A diffusion-advection model for Toxoplasma gondii propagation

Abstract

Toxoplasmosis is an infection caused by the parasite Toxoplasma gondii, affecting an extensive human and ani-mal population. It can cause severe damages when is contracted congenitally or in immunosuppressed people. The cats are the definitive hosts and warm-blooded animals are the intermediary hosts. The cats spread T. gondii oocysts after consuming preys (rodents and birds) and contaminated water. Humans are infected with T. gondii, mainly when raw meat containing viable tissue cysts is consumed, or when contaminated food or water with oocysts from the feces of infected cats are consumed.
This work presents a system in partial differential equations that models the propagation of the parasite through cats. The proposed model is an adaptation of a classical compartment model type SIR to which dispersion of T. gondii has been aggregated, and additionally, an advective term that represents the parasite transportation by water, simulating the hypothetical case where an infected cat place infecting forms on the ground or water, and these are transported through the water, by the rain and/or the rivers. The system is solved numerically, and some simulation results with various fields of velocities are presented.