Mathematical Model of Within‐Host HIV Infection With Variable CD4 Production, and Saturated Incidence

ABSTRACT

The latent reservoir remains the greatest obstacle to HIV eradication. This is due to infected cells persisting in a dormant state for prolonged periods and reactivating infection after treatment interruption. Mathematical modeling has been instrumental in describing the interaction between HIV and the host immune system. In this study, we develop a within‐host mathematical model of HIV infection that incorporates virus‐dependent CD4 ⁺ T‐cell recruitment, Holling type II saturated incidence, and a latent reservoir. The qualitative properties of the model are investigated by establishing the positivity and boundedness of solutions, deriving the basic reproduction number, and analyzing the stability of the disease‐free and endemic equilibria. A sensitivity analysis is performed to identify the parameters that most strongly influence disease transmission. Numerical simulations are carried out to validate the theoretical results and to examine the effects of key biological parameters on HIV dynamics. The results show that the viral clearance rate, infection rate, viral production efficiency, and burst size are the dominant determinants of infection persistence. Although the latent reservoir has only a limited influence on the basic reproduction number, it substantially enlarges the pool of infected cells capable of reigniting infection following treatment interruption. These findings demonstrate the importance of combining therapies that suppress viral replication with strategies that eliminate the latent reservoir to achieve long‐term HIV control.