Kaposi’s sarcoma is a common AIDS-defining cancer that has continued to afflict patients living with HIV-1, especially, individuals who are currently not on HAART or whose HIV-1 status is not known. Even individuals who have had a prior HHV-8 infection and are on HAART are at an increased risk of developing KS whenever drug failure occurs and when one develops drug resistance to the drugs being administered. Like other herpesvirus, KS associated herpesvirus (KSHV), also known as human herpesvirus-8 (HHV-8) is a lifelong infection in a host. The non-AIDS related KS is less life threatening than the HIV related KS. In this study, we first develop a mathematical model for the development of Classic KS that involves the interaction of infected B cells, infected progenitor cells, KS cells, HHV-8 virions and the innate immune response. The innate immune signalling molecules generated in response to viral infection lead to the production of a broad range of antiviral proteins and cytokines that generate the initial fight back against the infection. From this model we shall show that KS therapy alone is capable of reducing the HHV-8 load and consequently the tumor burden is diminished. The innate response above is followed by an adaptive immune response which is a more robust response involving the killer T cells. The adaptive immunity is the second arm of the immune response that is elicited following the failure of the innate immunity to clear an infection. We have also incorporated three controls to explore the roles of HAART and anti-KS therapy in reducing the burden of AIDS-KS infection. From the model we show that if HAART is administered at optimal levels, both HIV-1 and HHV-8 can be reduced to undetectable levels. In the second model, we have developed a mathematical model for non-AIDS-related KS (NAKS) that encompasses uninfected B and progenitor cells, HHV-8 specific effector cells, immune response that is tailored toward viral suppression, latently and lytically infected B cells, infected progenitor cells, Kaposi’s sarcoma cells and HHV-8. The motivation of this study comes from the realization that little attention has been paid towards finding treatment options to inhibit reactivation of lytic replication of HHV-8 and other therapies to reduce infection of B cells by HHV-8. It is therefore imperative that efficacious drugs are developed to ease the affliction of NAKS patients. Unlike AIDS-related KS, NAKS variant normally results is an indolent tumor that individuals can live with throughout their lives. However, sometimes the cancer cells can spread to other internal organs in the host where metastasis can be life threatening. Due to increasing cases being recorded in sub-Sahara Africa, there is an urgency to develop new drugs and to recommend ways to increase the efficacies of some already existing drugs for this cancer. This study has recommended the range of efficacies that we believe can adequately clear the KS infection, provided adherence protocols are maintained to avoid the emergence of drug resistance. The predictions of these mathematical model have the potential to offer more effective therapeutic interventions in the treatment of NAKS or AIDS-related KS (AKS

Thesis (PhD in Mathematics and Statistics Sciences) --Botswana International University of Science and Technology, 2021