A Global Stability Analysis of a Susceptible-Infected-Removed-Prevented-Controlled Epidemic Model

Muhammad A Yau,Hussaini S Ndakwo,A M Umar

doi:10.4236/am.2014.510131

Abstract

A mathematical model of HIV transmission dynamics is proposed and analysed. The population is partitioned into five compartments of susceptible S(t), Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t). Each of the compartments comprises of cohort of individuals. Five systems of nonlinear equations are derived to represent each of the compartments. The general stability of the disease free equilibrium (DFE) and the endemic equilibrium states of the linearized model are established using the linear stability analysis (Routh-Hurwitz) method which is found to be locally asymptotically stable when the infected individuals receive ART and use the condom. The reproduction number is also derived using the idea of Diekmann and is found to be strictly less than one. This means that the epidemic will die out.

Highlights

One of the greatest threats to human survival in contemporary times is the Human Immune deficiency Virus (HIV) pandemic
Antiretroviral Therapy (ART) does not cure HIV infection; it only boosts the immune system of infected people against secondary infections, thereby prolonging their life span Kimbir et al, (2008) [3]
The main aim of this research is to propose a modified mathematical model of HIV transmission dynamics that will be used to check for the spread of the epidemic and to check for the effectiveness of Antiretroviral Therapy (ART) and the use of a preventive measure is in controlling the spread of HIV/Acquired Immune Deficiency Syndrome (AIDS). These are some of the objectives of the research: To investigate the extent to which, Antiretroviral Therapy and the use of a preventive measure will reduce the spread of the virus; To provide information to guide advocacy and future program planning; Institutionalizing best practices in care and support for people living with HIV/AIDS; And to stimulate more researches on HIV/AIDS

Summary

Introduction

One of the greatest threats to human survival in contemporary times is the Human Immune deficiency Virus (HIV) pandemic. ART does not cure HIV infection; it only boosts the immune system of infected people against secondary infections, thereby prolonging their life span Kimbir et al, (2008) [3]. Another method of control includes the use of barrier contraceptives. More than 60% of the infected population has not yet finished elementary school according to the official data available in the site Yang et al, (1999) [5] In this social group, the number of people who have access to information about AIDS is insignificant. The low standards of public health services contribute to worsening of the situation

Objectives

Methods

Findings

Conclusion