the daily computed weighted averaging basic reproduction number r0 k ωn for mers cov in south korea abstract in this paper we propose the daily computed weighted averaging basic reproduction number r 0 k n for middle east respiratory syndrome coronavirus mers cov outbreak in south korea may to july 2015 we use an sir model with piecewise constant parameters contact rate and removed rate we use the explicit euler s method for the solution of the sir model and a nonlinear least square fitting procedure for finding the best parameters in r 0 k n the parameters n k and w denote days from a reference date the number of days in averaging and a weighting factor respectively we perform a series of numerical experiments and compare the results with the real world data in particular using the predicted reproduction number based on the previous two consecutive reproduction numbers we can predict the future behavior of the reproduction number

long time behavior of a stochastic sir model abstract in this paper we analyze long time behavior of densities of the distributions of the solution for a stochastic sir epidemic model we prove that the densities can converge in l 1 to an invariant density or can converge weakly to a singular measure

spread of information and infection on finite random networks the modeling of epidemic like processes on random networks has received considerable attention in recent years while these processes are inherently stochastic most previous work has been focused on deterministic models that ignore important fluctuations that may persist even in the infinite network size limit in a previous paper for a class of epidemic and rumor processes we derived approximate models for the full probability distribution of the final size of the epidemic as opposed to only mean values in this paper we examine via direct simulations the adequacy of the approximate model to describe stochastic epidemics and rumors on several random network topologies homogeneous networks erd os r enyi er random graphs barabasi albert scale free networks and random geometric graphs we find that the approximate model is reasonably accurate in predicting the probability of spread however the position of the threshold and the conditional mean of the final size for processes near the threshold are not well described by the approximate model even in the case of homogeneous networks we attribute this failure to the presence of other structural properties beyond degree degree correlations and in particular clustering which are present in any finite network but are not incorporated in the approximate model in order to test this hypothesis we perform additional simulations on a set of er random graphs where degree degree correlations and clustering are separately and independently introduced using recently proposed algorithms from the literature our results show that even strong degree degree correlations have only weak effects on the position of the threshold and the conditional mean of the final size on the other hand the introduction of clustering greatly affects both the position of the threshold and the conditional mean similar analysis for the barabasi albert scale free network confirms the significance of clustering on the dynamics of rumor spread for this network though with its highly skewed degree distribution the addition of positive correlation had a much stronger effect on the final size distribution than was found for the simple random graph

the entropic penalty approach to stochastic programming a penalty type decision theoretic approach to nonlinear programming problems with stochastic constraints is introduced the stochastic program sp is replaced by a deterministic program dp by adding a term to the objective function to penalize solutions which are not feasible in the mean the special feature of our approach is the choice of the penalty function pe which is given in terms of the relative entropy functional and is accordingly called entropic penalty it is shown that pe has properties which make it suitable to treat stochastic programs some of these properties are derived via a dual representation of the entropic penalty which also enable one to compute pe more easily in particular if the constraints in sp are stochastically independent the dual representation is also used to express the deterministic problem dp as a saddle function problem for problems in which the randomness occurs in the rhs of the constraints it is shown that the dual problem of dp is equivalent to expected utility maximization of the classical lagrangian dual function of sp with the utility being of the constant risk aversion type finally mean variance approximations of pe and the induced approximating deterministic program are considered

threshold of a stochastic sir epidemic model with levy jumps abstract this paper mainly investigates the effect of the levy jumps on the dynamics of a stochastic sir epidemic model taking the accumulated jump size into account a threshold of the considered model has been found out denoted by r 0 which can determine the extinction and persistence in mean of the epidemic more specifically if r 0 1 the disease ultimately vanishes from the population whereas if r 0 1 the disease persists in the population numerical simulations have been carried out to illustrate the theoretical results

global threshold dynamics of a stochastic differential equation sis model abstract in this paper we further investigate the global dynamics of a stochastic differential equation sis susceptible infected susceptible epidemic model recently proposed in gray et al 2011 8 we present a stochastic threshold theorem in term of a stochastic basic reproduction number r 0 s the disease dies out with probability one if r 0 s 1 and the disease is recurrent if r 0 s 1 we prove the existence and global asymptotic stability of a unique invariant density for the fokker planck equation associated with the sde sis model when r 0 s 1 in term of the profile of the invariant density we define a persistence basic reproduction number r 0 p and give a persistence threshold theorem the disease dies out with large probability if r 0 p 1 while persists with large probability if r 0 p 1 comparing the stochastic disease prevalence with the deterministic disease prevalence we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number r 0 d 2 this shows that noise may increase severity of disease finally we study the asymptotic dynamics of the stochastic sis model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic sis model in term of a limit stochastic threshold theorem

optimal stopping under uncertainty in drift and jump intensity this paper studies the optimal stopping problem in the presence of model uncertainty ambiguity we develop a numerically implementable method to solve this problem in a general setting allowing

a connection between a system of random walks and rumor transmission abstract we establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph more precisely we consider variations of the maki thompson epidemic model and the frog model of random walks which were introduced in the scientific literature independently and in different contexts we analyze the markov chains which describe these models and show a coupling between them our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph additionally we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics

persistence and extinction for a class of stochastic sis epidemic models with nonlinear incidence rate abstract in this paper a class of stochastic sis epidemic models with nonlinear incidence rate is investigated it is shown that the extinction and persistence of the disease in probability are determined by a threshold value r 0 that is if r 0 1 and an additional condition holds then disease dies out and if r 0 1 then disease is weak permanent with probability one to obtain the permanence in the mean of the disease a new quantity r 0 is introduced and it is proved that if r 0 1 the disease is permanent in the mean with probability one furthermore the numerical simulations are presented to illustrate some open problems given in remarks 1 3 and 5 of this paper

extinction and persistence of a stochastic nonlinear sis epidemic model with jumps abstract in this paper brownian motion and l e vy jumps are introduced to a sis type epidemic model with nonlinear incidence rate the dynamical behavior of the considered model is investigated in order to reveal the extinction and permanence of the disease two threshold values r 0 r 0 are showed we find that if r 0 1 the disease may die out and when r 0 1 the disease may be persistent finally the numerical simulations are presented to illustrate our mathematical results

two group sir epidemic model with stochastic perturbation a stochastic two group sir model is presented in this paper the existence and uniqueness of its nonnegative solution is obtained and the solution belongs to a positively invariant set furthermore the globally asymptotical stability of the disease free equilibrium is deduced by the stochastic lyapunov functional method if r 0 1 which means the disease will die out while if r 0 1 we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average in addition the intensity of the fluctuation is proportional to the intensity of the white noise when the white noise is small we consider the disease will prevail at last we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments

periodic solution for a stochastic nonautonomous sir epidemic model with logistic growth abstract in this paper we analyze the dynamics of a stochastic nonautonomous sir epidemic model in which population growth is subject to logistic growth in absence of disease for the periodic system we present sufficient conditions for persistence of the epidemic and in the case of persistence by constructing some suitable lyapunov functions we show that there is at least one nontrivial positive periodic solution one of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous sir epidemic model

certainty equivalents and information measures duality and extremal principles given a convex function ir ir the csiszar divergence csiszar 1978 is a function i ir n ir n ir

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

extinction and periodic solutions for an impulsive sir model with incidence rate stochastically perturbed abstract in this paper we consider an impulsive sir model with incidence rate stochastically perturbed first we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse second we obtain a sufficient condition which determines epidemic to extinct then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition finally we present a sufficient condition which allows the existence of a positive periodic solution

stationary distribution and threshold dynamics of a stochastic sirs model with a general incidence abstract in this paper we consider a stochastic epidemic model with relapse cure and a non linear incidence rate function firstly we show the existence and uniqueness of a global positive solution then in terms of a stochastic threshold r s 0 we prove the extinction of the disease when r s 0 1 we also establish the persistence in mean of the epidemic in the case of r s 0 1 furthermore we prove the existence of a stationary distribution and its asymptotic stability finally we present numerical simulations for the stochastic model to support the theoretical results

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

complete global analysis of a two scale network sirs epidemic dynamic model with distributed delay and random perturbations the model validation results are established the basic reproduction numbers at three human vector contact levels are computed the stochastic stability of equilibria is proven interplay between stability and human mobility are exhibited in real life scenarios a stochastic sirs epidemic dynamic model with distributed time delay for vector borne diseases in two scale network structured populations is presented the distributed delay accounts for the varying incubation period of the disease furthermore the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two scale human mobility process the basic reproduction numbers at three human vector contact levels in the two scale population are computed and the results for the stochastic asymptotic stability of the equilibria are presented moreover the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented numerical simulation results are presented

asymptotic behavior for a modified maki thompson model with directed inter group interactions abstract in this work we propose a new extension for the maki thompson rumor model which incorporates inter group directed contacts the model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed while individuals of one group have an active role in the spreading process individuals of the other group only contribute in stifling the rumor provided that they are contacted for this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process in addition we discuss some examples and possible applications

the maki thompson rumor model on infinite cayley trees in this paper we study the maki thompson rumor model on infinite cayley trees the basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals ignorants spreaders and stiflers a spreader tells the rumor to any of its nearest ignorant neighbors at rate one at the same rate a spreader becomes a stifler after a contact with other nearest neighbor spreaders or stiflers in this work we study this model on infinite cayley trees which is formulated as a continuous times markov chain and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences we study sufficient conditions under which the rumor either becomes extinct or survives with positive probability

introduction to convex optimization in financial markets convexity arises naturally in financial risk management in risk preferences concerning random cash flows convexity corresponds to the fundamental diversification principle convexity is a basic property also of budget constraints both in classical linear models as well as in more realistic models with transaction costs and constraints moreover modern securities markets are based on trading protocols that result in convex trading costs the first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simple optimization terms the second part reviews some convex optimization techniques used in mathematical and numerical analysis of financial optimization problems

dynamics of a stochastic siqr epidemic model with standard incidence abstract in this paper a stochastic siqr epidemic model with quarantine and standard incidence is investigated we first consider the existence and uniqueness of the global positive solution to the stochastic system further we obtain conclusions that the large noise can make the disease die out exponentially and the stationary distribution will exist under certain conditions

stationary distribution and extinction of a stochastic seir epidemic model with standard incidence abstract in this paper we consider a stochastic seir epidemic model with standard incidence by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution to the model our result does not depend on the positive endemic equilibrium e of the deterministic system which improves the previous result to a greater extent moreover we also establish sufficient conditions for extinction of the disease

constructing generalized mean functions using convex functions with regularity conditions the generalized mean function has been widely used in convex analysis and mathematical programming this paper studies a further generalization of such a function a necessary and sufficient condition is obtained for the convexity of a generalized function additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes of functions which guarantee the convexity of the generalized functions we show that some new classes of convex functions with certain regularity such as s regularity can be used as building blocks to construct such generalized functions

a stochastic threshold for an epidemic model with beddington deangelis incidence delayed loss of immunity and levy noise perturbation abstract in this paper we study a stochastic epidemic model with delayed loss of immunity and levy noise perturbation we establish the uniqueness of the global positive solution we also investigate the extinction and the persistence in mean of the disease

necessary and sufficient condition for extinction and persistence of sirs system with random perturbation abstract this paper characterizes the qualitative dynamics of a stochastic sirs epidemic model the study shows that the dynamics of the model are determined by a certain threshold quantity r s expressed in terms of the model parameters and the intensity of the noise if r s 1 the disease will be eliminated from the community whereas an epidemic occurs if r s 1 our results recover the known results in the earlier literature as special cases the presented results are illustrated by numerical simulations

rumor processes on mathbb n and discrete renewal processes we study two rumor processes on mathbb n the dynamics of which are related to an si epidemic model with long range transmission both models start with one spreader at site 0 and ignorants at all the other sites of mathbb n but differ by the transmission mechanism in one model the spreaders transmit the information within a random distance on their right and in the other the ignorants take the information from a spreader within a random distance on their left we obtain the probability of survival information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders the key step of our proofs is to show that in each model the position of the spreaders on mathbb n can be related to a suitably chosen discrete renewal process

robust portfolio choice and indifference valuation we solve theoretically and numerically the problems of optimal portfolio choice and indifference valuation in a general continuous time setting the setting features i ambiguity and time consistent ambiguity averse preferences ii discontinuities in the asset price processes with a general and possibly infinite activity jump part next to a continuous diffusion part and iii general and possibly nonconvex trading constraints we characterize our solutions as solutions to backward stochastic differential equations bsdes generalizing kobylanski s result for quadratic bsdes to an infinite activity jump setting we prove existence and uniqueness of the solution to a general class of bsdes encompassing the solutions to our portfolio choice and valuation problems as special cases we provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium and a further decomposition into a piece stemming from the diffusion part and a piece stemming from the ju

risk preferences and their robust representation to address the plurality of interpretations of the subjective notion of risk we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets this representation covers most instruments related to risk and allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings for random variables risk perception can be interpreted as model risk and we compute among others the robust representation of the economic index of riskiness for lotteries risk perception can be viewed as distributional risk and we study the value at risk for consumption patterns which excerpt an intertemporality dimension in risk perception we provide an interpretation in terms of discounting risk and discuss some examples

on invariant measures and the asymptotic behavior of a stochastic delayed sirs epidemic model abstract in this paper we consider a stochastic epidemic model with time delay and general incidence rate we first prove the existence and uniqueness of the global positive solution by using the krylov bogoliubov method we obtain the existence of invariant measures furthermore we study a special case where the incidence rate is bilinear with distributed time delay when the basic reproduction number r 0 1 the analysis of the asymptotic behavior around the disease free equilibrium e 0 is provided while when r 0 1 we prove that the invariant measure is unique and ergodic the numerical simulations also validate our analytical results

algorithms for ambiguity function processing calculation of the complex ambiguity function is viewed as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise in many applications the required accuracy leads to a need for integration over long data sets that can become a challenge for near real time digital processing the nature of the ambiguity processing is interpreted and an algorithm approach is shown that minimizes the processing burden over a broad category of applications without affecting performance

phase transition for the maki thompson rumour model on a small world network we consider the maki thompson model for the stochastic propagation of a rumour within a population in this model the population is made up of spreaders ignorants and stiflers any spreader attempts to pass the rumour to the other individuals via pair wise interactions and in case the other individual is an ignorant it becomes a spreader while in the other two cases the initiating spreader turns into a stifler in a finite population the process will eventually reach an equilibrium situation where individuals are either stiflers or ignorants we extend the original hypothesis of homogenously mixed population by allowing for a small world network embedding the model in such a way that interactions occur only between nearest neighbours this structure is realized starting from a k regular ring and by inserting in the average c additional links in such a way that k and c are tuneable parameters for the population architecture we prove that this system exhibits a transition between regimes of localization where the final number of stiflers is at most logarithmic in the population size and propagation where the final number of stiflers grows algebraically with the population size at a finite value of the network parameter c a quantitative estimate for the critical value of c is obtained via extensive numerical simulations

the critical contact process dies out by producing a finite box criterion for survival in a slab we show that the critical contact process dies out and that in two and more dimensions the critical parameter value coincides with the limit of slab thresholds using the techniques developed in this paper one may obtain the complete convergence and shape theorems for contact processes in all dimensions and for all infection rates our results apply also to the discrete time analogue of the contact process viz oriented percolation

dynamics of a stochastic hiv 1 infection model with logistic growth abstract this paper is concerned with a stochastic hiv 1 infection model with logistic growth firstly by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the hiv 1 infection model then we obtain sufficient conditions for extinction of the infection the stationary distribution shows that the infection can become persistent in vivo

dynamic behaviors of a two group stochastic sirs epidemic model with standard incidence rates abstract this paper deals with a two group stochastic sirs epidemic model with standard incidence rates on one hand we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model by constructing a suitable stochastic lyapunov function on the other hand we show the sufficient conditions for the diseases to be extinct

ambiguity aversion robustness and the variational representation of preferences we characterize in the anscombe aumann framework the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that for all acts f and g the function u represents the decision maker s risk attitudes while the index c captures his ambiguity attitudes these preferences include the multiple priors preferences of gilboa and schmeidler and the multiplier preferences of hansen and sargent this provides a rigorous decision theoretic foundation for the latter model which has been widely used in macroeconomics and finance

modelling the effect of telegraph noise in the sirs epidemic model using markovian switching abstract we discuss the effect of introducing telegraph noise which is an example of an environmental noise into the susceptible infectious recovered susceptible sirs model by examining the model using a finite state markov chain mc first we start with a two state mc and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence we then explain how the results can be generalised to a finite state mc the results for the sir susceptible infectious removed model with markovian switching ms are a special case numerical simulations are produced to confirm our theoretical results

limit theorems for a general stochastic rumour model we study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour we refer to this special kind of stifler as an uninterested individual our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does so that particular cases are the classical daley kendall and maki thompson models we prove a law of large numbers and a central limit theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it

asymptotic behavior of stochastic multi group epidemic models with distributed delays abstract in this paper we introduce stochasticity into multi group epidemic models with distributed delays and general kernel functions the stochasticity in the model is a standard technique in stochastic population modeling when the perturbations are small by using the method of stochastic lyapunov functions we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number r 0 if r 0 1 the solution of the stochastic system oscillates around the disease free equilibrium e 0 while if r 0 1 the solution of the stochastic model fluctuates around the endemic equilibrium e moreover we also establish sufficient conditions of these results

the extinction and persistence of the stochastic sis epidemic model with vaccination abstract in this paper we discuss the dynamics of a stochastic sis epidemic model with vaccination when the noise is large the infective decays exponentially to zero regardless of the magnitude of r 0 when the noise is small sufficient conditions for extinction exponentially and persistence in the mean are established the results are illustrated by computer simulations

a spatial stochastic model for rumor transmission we consider an interacting particle system representing the spread of a rumor by agents on the d dimensional integer lattice each agent may be in any of the three states belonging to the set 0 1 2 here 0 stands for ignorants 1 for spreaders and 2 for stiflers a spreader tells the rumor to any of its nearest ignorant neighbors at rate at rate a spreader becomes a stifler due to the action of other nearest neighbor spreaders finally spreaders and stiflers forget the rumor at rate one we study sufficient conditions under which the rumor either becomes extinct or survives with positive probability

the linear steklov method for sdes with non globally lipschitz coefficients we present an explicit numerical method for solving stochastic differential equations with non globally lipschitz coefficients a linear version of the steklov average under a split step formulation supports our new solver the linear steklov method converges strongly with a standard one half order also we present numerical evidence that the explicit linear steklov reproduces almost surely stability solutions with high accuracy for diverse application models even for stochastic differential systems with super linear diffusion coefficients

sde sis epidemic model with demographic stochasticity and varying population size an sde sis epidemic model with demographic stochasticity is developed existence of a unique non negative solution is shown an upper bound is found for the infectives in terms of the population size the infectives and susceptibles go extinct in finite time a s results are supported numerically some with real examples in this paper we look at the two dimensional stochastic differential equation sde susceptible infected susceptible sis epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size first we look at the sde model for the total population size and show that there exists a unique non negative solution then we look at the two dimensional sde sis model and show that there exists a unique non negative solution which is bounded above given the total population size furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely lastly we support our analytical results with numerical simulations using theoretical and realistic disease parameter values

nontrivial periodic solution of a stochastic non autonomous sisv epidemic model abstract in this paper we consider a stochastic non autonomous sisv epidemic model for the non autonomous periodic system firstly we get the threshold of the system which determines whether the epidemic occurs or not then in the case of persistence we show that there exists at least one nontrivial positive periodic solution of the stochastic system

threshold behaviour of a stochastic epidemic model with two dimensional noises abstract the aim of this work is to study a new stochastic sir epidemic model that includes two types of white noises these noises perturb two important parameters in the disease dynamic the disease transmission rate and the recovery rate by means of the lyapunov functions we prove the global existence and positivity of the solution we also investigate the conditions of the extinction and the persistence of the disease and use a suitable lyapunov function to study the stability of the model numerical simulations of our result are also presented

frequency difference of arrival accuracy the problem considered occurs in the geolocation of a fixed emitter using observations from two moving collectors estimates for the time difference and frequency difference of signal arrivals are used frequency difference of arrival fdoa is estimated through the use of a mixing product standard regression analysis procedures are then applied to estimate the slope of the unwrapped phase angle the derivation of an expression for the standard error of fdoa is given and this result is related to several other well known results

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

time delay estimation using phase data the estimation of time delays between two received signals using phase measurements is discussed and the accuracy of such estimates is detailed for the ideal case of statistically independent noise and no scattering at the receiver locations it is shown that phase data regression lines yield time delay estimates with the same accuracy as other optimal time delay estimation procedures for less ideal situations the potential advantages of time delay estimation using phase data are discussed and illustrated it is shown that regression analysis of phase estimates at properly selected frequencies can sometimes be employed to reduce bias errors in time delay estimates due to correlated receiver noise it is also shown that the estimation errors due to scattering at the receiver location can often be assessed in nonparametric terms to provide time delay estimates with a realistic error bound

brief paper dynamics of a multigroup sir epidemic model with stochastic perturbation in this paper we introduce stochasticity into a multigroup sir susceptible infective and recovered model the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modeling in the deterministic models the basic reproduction number r 0 is a threshold which completely determines the persistence or extinction of the disease we carry out a detailed analysis on the asymptotic behavior of the stochastic model also regarding of the value of r 0 if r email protected 1 the solution of the model is oscillating around a steady state which is the disease free equilibrium of the corresponding deterministic model whereas if r 0 1 there is a stationary distribution which means that the disease will prevail

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

penalty functions and duality in stochastic programming via φ divergence functionals the paper considers stochastically constrained nonlinear programming problems a penalty function is constructed in terms of a distance between random variables defined in terms of the divergence functional a generalization of the relative entropy a duality theory is developed in which a general relation between divergence and utility functions is revealed via the conjugate transform and a new type of certainty equivalent concept emerges

the threshold of a stochastic delayed sir epidemic model with temporary immunity abstract this paper is concerned with the asymptotic properties of a stochastic delayed sir epidemic model with temporary immunity sufficient conditions for extinction and persistence in the mean of the epidemic are established the threshold between persistence in the mean and extinction of the epidemic is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

stochastic regime switching sir model driven by levy noise abstract we propose a new stochastic regime switching sir model driven by levy noise a unique global positive solution is obtained under some appropriate conditions moreover we investigate the asymptotic behavior of the stochastic sir model with jumps under regime switching

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size abstract in this paper we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system

dynamics for a class of stochastic sis epidemic models with nonlinear incidence and periodic coefficients abstract in this paper we investigate the dynamics of a class of periodic stochastic sis epidemic models with general nonlinear incidence f s i some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established by using the khasminskii s boundary periodic markov processes the existence of stochastic nontrivial periodic solution for the models is also obtained the numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

threshold behavior in a stochastic sir epidemic model with logistic birth abstract in this paper we consider a stochastic sir epidemic model with logistic birth by using the stochastic lyapunov function method we show that the stochastic basic reproduction number r 0 s can be used to determine the threshold dynamics of the stochastic system if r 0 s 1 we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model while if r 0 s 1 under some extra conditions we obtain sufficient conditions for extinction of the disease finally some examples and numerical simulations are provided to illustrate the theoretical results

dynamic analysis of a stochastic rumor propagation model abstract the rapid development of the internet especially the emergence of the social networks leads rumor propagation into a new media era in this paper we are concerned with a stochastic rumor propagation model sufficient conditions for extinction and persistence in the mean of the rumor are established the threshold between persistence in the mean and extinction of the rumor is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

rumor spreading in complex networks under stochastic node activity abstract the research on rumor spreading has a long history and its wanton flooding has brought huge impact on people s life in the process of its spreading the individual s activity plays an important role however in the complex and changeable environment randomness cannot be ignored not to mention its influence on individual activity based on the i s r model of individual activity this paper explores the stochastic version of the rumor model including fluctuations in the activity then the influence of stratonovich stochastic noise on the asymptotic behavior of non linear rumor spreading model is studied through the mathematical analysis we get the critical values to measure whether the deterministic and stochastics models spread or not as well as the threshold conditions for rumor to spread wantonly at the same time the effects of stratonovich stochastic noise on the asymptotic behavior of rumor free equilibrium point e 0 and endemic equilibrium point e are obtained respectively and the condition that the rumor free equilibrium is globally asymptotically stable in the presence of noise is given finally the theoretical results are verified by numerical simulation

dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth abstract in this paper we investigate the dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model then we obtain sufficient conditions for extinction of the disease in two cases that is the first case is that the susceptible population survival and infected and exposed populations extinction the second case is that all the populations extinction

stability of sirs system with random perturbations epidemiological models with bilinear incidence rate si usually have an asymptotically stable trivial equilibrium corresponding to the disease free state or an asymptotically stable non trivial equilibrium i e interior equilibrium corresponding to the endemic state in this paper we consider an epidemiological model which is an sirs model with or without distributed time delay influenced by random perturbations we present the stability conditions of the disease free equilibrium of the associated stochastic sirs system

behavior of a stochastic sir epidemic model with saturated incidence and vaccination rules abstract in this paper the threshold behavior of a susceptible infected recovered sir epidemic model with stochastic perturbation is investigated firstly it is obtained that the system has a unique global positive solution with any positive initial value random effect may lead to disease extinction under a simple condition subsequently sufficient condition for persistence has been established in the mean of the disease finally some numerical simulations are carried out to confirm the analytical results

the threshold of a stochastic sivs epidemic model with nonlinear saturated incidence abstract a stochastic version of the sis epidemic model with vaccination sivs is studied when the noise is small the threshold parameter is identified which determines the extinction and persistence of the epidemic besides the results show that large noise will suppress the epidemic from prevailing regardless of the saturated incidence the results are illustrated by computer simulations

two stage predictions of evolutionary dynamics during the rumor dissemination abstract the spreading of rumor is the common type of collective actions as a macro social phenomenon the rumor spreading should be supported by the micro level actions and interactions of people agents therefore the agent based modeling is applied to modeling the micro level mechanism of rumor spreading which has more significance in the big data age the outcomes of simulations indicate that there exist a stage transfer and the turning point d which divides the whole spreading process into the linear od and nonlinear de stages in the linear stage od the spreading percentage increases rapidly into a relatively high level of spreading percentage however after the turning point d it increases slowly until the 100 is reached in the nonlinear stage de for the linear stage od we estimated the linear dynamics with the linear ols regression and it suggests that the adjusted r2 is as high as over 98 99 which is infinitely close to 100 for the nonlinear stage de we estimated the nonlinear stage via adding the quadratic term of time into the regression model it suggests that the adjusted r2 is as high as over 98 as well which is also close to 100 based on the predictions of linear and nonlinear stages with the highest accuracies we combined the linear and nonlinear stages oe od de to predict the whole process of rumor spreading eventually the smooth predicted curves spcs can be obtained to better fit the evolutionary dynamic of spreading curves in reality

expected utility penalty functions and duality in stochastic nonlinear programming we consider nonlinear programming problem p with stochastic constraints the lagrangean corresponding to such problems has a stochastic part which in this work is replaced by its certainty equivalent in the sense of expected utility theory it is shown that the deterministic surrogate problem ce p thus obtained contains a penalty function which penalizes violation of the constraints in the mean the approach is related to several known methods in stochastic programming such as chance constraints stochastic goal programming reliability programming and mean variance analysis the dual problem of ce p is studied for problems with stochastic righthand sides in the constraints and a comprehensive duality theory is developed by introducing a new certainty equivalent nce concept motivation for the nce and its potential role in decision theory are discussed as well as mean variance approximations

multiple epidemic waves in delayed susceptible infected recovered models on complex networks we consider a delayed susceptible infected recovered epidemic model on an uncorrelated complex network and address the effect of time lag on the shape and multiple waves of epidemic curves we show that when the transmission rate is above a threshold a large delay can cause multiple waves with larger amplitudes in the second and subsequent waves

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained

strong convergence of the partially truncated euler maruyama scheme for a stochastic age structured sir epidemic model abstract we study in this paper strong convergence of the partially truncated euler maruyama scheme for an age structured susceptible infected removed sir epidemic model with environmental noise using the semigroup theory the existence and uniqueness of global positive solution for the model is first proved we then define a truncated function and develop a partially truncated em numerical solutions to the stochastic age structured sir epidemic model we present the pth moment boundedness of the partially truncated em numerical approximate solutions under appropriate conditions furthermore the strong lq convergence is established for the condition of 2 q

measuring production with random inputs and outputs using dea and certainty equivalent this study evaluates production operations with inputs outputs under random influences we introduce a measurement of efficiency using utility function families applying data envelopment analysis dea and the certainty equivalent the proposed measurement is capable of accommodating various risk attitudes of evaluators