An Age-and-Phase Structured Model of the Malaria Asexual Erythrocytic Replication Cycle

We present a mathematical model of the asexual blood stage of a malaria infection from Plasmodium falciparum, including time, maturation of infection, and phase of infection. The phases of infection include the merozoite phase, immature trophozoite phase, trophozoite phase, schizont phase, as well as the production of gametocytes. Our model shows oscillatory behavior of the parasite between the phases with a period that strongly depends on the generation reproduction number of the parasite. We separate parasite evolution into different growth regimes classifying final sizes when the parasite population does not change and final proportions when it grows exponentially. Without fitting parameters, we compare our model to data for parasitized red blood cells showing excellent agreement. The phase structure of our model allows us to also gain insight into sequestered parasitized red blood cells which are unmeasured. We demonstrate how parameters within the phase structure can impact parasite growth and maturation with potential implications for antimalarial drugs and other therapies.