Analysis of a Chlamydia epidemic model with pulse vaccination strategy in a random environment

Guruprasad Samantaa,Shyam Pada Pada Bera

doi:10.15388/na.2018.4.1

Abstract

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate, and pulse vaccination strategy in a random environment. It has been shown that the Chlamydia epidemic model has global positive solutions and, under some conditions, it admits a unique positive periodic disease-free solution, which is globally exponentially stable in mean square. We have defined two positive numbers R1 and R2 (< R1). It is proved that the susceptible population will be persistent in the mean and the disease will be going to extinct if R1 < 1 and the susceptible population as well as the disease will be weakly persistent in the mean if R2 > 1. Our analytical findings are explained through numerical simulation, which show the reliability of our model from the epidemiological point of view.

Highlights

Infectious diseases have tremendous influence on human life, and so the development of vaccines against infectious disease has been a boon to human being
The susceptible population increases by the recruitment through new sexually-active individuals, migration, and the vaccinated individuals return to the susceptible class and decreases due to direct contact with infected individuals, natural death, and pulse vaccination strategy
We have considered a dynamical model of Chlamydia diseases with bilinear incidence rate under stochastic perturbation and the pulse vaccination scheme

Summary

Introduction

Infectious diseases have tremendous influence on human life, and so the development of vaccines against infectious disease has been a boon to human being. Immune system cells and the substances they make travel through the body to protect it from pathogens (germs) causing infections. Pathogens are any disease-producing agent, especially a virus, bacterium, or other microorganism, which are called foreign armies because they are not normally found in the body. They try to invade human body to use its resources to serve their own purposes, and so they can hurt the body in the process. The vaccine activates immune systems infection-attacking ability and memory without exposure to the actual disease-producing pathogens. Since 1993, attempts have been made to develop mathematical theory to control infectious diseases using pulse vaccination. The aim of the analysis of this model is to trace the parameters of interest for further study with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness

Model derivation and preliminaries

Disease-free periodic solution

Extinction and persistent of the disease

Numerical simulation

Conclusions