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

Andrés Ríos-Gutiérrez; Soledad Torres; Viswanathan Arunachalam

doi:10.1186/s13662-021-03445-2

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

Adv Differ Equ. 2021;2021(1):288. doi: 10.1186/s13662-021-03445-2. Epub 2021 Jun 12.

Authors

Andrés Ríos-Gutiérrez¹, Soledad Torres², Viswanathan Arunachalam¹

Affiliations

¹ Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia.
² CIMFAV, Universidad de Valparaiso, Valparaiso, Chile.

Abstract

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.

Keywords: Basic reproduction number; Brownian motion; Random perturbations; Stability analysis.