Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Abstract

In this study, a time-periodic viral infection model incorporating cell-to-cell infection and antiretroviral therapy has been investigated. The basic reproduction number ${\mathrm{ℛ}}_0$ has been defined as a threshold parameter which governs whether or not the disease dies out. Theoretical results indicate that the disease goes to extinction if ${\mathrm{ℛ}}_0<1$ and otherwise the disease will uniformly persist. The global stabilities of the equilibria for the corresponding autonomous model have been investigated by constructing suitable Lyapunov functions. Moreover, numerical simulations have been carried out to validate the obtained results. The results show that cell-to-cell infection mode may be a barrier to curing the viral infection and increasing the efficacy of protease inhibitors for blocking cell-to-cell infection which will benefit to weaken the severity of the viral infection.