相关论文: Global Threshold Dynamics of a Stochastic Differen…
We study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic…
In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We…
We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the…
In SIR-type epidemic models time derivative of prevalence $I$ can always be cast into the form $\dot{I}=(X-1)I$, where $X$ is the replacement number and recovery rate is normalized to one. Assuming $\dot{X}=f(X,I)$ for some smooth function…
We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al.…
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of…
We consider a standard \textit{susceptible-infected-susceptible} (SIS) model to study behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual…
We develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
The aim of this paper is to study the stochastic SIR equation with general incidence functional responses and in which both natural death rates and the incidence rate are perturbed by white noises. We derive a sufficient and almost…
Physiological stress fundamentally alters disease susceptibility in aquatic environments. In this paper, we develop a stress-structured epidemiological model where host vulnerability is dynamically driven by water quality. Analytically, we…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susceptible individuals tend to move away from higher…
This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…