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Mathematical Model of Classical Kaposi’s Sarcoma
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
- 1 Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
- 2 Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
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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, R 0 is less than unity, the virus free equilibrium point, ε 0 , is globally asymptotically stable (GAS). We further show that if R 0 is greater than unity, then both the immune absent and infection persistent steady states are GAS.
KeywordsHuman Herpesvirus-8Lyapunov FunctionClassical Kaposi’s Sarcoma
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