HIV models with non‐exponential probability distributed infection progression

Abstract

Existing HIV infection dynamics models are based on the classical target cell‐infected cell‐free virus compartment model. In fact, in order to facilitate modeling and dynamical analysis, these models assume that the probability of infected cells staying in different infection stages obeys an exponential distribution. However, this does not accurately describe the process of HIV infection from target cells to budding of virus, that is, fusion‐reverse transcription‐reproductivity formation‐budding process. Therefore, to expand the idea of HIV modeling, in this paper, we first establish the HIV integral‐differential equation model that obeys the general distribution, and then degenerate the model into a subclass ODEs model under the assumption of gamma distribution. Finally, an equivalent age structure model is given, and numerical simulations are conducted to describe the integral‐differential equations model. It is worth mentioning that ODEs models with subclasses can provide good numerical implementations for age structure as well as other PDEs HIV models. This is another important purpose of our work.