Qualitative analysis of a two-group SVIR epidemic model with random effect

Kaiyan Zhao,Shaojuan Ma

doi:10.1186/s13662-021-03332-w

Abstract

In this paper, we investigate the dynamical behavior of a two-group SVIR epidemic model with random effect. Firstly, the two-group SVIR epidemic model with random perturbation of natural death rate is established. The existence and uniqueness of positive solution are proved by using stopping time theory and the Lyapunov analysis method. Secondly, a property of the system solution is obtained by using the law of strong numbers and the continuous local martingale. Finally, a new combination of Lyapunov functions is applied. The solution of the model we obtained is oscillating around a steady state if the basic reproduction number is less than one, which is the disease-free equilibrium of the corresponding deterministic model. A numerical simulation is presented to verify our theoretical results.

Highlights

The epidemic is one of the most important diseases which are caused by various pathogens and are harmful to the health of humans
7 Conclusions Environmental noise can be described to have a significant effect on the advancement of an epidemic
We present the dynamics of a stochastic two-group SVIR model under the noises of environment

Summary

Introduction

The epidemic is one of the most important diseases which are caused by various pathogens and are harmful to the health of humans. The use of differential equation theory to study the stochastic epidemic model mainly draws dynamic conclusions such as global existence and uniqueness, stochastic stability, and progressive behavior of solutions [26, 27] On this basis, the deterministic model and the corresponding random model are compared to analyze the changes that occur under the interference of random factors and to grasp the trend of disease development, and provide important analysis for the study of the spread of diseases, disease prevention, and control departments [28].

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Conclusions