Mathematical Modeling of the HIV/Kaposi’s Sarcoma Coinfection Dynamics in Areas of High HIV Prevalence

E Lungu,N J Malunguza,E Ndelwa,T J Massaro,S Chibaya,N Ainea

doi:10.1155/2013/753424

Abstract

We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛ k < 1. A unique endemic equilibrium exists and is locally stable whenever ℛ k > 1. Therefore, reducing ℛ k to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.

Highlights

Kaposi’s Sarcoma is a cancer that occurs mostly in humans with suppressed immune systems [1]
Acquisition of human herpesvirus-8 (HHV-8) does not guarantee the development of Kaposi’s Sarcoma (KS); most individuals with a strong immune response could remain latently infected with HHV-8 throughout their lifetime [2]
The activation of latently infected B-cells to proliferate only leads to production of more HHV-8 that, according to the theory proposed by Foreman et al [2], may be responsible for infection of progenitor cells of endothelial origin, which once infected with HHV-8 develop into Kaposi’s Sarcoma cells [2]

Summary

Introduction

Kaposi’s Sarcoma is a cancer that occurs mostly in humans with suppressed immune systems [1]. From what has been described above, we formulate a mathematical model which includes the following classes: a susceptible class, S, two infected classes of individuals infected with HIV-1 only, I, individuals coinfected with HHV-8 and HIV-1, Ik, two classes of asymptomatic infectives with HIV only, P, asymptomatic coinfected, Pk, a class of treated individuals, T, and two AIDS classes, namely, individuals with full-blown AIDS only, A, and individuals coinfected with full-blown AIDS and Kaposi’s Sarcoma. AIDS is the progressive stage at which an HIV-infected individual loses competency of his immune system and becomes prone to opportunistic infections. For this reason, HIV coinfection models have found a lot of space in HIV epidemiology studies. Because our model incorporates HAART administration to all infective classes, it can provide insights into treatment strategies and, in particular, decide whether the current policy based on a CD4 count threshold to access treatment should be continued as a strategy

Model Formulation

Basic Properties

ΛK22K32K42K52

Numerical Simulations

Findings

Discussion