existence of multiple periodic solutions for an sir model with seasonality abstract we study an sir model with a seasonal contact rate and a staged treatment strategy which is an extension of our previous work z bai y zhou existence of two periodic solutions for a non autonomous sir epidemic model appl math model 35 2011 382 391 it is proved that the persistence and extinction of the disease are determined by the basic reproductive number r 0 and a threshold parameter r c it is obtained that the model exhibits two different bistable behaviors under certain conditions the stable disease free state coexists with a stable endemic periodic solution and three endemic periodic solutions coexist with two of them being stable numerical simulations are presented to illustrate theoretical results

bifurcations in an epidemic model with constant removal rate of the infectives an epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread it is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease it is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters it is also shown that the model undergoes a sequence of bifurcations including saddle node bifurcation subcritical hopf bifurcation and homoclinic bifurcation

computing gaussian likelihoods and their derivatives for general linear mixed models algorithms are described for computing the gaussian likelihood or restricted likelihood corresponding to a general linear mixed model included are arbitrary covariance structures for both the random effects and errors formulas are also given for the first and second derivatives of the likelihoods thus enabling a newton raphson implementation the algorithms make heavy use of the cholesky decomposition the sweep operator and the w transformation also described are the modifications needed for variance profiling fisher scoring and mivque 0 as well as the computational order of the procedures

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

nonlinear oscillations in epidemic models constant parameter epidemic models for a closed population described by integral and integrodifferential equations are analyzed to determine whether time delays can give rise to periodic oscillations delays can destabilize the steady state in one finite delay case and in one infinite delay case considered hopf bifurcation techniques are used to show the existence of locally asymptotically stable periodic solutions for certain parameter values inclusion of time delays in another related model does not alter the local asymptotic stability of the endemic steady state

bifurcation analysis of a delayed epidemic model in this paper hopf bifurcation for a delayed sis epidemic model with stage structure and nonlinear incidence rate is investigated through theoretical analysis we show the positive equilibrium stability and the conditions that hopf bifurcation occurs applying the normal form theory and the center manifold argument we derive the explicit formulas determining the properties of the bifurcating periodic solutions in addition we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions to illustrate our theoretical analysis some numerical simulations are also included

analysis of a model for the dynamics of prions ii abstract a new mathematical model for the dynamics of prion proliferation involving an ordinary differential equation coupled with a partial integro differential equation is analyzed continuing the work in j pruss l pujo menjouet g f webb r zacher analysis of a model for the dynamics of prions discrete contin dyn syst 6 2006 225 235 we show the well posedness of this problem in its natural phase space z r l 1 x 0 x d x i e there is a unique global semiflow on z associated to the problem a theorem of threshold type is derived for this model which is typical for mathematical epidemics if a certain combination of kinetic parameters is below or at the threshold there is a unique steady state the disease free equilibrium which is globally asymptotically stable in z above the threshold it is unstable and there is another unique steady state the disease equilibrium which inherits that property

global dynamics of an epidemic model with an unspecified degree in this paper we give the global dynamical behaviors of a reduced sirs epidemic model with a nonlinear incidence rate ki ps q we first discuss the qualitative properties of the equilibria in the interior of the first quadrant and study the bifurcations including saddle node bifurcation transcritical bifurcation hopf bifurcation and bogdanov takens bifurcation then we consider equilibria at infinity determining the number of orbits in exceptional directions for the global tendency in this discussion the unspecified degree p q of polynomials and their high degeneracy prevent us from using the methods of blowing up or normal sectors in some cases we lastly discuss the existence and uniqueness of limit cycles

signal to noise ratios performance criteria and transformations for the analysis of designed experiments taguchi uses performance criteria that he calls signal to noise sn ratios three such criteria are here denoted by sn t sn l and sn s the criterion sn t was to be used in preference to the standard deviation for the problem of achieving for some quality characteristic y the smallest mean squared error about an operating target value leon shoemaker and kacker 1987 showed how sn t was appropriate to solve this problem only when y was proportional to y on that assumption the same result could be obtained more simply by conducting the analysis in terms of log y rather than y a more general transformation approach is here introduced for other commonly met kinds of dependence between y and y including no dependence and a lambda plot is presented that uses the data to suggest an appropriate transformation the criteria sn l and sn s were for problems in which the objective was to make the response as large or as small as possible it is arg

bifurcation analysis of an sis epidemic model with saturated incidence rate and saturated treatment function this paper introduces a saturated treatment function into an sis model with saturated incidence rate the treatment function is a continuous and differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large sufficient conditions for the existence and global asymptotical stability of the disease free and endemic equilibria are given in this paper and the nonexistence of limit cycles is also demonstrated a backward bifurcation is found when the capacity of the treatment is low it indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of diseases by mathematical analysis and numerical simulations it is shown that the system undergoes hopf bifurcation and bogdanov takens bifurcation

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

stability and bifurcation of an sir epidemic model with nonlinear incidence and treatment the dynamical behaviors of an sir epidemic model with nonlinear incidence and treatment is investigated it is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity it is found that a backward bifurcation occurs if the capacity is small it is also found that there exist bistable endemic equilibria if the capacity is low theoretical and numerical results suggest that decreasing the basic reproduction number below one is insufficient for disease eradication

dynamical behavior of an epidemic model with a nonlinear incidence rate abstract in this paper we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action by carrying out global qualitative and bifurcation analyses it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region when such a region exists it is shown that the model undergoes a bogdanov takens bifurcation i e it exhibits a saddle node bifurcation hopf bifurcations and a homoclinic bifurcation existence of none one or two limit cycles is also discussed

performance measures independent of adjustment an explanation and extension of taguchi s signal to noise ratios parameter design is a method popularized by japanese quality expert g taguchi for designing products and manufacturing processes that are robust to uncontrollable variations in parameter design taguchi s stated objective is to find the settings of product or process design parameters that minimize average quadratic loss that is the average squared deviation of the response from its target value yet in practice to choose the settings of design parameters he maximizes a set of measures called signal to noise ratios in general he gives no connection between these two optimization problems in this article we show that for certain underlying models for the product or process response maximization of the signal to noise ratio leads to minimization of average quadratic loss the signal to noise ratios take advantage of the existence of special design parameters called adjustment parameters when these parameters exist use of the signal to noise ratio allows the parameter design optimization procedu

uniform decay in a timoshenko type system with past history abstract fernandez sare and rivera h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502 considered the following timoshenko type system 1 t t k x x 0 2 t t b x x 0 g t x x t s d s k x 0 where g is a positive differentiable exponentially decaying function they established an exponential decay result in the case of equal wave speed propagation and a polynomial decay result in the case of nonequal wave speed propagation in this paper we study the same system for g decaying polynomially and prove polynomial stability results for the equal and nonequal wave speed propagation our results are established under conditions on the relaxation function weaker than those in h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

joint estimation of location dispersion and random effects in robust design this article presents a methodology for simultaneously modeling three components of a general mixed model approach to robust design location fixed effects dispersion effects and random effects control noise and random factors can be accommodated with this approach parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches

on the stability of damped timoshenko systems cattaneo versus fourier law we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction while exponential stability under the fourier law of heat conduction holds it turns out that the coupling via the cattaneo law does not yield an exponentially stable system this seems to be the first example that a removal of the paradox of infinite propagation speed inherent in fourier s law by changing to the cattaneo law causes a loss of the exponential stability property actually for systems with history the fourier law keeps the exponential stability known for the pure timoshenko system without heat conduction but introducing the cattaneo coupling even destroys this property

global existence and decay estimates for the solution of a nonlinear bresse system abstract our main focus in the present paper is to study the global existence and asymptotic behavior of a nonlinear version of the bresse system as it has been already proved in soufyane and said houari 2014 the linear version of this system is of regularity loss type this regularity loss creates difficulties when dealing with the nonlinear problem since the dissipative property of the problem becomes very weak in the high frequency region and as a result the classical energy method fails to overcome this difficulty following ide and kawashima 2008 and ikehata 2002 we use an energy method with negative weights to create an artificial damping which allows us to control the nonlinearity

global existence asymptotic behavior and uniform attractors for a non autonomous timoshenko system of thermoelasticity of type iii with a time varying delay abstract in this paper we first establish the global existence by using the variable norm technique of kato and semigroup method second under suitable assumptions on the data we obtain the asymptotic behavior of the solution last we prove the existence of a uniform attractor by using the method of uniform contractive functions

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

dynamic threshold probe of stochastic sir model with saturated incidence rate and saturated treatment function abstract in this discourse we establish and investigate the pervasive of environmental variability in a deterministic epidemic model with saturated incidence rate and saturated treatment function we exemplify that the proposed stochastic model reveals an exclusive and universal positive solution we deal with equilibrium solution of stochastic model which contribute few biological intrinsic manifestation for the model we attain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic epidemic model with probability one if 0 1 and if 0 1 respectively eventually numerical probing is furnished to elucidate the analytical outcomes

global well posedness and polynomial decay for a nonlinear timoshenko cattaneo system under minimal sobolev regularity abstract we consider the nonlinear stability of the timoshenko cattaneo system in the one dimensional whole space the timoshenko system consists of two coupled wave equations with non symmetric relaxation and describes vibrations of the beam with shear deformation and rotational inertia effect generally if the relaxation is not symmetric the dissipation is produced through the complicated interaction of the components of the system and their decay estimates and the energy estimates are of regularity loss type in this paper we introduce the mathematical method to control such a weak dissipativity by investigating the timoshenko system with cattaneo s law which is the first order approximation of fourier s law with its time delay effect racke said houari 2012 showed the global existence and the decay estimate of solutions by assuming high regularity h 8 l 1 on the small initial data to control their weak dissipativity in contrast we prove the global existence in h 2 by energy methods without any negative weights our regularity assumption is the same as that needed to show the local existence that is we do not need to assume the extra higher regularity on the initial data besides the optimal decay estimate in h 2 l 1 is shown by using the time decay inequality of l p l q l r type

epidemic waves of a spatial sir model in combination with random dispersal and non local dispersal abstract in this paper a spatial sir model in combination with random dispersal and non local dispersal is proposed we establish the existence and non existence of the traveling wave solutions connecting the disease free equilibrium and the endemic equilibrium for the model the main difficulties lie in the fact that the semiflow generated here does not admit the order preserving property and the solutions lack of regularity we use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the schauder s fixed point theorem polar coordinates transform to study the threshold dynamics of the model that is we show that if the basic reproduction number of the model r 0 1 there is a positive constant critical number c such that for each c c the model admits a non trivial and positive traveling wave with wave speed c and if r 0 1 and 0

homoclinic bifurcation in an siqr model for childhood diseases abstract we consider a system of odes which describes the transmission dynamics of childhood diseases a center manifold reduction at a bifurcation point has the normal form x y y axy bx2y o 4 indicating a bifurcation of codimension greater than two a three parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations it is shown that the perturbed system produces homoclinic bifurcation

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

coexistence of limit cycles and homoclinic loops in a sirs model with a nonlinear incidence rate recently ruan and wang j differential equations 188 2003 pp 135 163 studied the global dynamics of a sirs epidemic model with vital dynamics and a nonlinear saturated incidence rate under certain conditions they showed that the model undergoes a bogdanov takens bifurcation i e it exhibits saddle node hopf and homoclinic bifurcations they also considered the existence of none one or two limit cycles in this paper we investigate the coexistence of a limit cycle and a homoclinic loop in this model one of the difficulties is to determine the multiplicity of the weak focus we first prove that the maximal multiplicity of the weak focus is 2 then feasible conditions are given for the uniqueness of limit cycles the coexistence of a limit cycle and a homoclinic loop is obtained by reducing the model to a universal unfolding for a cusp of codimension 3 and studying degenerate hopf bifurcations and degenerate bogdanov takens bifurcations of limit cycles and homoclinic loops of order 2

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

diffusion phenomenon for linear dissipative wave equations in an exterior domain abstract under the general condition of the initial data we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain in order to derive the diffusion phenomenon for dissipative wave equations the time integral method which was developed by ikehata and matsuyama sci math japon 55 2002 33 plays an effective role

global dynamics and sliding motion in a h7n9 epidemic models with limited resources and filippov control abstract this paper investigates the effects of different control measures on the dynamics of a h7n9 virus transmission from poultry to human an si sir model with nonlinear incidence and recovery rates is formulated to evaluate the combined impacts of government intervention strategies and available hospital resources the global stability of the disease free and endemic equilibria is obtained by constructing lyapunov and dulac functions furthermore based on the threshold policy the si sir model is extended to a novel three dimensional filippov one to represent the control measures being triggered once the total number of infected poultry and human reaches the tolerant level i c model solutions are able to approach either one real equilibrium or the pseudo equilibrium depending on the tolerant threshold our results suggest that in order to diminish the outbreak of a h7n9 virus or lead the number of infections to an expected level it requires not only adequate hospital resources and certain government interventions but also a good threshold policy

backward bifurcation of an epidemic model with saturated treatment function an epidemic model with saturated incidence rate and saturated treatment function is studied here the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited the global dynamics of the model indicate that the basic reproduction number being the unity is a strict threshold for disease eradication when such effect is weak however it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong therefore driving the basic reproduction number below the unity is not enough to eradicate the disease and a critical value at the turning point is deduced as a new threshold some sufficient conditions for the disease free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained mathematical results in this paper suggest that giving the patients timely treatment improving the cure efficiency and decreasing the infective coefficient are all valid methods for the control of disease

global existence and decay property of the timoshenko system in thermoelasticity with second sound abstract our main focus in the present paper is to study the asymptotic behavior of a nonlinear version of the timoshenko system in thermoelasticity with second sound as it has been already proved in said houari and kasimov 2012 29 the linear version of this system is of regularity loss type it is well known hosono and kawashima 2006 34 ide and kawashima 2008 27 kubo and kawashima 2009 41 that the regularity loss property of the linear problem creates difficulties when dealing with the nonlinear problem in fact the dissipative property of the problem becomes very weak in the high frequency region and as a result the classical energy method fails to overcome this difficulty and following ide and kawashima 2008 27 and ikehata 2002 30 we use an energy method with negative weights to create an artificial damping which allows us to control the nonlinearity we prove that for 0 k s 2 2 with s 8 the solution of our problem is global in time and decays as x k u t 2 c 1 t 1 4 k 2 provided that the initial datum u 0 h s r l 1 r

cost driven parameter design parameter design methodology has focused primarily on the quadratic loss function which can often be solved by using a two step procedure involving the minimization of a dispersion measure and then adjusting the mean to target in some practical situations however the loss can be nonquadratic or highly skewed by building on a theory of leon and wu we develop a modeling and data analysis strategy for a general loss function in which the quality characteristic follows a location scale model the only difference from the two step procedure just mentioned is the adjustment step in which the mean is moved to that side of the target with lower cost the technique is illustrated on an experiment involving epitaxial layer growth in integrated circuit fabrication

stability of timoshenko systems with past history we consider vibrating systems of timoshenko type with past history acting only in one equation we show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds otherwise the corresponding system does not decay exponentially as time goes to infinity in the case that the wave speeds of the equations are different which is more realistic from the physical point of view we show that the solution decays polynomially to zero with rates that can be improved depending on the regularity of the initial data

bayesian inference using record values from rayleigh model with application in this article based on a set of upper record values from a rayleigh distribution bayesian and non bayesian approaches have been used to obtain the estimators of the parameter and some lifetime parameters such as the reliability and hazard functions bayes estimators have been developed under symmetric squared error and asymmetric linex and general entropy ge loss functions these estimators are derived using the informative and non informative prior distributions for we compare the performance of the presented bayes estimators with known non bayesian estimators such as the maximum likelihood ml and the best linear unbiased blu estimators we show that bayes estimators under the asymmetric loss functions are superior to both the ml and blu estimators the highest posterior density hpd intervals for the rayleigh parameter and its reliability and hazard functions are presented also bayesian prediction intervals of the future record values are obtained and discussed finally practical examples using real record values are given to illustrate the application of the results