Mathematical model of susceptibility, resistance, and resilience in the within-host dynamics between a Plasmodium parasite and the immune system

•We study the interaction between a Plasmodium parasite and the immune system.•We propose a mathematical model for this interaction and prove that the model is well posed.•We determine the conditions for resilience, resistance and susceptibility of the host.•We conduct numerical simulations demonstrating the mains results.

We developed a coupled age-structured partial differential equation model to capture the disease dynamics during blood-stage malaria. The addition of age structure for the parasite population, with respect to previous models, allows us to better characterize the interaction between the malaria parasite and red blood cells during infection. Here we prove that the system we propose is well-posed and there exist at least two global states. We further demonstrate that the numerical simulation of the system coincides with clinically observed outcomes of primary and secondary malaria infection. The well-posedness of this system guarantees that the behavior of the model remains smooth, bounded, and continuously dependent on initial conditions; calibration with clinical data will constrain domains of parameters and variables to physiological ranges.