Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks

Yue Zhang,Yuxuan Li

doi:10.1155/2020/3768083

Abstract

In this paper, a stochastic SEIR (Susceptible-Exposed-Infected-Removed) epidemic dynamic model with migration and human awareness in complex networks is constructed. The awareness is described by an exponential function. The existence of global positive solutions for the stochastic system in complex networks is obtained. The sufficient conditions are presented for the extinction and persistence of the disease. Under the conditions of disease persistence, the distance between the stochastic solution and the local disease equilibrium of the corresponding deterministic system is estimated in the time sense. Some numerical experiments are also presented to illustrate the theoretical results. Although the awareness introduced in the model cannot affect the extinction of the disease, the scale of the disease will eventually decrease as human awareness increases.

Highlights

Infectious diseases have been threatening human health and affecting people’s life
Liu et al researched the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium for a stochastic delayed SEIR epidemic model with nonlinear incidence
Inspired by the abovementioned factors, we will establish a stochastic SEIR models with human awareness in complex networks in this paper, which consider the effects of undiagnosed populations, human awareness, and external uncertainties on the spread of infectious diseases

Summary

Introduction

Infectious diseases have been threatening human health and affecting people’s life. Many researchers use mathematical models to study the spread and control strategies of infectious diseases. In order to comprehend the spread tendency of infectious diseases, more and more researchers concerned about the stability and asymptotic behavior of epidemic models on complex networks. Li et al studied a stochastic SIRS epidemic model with nonlinear incidence rate and varying population size and obtained sufficient conditions for extinction and persistence of the disease (see [22]). Liu et al researched the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium for a stochastic delayed SEIR epidemic model with nonlinear incidence (see [27]). Inspired by the abovementioned factors, we will establish a stochastic SEIR models with human awareness in complex networks in this paper, which consider the effects of undiagnosed populations, human awareness, and external uncertainties on the spread of infectious diseases. We close the paper with the summary of main results

The Model with Migration and Human Awareness

Existence of the Global and Positive Solution

Persistence of the Disease

Extinction of a Disease

Numerical Simulations

Conclusion