A HIV Infection Model with Periodic Multidrug Therapy (Journal of Nonlinear Modeling and Analysis, 2024)
This paper investigates the effects of periodic drug treatment on a HIV infection model with two co-circulation populations of target cells. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable if $\mathcal{R}_0 < 1$, while the infection persists and there exists at least one positive periodic state when $\mathcal{R}_0 > 1$. Therefore, $\mathcal{R}_0$ serves as a threshold parameter for the infection. We then consider an optimization problem by shifting the phase of drug efficacy functions, which corresponds to change the dosage time of drugs in each time interval. It turns out that shifting the phase affects critically on the stability of the infection free steady state. Finally, exhaustive numerical simulations are carried out to support our theoretical analysis and explore the optimal phase shift.
Keywords: HIV infection; periodic drug treatment; basic reproduction ratio; global stability; optimization.