Effect of public awareness, behaviours and treatment on infection-age-structured of mathematical model for HIV/AIDS dynamics

Nurudeen Oluwasola Lasisi

doi:10.21595/mme.2020.21249

Abstract

Since the discovering of the HIV/AIDS epidemic, more people have been infected with the HIV/AIDS infection and several individuals have died of HIV/AIDS virus. In this research work, an infection-age-structured mathematical model for HIV/AIDS transmission dynamics is developed and investigated, taking into consideration the public awareness, Treatment and Sex behaviours. It is assumed that the infectious population is structured according to time and age of infection. We established the criteria for the existence and uniqueness of solution. An explicit formula for the effective reproduction number RE of the model is obtained. We showed that the disease-free-equilibrium (DFE) state is stable if RE<1. Constructing a Lyaponov function, the global stability of the DFE state of the system is obtained for RE<1. Endemic Equilibrium (EE) state was analyzed locally and globally with the method of linear and nonlinear Lyapunov function; it was found that EE is locally asymptotically stable if RE>1 and globally stable if RE>1 for X1<X2.

Highlights

Human Immunodeficiency Virus (HIV) Infection is a virus that destroys the immune system in an individual’s system which natural defence against illness
We considered infection-age-structured of mathematical model of HIV/Acquired Immunodeficiency Syndrome (AIDS) dynamics incorporating public awareness, behaviours and treatment
An infection-age-structured mathematical model to study the effect of HIV public awareness program, with unaware HIV susceptible on HIV/AIDS dynamics was developed and analysed

Summary

Introduction

Human Immunodeficiency Virus (HIV) Infection is a virus that destroys the immune system in an individual’s system which natural defence against illness. HIV advance to AIDS, at this point, the immune system is too weak to fight off life-threatening disease and infection [1]. HIV/AIDS destroys T cells called CD4 cell, these cells help immune system fight infections of individuals. AIDS weakens the immune system to the point where it can no longer fight off most diseases and infections. This makes individuals more vulnerable to a wide range of illnesses [3]. EFFECT OF PUBLIC AWARENESS, BEHAVIOURS AND TREATMENT ON INFECTION-AGE-STRUCTURED OF MATHEMATICAL MODEL FOR HIV/AIDS DYNAMICS. We considered infection-age-structured of mathematical model of HIV/AIDS dynamics incorporating public awareness, behaviours and treatment

Model formulation

Basic properties of the model

Existence and uniqueness of solution

Effective reproduction number

Findings

12. Conclusions