Abstract
In this paper, the global properties of a classical Kaposi’s sarcoma model are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the virus free and virus (or infection) present steady states. The model considers the interaction of B and progenitor cells in the presence of HHV-8 virus. And how this interaction ultimately culminates in the development of this cancer. We have proved that if the basic reproduction number, R0 is less than unity, the virus free equilibrium point, e0, is globally asymptotically stable (GAS). We further show that if R0 is greater than unity, then both the immune absent and infection persistent steady states are GAS.
Highlights
acquired immune deficiency syndrome (AIDS)-related malignancies such as Kaposi’s sarcoma, non-Hodgkin’s lymphoma, Hodgkin’s disease, primary effusion lymphoma, remain a significant burden for people living with HIV virus
The paper is structured as follows: In Section 2, we develop a mathematical model for the pathogenesis of classical Kaposi’s sarcoma based on [1]
In this study we present a mathematical model of the progression of Kaposi’s sarcoma (KS) in the absence of HIV-1, by including the interactions of B-cells, HHV-8 infected B cells and progenitor cells, effector cells such as the cytotoxic T lymphocytes (CTLs)
Summary
AIDS-related malignancies such as Kaposi’s sarcoma, non-Hodgkin’s lymphoma, Hodgkin’s disease, primary effusion lymphoma, remain a significant burden for people living with HIV virus. According to Foreman et al [1], KS SCs are poorly differentiated endothelial cells (ECs), similar to lymphatic ECs, that are mistakenly infected by the KSHV/HHV-8 This infection is transmitted either sexually or via saliva and its development is known to be enhanced in individuals with suppressed immune systems. In an endeavour to understand the pathogenesis of the KS, we develop an in-host model of KS and find the steady states and establish their local and global stability
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