STABILITY OF NONLINEAR HIV MATHEMATICAL MODEL OF
Mathematical models have played a crucial role in enhancing our understanding of the dynamics of HIV infection. Through the comparison of these models, we have been able to quantify various aspects of the interaction between HIV and the infected cells, shedding light on HIV pathogenesis and influencing the treatment approaches for AIDS patients. In this study, we propose and examine a nonlinear three-dimensional mathematical model for HIV, incorporating healthy CD4+ T cells, infected T cells, and free virus V. The model considers the logistic growth of healthy T cells with a source term S, as well as the conversion of healthy T cells into infected T cells through a Holling type second functional response. Analysis of the nonlinear model reveals its bounded nature. We explore the equilibrium points of the model, noting that the disease-free equilibrium exhibits a saddle point and undergoes bifurcation. By applying the Routh-Hurwitz criterion, we establish the asymptotic stability of the equilibrium point involving T cells. When the death rate of infected T cells is not assumed to be zero, the infected equilibrium converges to the disease-free equilibrium. Furthermore, we investigate the stability conditions of the non-zero equilibrium and utilize several theorems to analyze the model comprehensively.
AIDS, Mathematical modeling, HIV, CD4+ T cells, Routh-Hurwitz criterion, Holling type second functional response
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