Abstract
In a world of raging epidemic spreads, HIV has a major impact on the health of the global public. Immune system cells play a major role in defending the body from the impact of the virus. HIV’s major effect is on CD4+ cells (or T cells) and CD8+ cells (or Z cells). The activation of CD8 cells has a major impact as it helps in fighting against this virus. Therefore, this paper focuses on the development of a novel mathematical model incorporating the immune cells(T and Z cells) and studies the dynamics of the model. The study of the dynamics of HIV-immune cells and the CD8 cell response can provide a rational selection of strategies for treatment and cure based on CD8 cells. A critical threshold (basic reproduction number) ρ0 is obtained along with the existence of disease-free equilibrium, and endemic equilibrium without and with the immune response for the model. Further, a Lyapunov function is constructed using the graph-theoretic approach to establish the global dynamics for endemic equilibrium(with and without immune response) point and matrix theoretic method for disease-free equilibrium. Local sensitivity analysis for ρ0 and E2 has also been carried out to recognize the sensitive parameters which may help in controlling the disease. The numerical discussion is carried out to validate our theoretical results. Sensitivity analysis has also been carried out for basic reproduction number and endemic equilibrium point with the immune response to recognize the sensitive parameters which may help in controlling the disease. Finally, the impact of the immune response of activated cells directly helping in suppressing the viral replication is shown by uncertainty analysis using PRCC. We were motivated to develop the novel model of HIV with immune response and study the dynamics of the model in the presence of CD8 cells as activated CD8-cells based immune response treatments can help control the disease at a mild stage itself due to its cytotoxic potential.
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