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

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.

Optimal Control and Bifurcation Analysis of HIV Model

“…Human immunodeficiency virus (HIV) is a virus causing HIV infection and results in economic and life devastating crisis if immediate action is not taken to halt further prevalence of the infection [1][2][3][4][5][6][7][8][9][10][11]. Moreover, this infection has no curing medication, but antiretroviral therapy (ART) or its combination is used for halting further progression of infection by inhibiting the virus in human blood, but if left untreated leads to a sever stage called acquired immunodeficiency syndrome (AIDS) [12][13][14][15][16][17][18][19][20][21][22][23]. HIV infection progress through stages as follows: (i) primary stage (asymptomatic stage): this stage faces human individual where the virus is in the blood cannot be diagnosed with medical instruments; (ii) asymptomatic stage: this stage is symptomless stage of HIV infection but diagnosable with medical test; (iii) symptomatic stage: in this stage, the symptom of HIV infection like tiredness, loss of weight, and extreme loss of water starts to manifest in the life of HIV infected individuals; and (iv) AIDS stage: this is advanced stage of HIV infection where it is difficult for treatment and leads to death soon if special care is not taken [24][25][26][27][28][29][30][31][32].…”

A novel mathematical model of AIDS-associated Kaposi's sarcoma: Analysis and optimal control

“…Appearance of the cancer can be in several parts or a specific part of the body [43]. KS remains the most common cancer in sub-Sahara Africa and the second most common cancer in HIV-infected patients worldwide [26]. Infection with HIV afflicts approximately 37.9 million people worldwide (end 2018) [47] and results in impaired immune responses which may affect defenses against pathogens [48].…”

“…Despite the introduction of highly active antiretroviral therapy (HAART), KS still continues to be diagnosed in HIV-infected patients [7]. The distribution of KS is concentrated in sub-Sahara Africa where the heaviest burden of HIV-AIDS is concentrated [7,26]. Since HIV is an immunosuppressive virus, it promotes the development of KS in individuals dually infected with both viruses, HIV-1 and HHV-8, a combination which has proved to be fatal [26].…”

Mathematical Model of Classical Kaposi’s Sarcoma

“…Several studies [1] [2] have indicated that additional factors contribute to the development of KS in asymptomatic as well as symptomatic KSHV/HHV-8 infected persons. It is known that not every AIDS patient develops KS even in the face of profound immunosuppression, only a minority of KSHV/HHV-8 infected transplant recipients develop iatrogenic KS, and people with classical or endemic KS are not typically immunosuppressed [3] [4].…”