Related papers: Permanence and Extinction for the Stochastic SIR E…
A comparative stochastic and deterministic study of a family of SEIRS epidemic dynamic models for malaria is presented. The family type is determined by the qualitative behavior of the nonlinear incidence rates of the disease. Furthermore,…
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability…
In this paper we analyze and classify the dynamics of SIQRS epidemiological models with susceptible, infected, quarantined, and recovered classes, where the recovered individuals can become reinfected. We are able to treat general incidence…
In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…
This paper provides a first attempt to incorporate the massive discontinuous changes in the spatio-temporal dynamics of epidemics. Namely, we propose an extended class of epidemic models, governed by coupled stochastic semilinear partial…
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The…
The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises.…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
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…
TThis paper presents the dynamics of mosquitoes and humans, with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless…
We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
We propose a unified stochastic SIR model driven by L\'{e}vy noise. The model is structural enough to allow for time-dependency, nonlinearity, discontinuity, demography and environmental disturbances. We present concise results on the…
In this study we investigate a novel approach to stochastically perturb the disease transmission coefficient, which is a key parameter in susceptible-infected-susceptible (SIS) models. Motivated by the papers [2] and [5], we perturb the…
The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…
Using a stochastic Susceptible-Infected-Removed (SIR) meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a…
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…
A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and…
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…
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…