Related papers: Stochastic Dynamics and Probability Analysis for a…
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…
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the…
We establish a stochastic HIV/AIDS model for the individuals with protection awareness and reveal how the protection awareness plays its important role in the control of AIDS. We firstly show that there exists a global positive solution for…
Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
A recent article that combines normalized epidemic compartmental models and population games put forth a system theoretic approach to capture the coupling between a population's strategic behavior and the course of an epidemic. It…
We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…