple description with two levels of receivers the problem of l multiple descriptions of a stationary and ergodic gaussian source with two levels of receivers is investigated each of the first level receivers receive an arbitrary subset k of the l descriptions k l the second level receiver receives all l descriptions all the receivers both at the first level and the second level reconstruct the source using the subset of descriptions they receive the corresponding reconstructions are subject to quadratic distortion constraints our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met we show that an analog digital separation architecture involving joint gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios these scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k 2 and l 3

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

approximating the gaussian multiple description rate region under symmetric distortion constraints we consider multiple description md coding for the gaussian source with k descriptions under the symmetric mean squared error mse distortion constraints and provide an approximate characterization of the rate region we show that the rate region can be sandwiched between two polytopes between which the gap can be upper bounded by constants dependent on the number of descriptions but independent of the distortion constraints underlying this result is an exact characterization of the lossless multilevel diversity source coding problem a lossless counterpart of the md problem this connection provides a polytopic template for the inner and outer bounds to the rate region in order to establish the outer bound we generalize ozarow s technique to introduce a strategic expansion of the original probability space by more than one random variable for the symmetric rate case with any number of descriptions we show that the gap between the upper bound and the lower bound for the individual description rate distortion function is no larger than 0 92 bit the results developed in this work also suggest that the ldquoseparationrdquo approach of combining successive refinement quantization and lossless multilevel diversity coding is a competitive one since its performance is only a constant away from the optimum the results are further extended to general sources under the mse distortion measure where a similar but looser bound on the gap holds

on rate reliability distortion function for a robust descriptions system a source coding problem is considered for a robust description system with one encoder and many decoders the rate reliability distortion function is specified an example is given showing the distinction in the calculation of the rate reliability distortion function as compared with the rate distortion function

multiple description quantization via gram schmidt orthogonalization the multiple description md problem has received considerable attention as a model of information transmission over unreliable channels a general framework for designing efficient md quantization schemes is proposed in this paper we provide a systematic treatment of the el gamal cover egc achievable md rate distortion region and show it can be decomposed into a simplified egc segc region and a superimposed refinement operation furthermore any point in the segc region can be achieved via a successive quantization scheme along with quantization splitting for the quadratic gaussian case the proposed scheme has an intrinsic connection with the gram schmidt orthogonalization which implies that the whole gaussian md rate distortion region is achievable with a sequential dithered lattice based quantization scheme as the dimension of the optimal lattice quantizers becomes large moreover this scheme is shown to be universal for all independent and identically distributed i i d smooth sources with performance no worse than that for an i i d gaussian source with the same variance and asymptotically optimal at high resolution a class of md scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically the performance is analyzed in the high resolution regime which exhibits a noticeable improvement over the existing md scalar quantization schemes

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

a spatial sis model in advective heterogeneous environments abstract we study the effects of diffusion and advection for a susceptible infected susceptible epidemic reaction diffusion model in heterogeneous environments the definition of the basic reproduction number r 0 is given if r 0 1 the unique disease free equilibrium dfe is globally asymptotically stable asymptotic behaviors of r 0 for advection rate and mobility of the infected individuals denoted by d i are established and the existence of the endemic equilibrium when r 0 1 is studied the effects of diffusion and advection rates on the stability of the dfe are further investigated among other things we find that if the habitat is a low risk domain there may exist one critical value for the advection rate under which the dfe changes its stability at least twice as d i varies from zero to infinity while the dfe is unstable for any d i when the advection rate is larger than the critical value these results are in strong contrast with the case of no advection where the dfe changes its stability at most once as d i varies from zero to infinity

the explicit coding rate region of symmetric multilevel diversity coding it is well known that superposition coding namely separately encoding the independent sources is optimal for symmetric multilevel diversity coding smdc yeung zhang 1999 for any l geq 2 where l is the number of levels of the coding system however the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term i e the lower bound in each inequality is given in terms of the solution of a linear optimization problem thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple in principle the achievability of a given rate tuple can be determined by direct computation but the complexity is prohibitive even for l 5 in this paper for any fixed l we obtain in closed form a finite set of linear inequalities for characterizing the coding rate region we further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple yet the cardinality of this smaller set grows at least exponentially fast with l we also present a subset entropy inequality which together with our explicit characterization of the coding rate region is sufficient for proving the optimality of superposition coding

asymptotic profiles of the endemic equilibrium to a diffusive sis epidemic model with mass action infection mechanism abstract in this paper we are concerned with the endemic equilibrium to a diffusive sis epidemic model with mass action infection mechanism under much weaker assumptions we determine the asymptotic profile of the endemic equilibrium as the diffusion rate d s of the susceptible population goes to zero in one space dimension we also discuss the asymptotic profile of the endemic equilibrium as the diffusion rate d i of the infected population goes to zero our theoretical analysis shows that the infectious disease still exists in the above two situations and such behaviors are very different from that of other sis epidemic systems our first result essentially improves the main ones of wu and zou 2016 29 and in one space dimension our second result solves an open problem left there

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

dynamics of a nonlocal dispersal sis epidemic model with neumann boundary conditions abstract in this paper we study a nonlocal dispersal susceptible infected susceptible sis epidemic model with neumann boundary condition where the spatial movement of individuals is described by a nonlocal convolution diffusion operator the transmission rate and recovery rate are spatially heterogeneous and the total population number is constant we first define the basic reproduction number r 0 and discuss the existence uniqueness and stability of steady states of the nonlocal dispersal sis epidemic model in terms of r 0 then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease the obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease in particular our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease

rate region of gaussian multiple description coding with individual and central distortion constraints the rate region of gaussian multiple description coding with individual and central distortion constraints is completely characterized specifically a lower bound and an upper bound are derived for each supporting hyperplane of the rate region where the lower bound is associated with a max min game while the upper bound is associated with a min max game furthermore it is shown that these two bounds coincide due to the existence of a saddle point

ideal point discriminant analysis a new method of multiple discriminant analysis was developed that allows a mixture of continuous and discrete predictors the method can be justified under a wide class of distributional assumptions on the predictor variables the method can also handle three different sampling situations conditional joint and separate in this method both subjects cases or any other sampling units and criterion groups are represented as points in a multidimensional euclidean space the probability of a particular subject belonging to a particular criterion group is stated as a decreasing function of the distance between the corresponding points a maximum likelihood estimation procedure was developed and implemented in the form of a fortran program detailed analyses of two real data sets were reported to demonstrate various advantages of the proposed method these advantages mostly derive from model evaluation capabilities based on the akaike information criterion aic

asymptotic profiles of the positive steady state for an sis epidemic reaction diffusion model part i abstract to capture the impact of spatial heterogeneity of environment and movement of individuals on the persistence and extinction of a disease allen et al in l j s allen b m bolker y lou a l nevai asymptotic profiles of the steady states for an sis epidemic reaction diffusion model discrete contin dyn syst ser a 21 1 2008 1 20 proposed a spatial sis susceptible infected susceptible reaction diffusion model and studied the existence uniqueness and particularly the asymptotic behavior of the endemic equilibrium as the diffusion rate of the susceptible individuals goes to zero in the case where a so called low risk subhabitat is created in this work we shall provide further understanding of the impacts of large and small diffusion rates of the susceptible and infected population on the persistence and extinction of the disease which leads us to determine the asymptotic behaviors of the endemic equilibrium when the diffusion rate of either the susceptible or infected population approaches to infinity or zero in the remaining cases consequently our results reveal that in order to eliminate the infected population at least in low risk area it is necessary that one will have to create a low risk subhabitat and reduce at least one of the diffusion rates to zero in this case our results also show that different strategies of controlling the diffusion rates of individuals may lead to very different spatial distributions of the population moreover once the spatial environment is modified to include a low risk subhabitat the optimal strategy of eradicating the epidemic disease is to restrict the diffusion rate of the susceptible individuals rather than that of the infected ones

vector gaussian multiple description with individual and central receivers t multiple descriptions of a vector gaussian source for individual and central receivers are investigated the sum rate of the descriptions with covariance distortion measure constraints in a positive semidefinite ordering is exactly characterized for two descriptions the entire rate region is characterized the key component of the solution is a novel information theoretic inequality that is used to lower bound the achievable multiple description rates jointly gaussian descriptions are optimal in achieving the limiting rates we also show the robustness of this description scheme the distortions achieved are no larger when used to describe any non gaussian source with the same covariance matrix

discrimillant analysis with discrete and continuous variables a paradigmatic methodologic approach does not exist for the problem of discriminant analysis with both discrete and continuous explanatory variables procedures that have been employed in this situation include fisher s linear discriminant function the quadratic discriminant function the linear discriminant furlction with higher order terms discriminant functions with logistic regression estimates of the coefficients and the location model average optimal error rates for these procedures are reported for the case of one normal variable and two binary variables these approaches are also compared for the prediction of two year survival following recovery from myocardial infarction employing resubstitution jackknife and independent sample estimates of the error rates recommendations for applications are presented

dynamics and asymptotic profiles of steady states of an epidemic model in advective environments abstract we study the dynamics of a sis epidemic model of reaction diffusion advection type the persistence of infected and susceptible populations and the global stability of the disease free equilibrium are established when the basic reproduction number is greater than or less than or equal to one respectively we further consider the effects of diffusion and advection on asymptotic profiles of endemic equilibrium when the advection rate is relatively large comparing to the diffusion rates of both populations then two populations persist and concentrate at the downstream end as the diffusion rate of the susceptible population tends to zero the density of the infected population decays exponentially for positive advection rate but linearly when there is no advection our results suggest that advection can help speed up the elimination of disease

an on line universal lossy data compression algorithm via continuous codebook refinement i basic results a new on line universal lossy data compression algorithm is presented for finite memoryless sources with unknown statistics its performance asymptotically approaches the fundamental rate distortion limit the codebook is generated on the fly and continuously adapted by simple rules there is no separate codebook training or codebook transmission candidate codewords are randomly generated according to an arbitrary and possibly suboptimal distribution through a carefully designed gold washing or information theoretic sieve mechanism good codewords and only good codewords are promoted to permanent status with high probability we also determine the rate at which our algorithm approaches the fundamental limit

new coding schemes for the symmetric k description problem we propose novel coding schemes for the k description problem with symmetric rates and symmetric distortion constraints there are two main new ingredients in these schemes the first one is akin to the method seen in the well known butterfly network of network coding literature and systematic erasure channel codes are applied on certain carefully chosen source coding component the second approach is built on the quantization splitting technique which was previously proven useful in the gaussian ceo problem we first focus on a special case of the three description problem where any two descriptions are rate distortion optimal jointly referred to as the no two description excess rate case for this special case and the quadratic gaussian source we show that the two aforementioned approaches lead to rate distortion points outside the achievable region based on the source channel erasure codes previously proposed by pradhan puri and ramchandran interestingly though only the symmetric problem is considered in our work the proposed schemes in fact benefit from time sharing several asymmetric rate distortion points the insights gained through the no two description excess rate case lead to strategic combination of the new ingredients with the existing coding scheme yielding new coding schemes for the symmetric k description problem

strong functional representation lemma and applications to coding theorems this paper shows that for any random variables x and y it is possible to represent y as a function of x z such that z is independent of x and i x z y le log i x y 1 4 bits we use this strong functional representation lemma sfrl to establish a bound on the rate needed for one shot exact channel simulation for general discrete or continuous random variables strengthening the results by harsha et al and braverman and garg and to establish new and simple achievability results for one shot variable length lossy source coding multiple description coding and gray wyner system we also show that the sfrl can be used to reduce the channel with state noncausally known at the encoder to a point to point channel which provides a simple achievability proof of the gelfand pinsker theorem

a spatial seirs reaction diffusion model in heterogeneous environment abstract we propose a susceptible exposed infected recovered susceptible seirs reaction diffusion model where the disease transmission and recovery rates can be spatially heterogeneous the basic reproduction number r 0 is connected with the principal eigenvalue of a linear cooperative elliptic system threshold type results on the global dynamics in terms of r 0 are established the monotonicity of r 0 with respect to the diffusion rates of the exposed and infected individuals which does not hold in general is established in several cases finally the asymptotic profile of the endemic equilibrium is investigated when the diffusion rate of the susceptible individuals is small our results reveal the importance of the movement of the exposed and recovered individuals in disease dynamics as opposed to most of previous works which solely focused on the movement of the susceptible and infected individuals

global stability of the steady states of an sis epidemic reaction diffusion model abstract in this work we investigate the sis epidemic reaction diffusion model under heterogeneous environment studied by allen et al in l j s allen b m bolker y lou a l nevai asymptotic profiles of the steady states for an sis epidemic reaction diffusion model discrete contin dyn syst a 21 1 2008 1 20 in the two cases 1 the diffusion rate d s of the susceptible individuals is equal to the diffusion rate d i of the infected individuals 2 x r x for any fixed constant r 0 where x and x respectively represent the rates of disease transmission and disease recovery we completely determine the global stability of the disease free equilibrium and the unique endemic equilibrium if it exists our results partially answer the conjecture proposed by allen et al

new results on multiple descriptions in the wyner ziv setting some new results of multiple descriptions in the wyner ziv setting mdwz are presented mdwz uses two pieces of side information si for two different side decoders both si are available to the central decoder but none to the encoder the complete achievable region for a quadratic gaussian mdwz system is derived this result is an extension of ozarow s result on multiple descriptions of a gaussian source without si and diggavi vaishampayan s result on common si it is shown that a refinement layer for the central decoder is indispensable if the central distortion is sufficiently small the tight rate distortion region is also given if one of the side decoders is required to perfectly reconstruct a deterministic function of the source

combinatorial message sharing and a new achievable region for multiple descriptions this paper presents a new achievable rate distortion region for the general l channel multiple descriptions mds problem a well known general region for this problem is due to venkataramani kramer and goyal vkg their encoding scheme is an extension of the el gamal cover ec and zhang berger zb coding schemes to the l channel case and includes a combinatorial number of refinement codebooks one for each subset of the descriptions as in zb the scheme also allows for a single common codeword to be shared by all descriptions this paper proposes a novel encoding technique involving combinatorial message sharing cms where every subset of the descriptions may share a distinct common message this introduces a combinatorial number of shared codebooks along with the refinement codebooks of these shared codebooks provide a more flexible framework to tradeoff redundancy across the messages for resilience to descriptions loss we derive an achievable rate distortion region for the proposed technique and show that it subsumes the vkg region for general sources and distortion measures we further show that cms provides a strict improvement of the achievable region for any source and distortion measures for which some two description subset is such that zb achieves points outside the ec region we then show a more surprising result cms outperforms vkg for a general class of sources and distortion measures including scenarios where the zb and ec regions coincide for all two description subsets in particular we show that cms strictly improves on vkg for the l channel quadratic gaussian md problem for all l geq 3 despite the fact that the ec region is complete for the corresponding two descriptions problem consequently the correlated quantization scheme an extreme special case of vkg that has been proven to be optimal for several cross sections of the l channel quadratic gaussian md problem is strictly suboptimal in general using the encoding principles derived we show that the cms scheme achieves the complete rate distortion region for several asymmetric cross sections of the l channel quadratic gaussian md problem

a sis reaction diffusion advection model in a low risk and high risk domain abstract a simplified sis model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease the free boundary is introduced to model the spreading front of the disease the basic reproduction number associated with the diseases in the spatial setting is introduced sufficient conditions for the disease to be eradicated or to spread are given our result shows that if the spreading domain is high risk at some time the disease will continue to spread till the whole area is infected while if the spreading domain is low risk the disease may be vanishing or keep spreading depending on the expanding capability and the initial number of the infective individuals the spreading speeds are also given when spreading happens numerical simulations are presented to illustrate the impacts of the advection and the expanding capability on the spreading fronts

on team guessing with independent information team theory is the study of situations in which a set of cooperating agents called a team each with access to different data or information attempt to optimize a common criterion under rules which restrict communication between agents team theory is of interest in theoretical studies in economics communication and control a very simple example of a team situation is the following each of the team s n agents attempts to ascertain whether or not a certain random event e of probability has occurred agent i must base his decision solely on the observation of random variable ui and the team s goal is to minimize pi n 1 pi where pi is the probability that agent i makes an error the main result of this paper is to show that when the variables u1 un are independent this alone places a positive lower bound on pi no matter what the joint distribution of e and the data ui may be for each n the exact lower bound is determined it is frac 1 2 sqrt 2 1 for n 2 for n 3 and as n goes to infinity it is asymptotic to frac 1 2 left1 sqrt frac 2 pi n right

n channel symmetric multiple descriptions part i n k source channel erasure codes in this two part paper we present a new achievable rate region for the general n channel symmetric multiple descriptions problem in part i inspired by the concept of maximum distance separable mds erasure channel codes we consider a special case of this rate region where the source is encoded into n descriptions each with rate r these descriptions are transmitted over n bandwidth constrained and errorless channels during transmission a subset of these channels can break down thus erasing the corresponding descriptions the decoder is interested in recovering the source with the reception of at least k descriptions thus the encoder is allowed to sample only one realization of this breakdown process during the entire transmission for gaussian sources we have the following interesting result when any k descriptions arrive the achievable distortion exactly matches the optimal distortion rate performance corresponding to a source rate of kr bits with the reception of any m k descriptions the source reconstruction quality is strictly better the improvement being nearly linear in the number of descriptions received

a nonlocal and time delayed reaction diffusion model of dengue transmission a nonlocal and time delayed reaction diffusion model of dengue fever is first proposed that incorporates the aquatic stage the winged stage and the incubation periods of the dengue virus within mosquitos and hosts then the basic reproduction number r 0 is established for the model system and an explicit formula of r 0 is obtained in the case of spatially homogeneous infections it is shown that this r 0 gives the threshold dynamics in the sense that the disease free equilibrium is asymptotically stable if r 0 1 the influences of diffusion coefficients time delays and infection heterogeneity on the spread of the disease are also studied via numerical simulations it turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections

optimal filter banks for multiple description coding analysis and synthesis multiple description md coding is a source coding technique for information transmission over unreliable networks in md coding the coder generates several different descriptions of the same signal and the decoder can produce a useful reconstruction of the source with any received subset of these descriptions in this paper we study the problem of md coding of stationary gaussian sources with memory first we compute an approximate md rate distortion region for these sources which we prove to be asymptotically tight at high rates this region generalizes the md rate distortion region of el gamal and cover 1982 and ozarow 1980 for memoryless gaussian sources then we develop an algorithm for the design of optimal two channel biorthogonal filter banks for md coding of gaussian sources we show that optimal filters are obtained by allocating the redundancy over frequency with a reverse water filling strategy finally we present experimental results which show the effectiveness of our filter banks in the low complexity low rate regime

solving the inverse problem of an sis epidemic reaction diffusion model by optimal control methods in this contribution a novel inverse problem on an sis epidemic reaction diffusion model is investigated by employing the optimal control methods by setting a proper regular cost functional and choosing the coefficients to be identified as control variables we embed the original inverse problem which is very difficult to solve into an optimal control problem the existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established respectively in particular the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques

qualitative analysis of steady states to the sel kov model in this work we are concerned with a reaction diffusion system well known as the sel kov model which has been used for the study of morphogenesis population dynamics and autocatalytic oxidation reactions we derive some further analytic results for the steady states to this model in particular we show that no nonconstant positive steady state exists if 0 1 and large where nonconstant positive steady states can occur thus these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants the a priori estimates are fundamental to our mathematical approaches

on the neumann problem for some semilinear elliptic equations and systems of activator inhibitor type on deduit des estimations a priori pour des solutions positives du probleme de neumann pour des systemes elliptiques semilineaires ainsi que pour des equations isolees semilineaires reliees a ces systemes

tabu search based multi watermarks embedding algorithm with multiple description coding digital watermarking is a useful solution for digital rights management systems and it has been a popular research topic in the last decade most watermarking related literature focuses on how to resist deliberate attacks by applying benchmarks to watermarked media that assess the effectiveness of the watermarking algorithm only a few papers have concentrated on the error resilient transmission of watermarked media in this paper we propose an innovative algorithm for vector quantization vq based image watermarking which is suitable for error resilient transmission over noisy channels by incorporating watermarking with multiple description coding mdc the scheme we propose to embed multiple watermarks can effectively overcome channel impairments while retaining the capability for copyright and ownership protection in addition we employ an optimization technique called tabu search to optimize both the watermarked image quality and the robustness of the extracted watermarks we have obtained promising simulation results that demonstrate the utility and practicality of our algorithm

asymptotic profiles of steady states for a diffusive sis epidemic model with mass action infection mechanism abstract mass action and standard incidence are two major infection mechanisms in modelling spread of infectious diseases spatial heterogeneity plays an important role in spread of infectious diseases and hence motivates and advocates diffusive models for disease dynamics by analyzing a diffusive sis model with the standard incidence infection mechanism some recent works 2 12 have investigated the asymptotical profiles of the endemic steady state for large and small diffusion rates and the results show that controlling the diffusion rate of the susceptible individuals can help eradicate the infection while controlling the diffusion rate of the infectious individuals cannot this paper aims to reveal the difference between the two infection mechanisms in a spatially heterogeneous environment to this end we consider a diffusive sis model of the same structure but with the mass action infection adopted and explore the asymptotic profiles of the endemic steady state for small and large diffusion rates it turns out that the new model poses some new challenges due to the nonlocal term in the equilibrium problem and the unboundedness of the nonlinear term our results on this new model reveal some fundamental differences between the two transmission mechanisms in such spatial models which may provide some implications on disease modelling and controls

traveling waves for a two group epidemic model with latent period in a patchy environment abstract in this paper we derive a two group sir epidemic model with latent period in a patchy environment by applying discrete fourier transform it is assumed that the infectious disease spreads between two groups and it has a fixed latent period when the basic reproduction number r 0 1 we prove that the system admits a nontrivial traveling wave solution for each admissible speed c namely c c where c is the minimal wave speed we also show that there is no positive traveling wave solution 1 2 1 2 satisfying i 0 i s i 0 and i s i when r 0 1 and c 0 or r 0 1 and c 0 c where i 1 2