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) ...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 <em>B</em> 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<sub>0</sub> is less than unity, the virus free equilibrium point, <em>ε</em><sup>0</sup>, is globally asymptotically stable (GAS). We further show that if R<sub>0</sub> is greater than unity, then both the immune absent and infection persistent steady states are GAS.展开更多
文摘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 <em>B</em> 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<sub>0</sub> is less than unity, the virus free equilibrium point, <em>ε</em><sup>0</sup>, is globally asymptotically stable (GAS). We further show that if R<sub>0</sub> is greater than unity, then both the immune absent and infection persistent steady states are GAS.
