Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaKaposis sarcoma (KS), the most common tumor associated with human immunodeficiency virus-
I (HIV-I) and human herpesvirus-8 (HHV-8) (also referred to as Kaposis associated herpesvirus
(KSHV) infection, develops in approximately 20 percent of patients infected with HIV-I. The
lesions of this multicentric vascular neoplasm are purplish patches, plaques, or nodules. Although
highly active antiretroviral therapy (HAART) can prolong the time to treatment failure in patients
with KS, nearly every patient with AIDS-related (or epidemic) KS eventually develops
disseminated disease. Progression usually occurs in an orderly fashion from new localized or
widespread mucocutaneous lesions to more numerous lesions and generalized skin disease with
involvement of lyrnph nodes, gastrointestinal tract (GIT), lungs and other organs. Studies have
shown that KS cells themselves are not infected with HIV-I; therefore, it is widely accepted than
HIV-I does not play a direct oncogenic role in AIDS-KS. However, the precise role of HIV-I in
AIDS-KS is still not completely understood, and there is considerable debate over whether HIVI
plays a passive role (through the induction of immunosuppression) or a more direct role in the
pathogenesis of this disease. We formulate a mathematical model to study the dynamics of HIVI
related KS pathogenesis. In this model, it is assumed that HIV-I infects only the CD4 +
T cells and HHV-8 infects the B- cells, which largely remain latently infected and only
become reactivated after exposure to inflammatory cytokines and other growth factors
secreted from HIV-I infected cells. The Infection free and Infection persistent equilibria
have been found and their stability established. It is found that the disease can exist even
if both sub-group reproduction numbers, relating to HIV-I and HHV-8, are less than unity.Botswana International University of Science and Technology Palapye, Botswana
