Modelling cancer that is HIV-related in the presence of treatment

Abstract

In this study, a theoretical nonlinear mathematical model was revised to understand the inter action of HIV-related cancer cells dynamics with treatment. The work done is adopted from the paper by Lou et al. This work develops a mathematical model that combines healthy CD4+ cells, cancer cells, HIV-infected T cells, and cancer HIV-infected cells. The well-posedness of the model is established and discussed. The computation of reproduction numbers, equilibria, and stabilities are analyzed. Numerical simulations are carried out to determine the parameters that have a high impact on the spread of the disease and Matlab software was used for the numerical simulations. The numerical simulations for the model with no treatment show that the disease will persist. To curb this situation, we introduced the model that incorporated treatment, that is, HAART coupled with Chemotherapy to control the rate of infected T-cells with time. The results obtained are consistent with those obtained by Carvalho et al., Aogo et al., and Kaondera et a