Modeling erythropoiesis subject to malaria infection

A mathematical model of erythropoiesis subject to malaria infection is developed by combining ideas from previous models that addressed only one of the two phenomena. The nature of the model allows one to account for suppression of erythropoiesis by the toxin hemozoin, which is a by-product of digested hemoglobin. Following the derivation of the model, numerical simulations are performed and show that the number of parasites produced per bursting erythrocyte has the most significant effect of erythropoiesis. It is also shown that removing hemozoin may be an effective method for aiding the recovery of the erythrocyte population, but is not effective in maintaining a healthy population in the early stages of infection. The second half of the paper introduces an implicit finite difference scheme that was used to perform the simulations previously mentioned. An existence-uniqueness result is then provided via the numerical method.