Global exponential stability of positive periodic solutions for a cholera model with saturated treatment

Xueyong Zhoub,Hongzheng Quana,Jianzhou Liua

doi:10.15388/na.2018.5.1

Abstract

In this paper, we consider a cholera model with periodic incidence rate and saturated treatment function. Under certain conditions, we establish a criterion on the global exponential stability of positive periodic solutions for this model by using a novel method. We illustrate our theoretical results with numerical simulations by using Matlab.

Highlights

Cholera is an acute intestinal infectious disease caused by infection of the bacterium Vibrio cholerae, such as Vibrio cholerae serogroups O1 and O139, which is the major public health problem and affect primarily developing world populations with no proper access to adequate water and sanitation resources
To the best of our knowledge, there is no result on the global exponential stability of positive periodic solutions for the cholera model with periodic incidence rate and saturated treatment function
We considered a non-autonomous cholera epidemic model, which involves almost periodic incidence rate and saturated treatment function

Summary

Introduction

Cholera is an acute intestinal infectious disease caused by infection of the bacterium Vibrio cholerae, such as Vibrio cholerae serogroups O1 and O139, which is the major public health problem and affect primarily developing world populations with no proper access to adequate water and sanitation resources. Mwasa et al formulated a mathematical model that captures some essential dynamics of cholera transmission to study the impact of some control strategies, such as public health educational campaigns, vaccination and treatment in reducing the incidence of disease [15, 20]. To the best of our knowledge, these is no paper to consider a cholera model with both periodic incidence rate and saturated treatment function. As it is well known, many infectious diseases exhibit seasonal fluctuations, and there is a saturation phenomenon during the treatment process.

Preliminaries and lemmas

Main results

Simulations

Findings

Discussion