A Mathematical Model Analysis for the Transmission Dynamics of HIV/AIDS with Control Strategy

Bogale Assefa Belayneh,Purnachandra Rao Koya

doi:10.11648/j.mma.20210603.11

Bogale Assefa Belayneh, Purnachandra Rao Koya

Open Access

https://doi.org/10.11648/j.mma.20210603.11

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Abstract

This paper examines the transmission dynamics of HIV infection with public health intervention strategies treatment and awareness on the proper procedure of ART treatment. For the problem, a deterministic mathematical model is proposed and analysed qualitatively using the concept of stability of differential equations. The effective reproduction number is computed in terms of model parameters. The existence and stability of disease free and endemic steady states are recognized. The disease free and endemic equilibria are indicated to be locally and globally asymptotically stable whenever the effective reproduction number is less than unity and greater than unity respectively. This means that, HIV infection will die out in the community when the effective reproduction number is less than the threshold value and persist otherwise. Based on the sensitivity analysis of the effective reproduction number, we found that the rate of ART treatment and the rate of awareness on the proper procedure of ART are influential in reducing the magnitude of the reproduction number and thus they are important in decreasing the number of infected population. Numerical simulations support our analytical results that implementing ART treatment at every stage of HIV/AIDS had high impact in reducing the infected population than implementing on a single stage for those who follow the proper procedure of ART treatment. It also verifies the positive impact of awareness on the proper procedure of ART treatment in reducing infected individuals by reducing treatment waning rate. Therefore, our result suggests that ART treatment should be implemented together with awareness on the proper procedure of ART treatment to control the spread of HIV in the community.

Highlights

Human immunodeficiency virus (HIV) infection is a disease of immune system caused by HIV virus and it is transmitted primarily via unprotected sexual intercourse, contaminated blood transfusions (Horizontal transmission) and from mother to child during pregnancy, delivery or breastfeeding (Vertical transmission)
It was established that the disease free and endemic equilibria are locally and globally asymptotically stable for the effective reproduction number pg < 1 and pg > 1 respectively
This shows that HIV/AIDS dies out in the community, if the effective reproduction number is less than unity and persist otherwise

Summary

Introduction

Human immunodeficiency virus (HIV) infection is a disease of immune system caused by HIV virus and it is transmitted primarily via unprotected sexual intercourse, contaminated blood transfusions (Horizontal transmission) and from mother to child during pregnancy, delivery or breastfeeding (Vertical transmission). With no public health interventions, as the illness progresses, it weakens the immune system more and more making the infected individual much more likely to get other infections called opportunistic infections that are unusual for healthy individuals (AIDS stage) according to CDC. Even though this virus contains on saliva, tear, and urine, but it does not show to be at risk of transmitting the infection among human population since the virus levels on these liquids are very low [1,2,3,4]. There is no cure or effective vaccine against HIV, antiretroviral treatment can slow the course of the disease and may lead to a near -normal life expectancy [6,7,8,9,10]

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