Time periodic reaction–diffusion equations for modeling 2-LTR dynamics in HIV-infected patients

Abstract

Considering multiple effects of spatial factors (spatial heterogeneity and mobility) and temporal heterogeneity (the periodic administration of the drug) in HIV infection and treatment, we formulate a time periodic reaction–diffusion equation model to study the HIV viral dynamics. The basic reproduction number R0 is derived and the global threshold dynamics is explored in terms of R0. When R0<1, the infection-free periodic solution is globally attractive. When R0>1, the model system is uniformly persistent. The global stability analysis is also performed in the critical case of R0=1 with spatial heterogeneity but without time periodicity. The global asymptotic stability of the infection steady state for the spatial homogeneous model is discussed. Furthermore, numerical simulations reveal that (i) the value of R0 depends on spatial heterogeneity, which indicates that different human individuals or different organs in one individual may have different infection states even if the drug efficacy is the same; and (ii) the 2-LTR level at the steady state may increase and the steady-state viral load may decrease dramatically if raltegravir is administered from the beginning of thetreatment.