Modeling and Control of Acute Infection of Toxoplasma Gondii

Toxoplasma gondii is a protozoan capable of replicating sexually in cats and asexually in other warm-blooded animals. When the parasites first enter a host, the replication process begins very quickly as the free parasites invade healthy host cells, until a host-mediated immune response suppresses replication of the rapidly replicating parasites. To study the effects of this process, a data-driven model is developed where the number of parasites and the IFN-γ level are selected as state variables. The reproduction number, R₀ is calculated to determine the criteria for sustaining infection within the host. Stability analyses are carried out for the endemic equilibriums. Parameter fitting is performed using maximum likelihood to match existing data to the model. Finally, an optimal control problem is formulated to investigate the optimal immune strategy when minimizing the negative host reaction to increased IFN-γ levels. The results shed light into the role the immune response plays in suppressing acute infection of Toxoplasma gondii.