Studies on the basic reproduction number in stochastic epidemic models with random perturbations

Advances in Difference Equations

Soledad Torres¹  Andrés Ríos-Gutiérrez²  Viswanathan Arunachalam² 

[1] CIMFAV, Universidad de Valparaiso, Valparaiso, Chile;Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia;

关键词: Basic reproduction number;    Random perturbations;    Brownian motion;    Stability analysis;   

DOI  :  10.1186/s13662-021-03445-2

来源: Springer

【 摘 要 】

In this paper, we discuss the basic reproduction number of stochastic epidemic models with random perturbations. We define the basic reproduction number in epidemic models by using the integral of a function or survival function. We study the systems of stochastic differential equations for SIR, SIS, and SEIR models and their stability analysis. Some results on deterministic epidemic models are also obtained. We give the numerical conditions for which the disease-free equilibrium point is asymptotically stable.

【 授权许可】

CC BY