Two strain competition: Trypanosoma cruzi
Chagas disease is a tropical parasitic disease that affects Latin America. The parasite causing Chagas, Trypanosoma cruzi, is transmitted by an insect vector of the subfamily Triatominae. Chagas is uncommon in the United States, but is becoming more common in the southern part of the country. This may be due to a more virulent strain type of the parasite moving northward from Mexico and invading the less virulent, native strain type. A region in southern Texas where there is a mixing of two Triatoma species is modeled with two different modeling frameworks. A mathematical deterministic model is created to describe the interactions between one host and one vector and determine the outcome of an invasion of a non-native strain type into the region. A stochastic, agent based model is created to determine the effect space and randomness may have on the interactions. Within the models, three modes of parasite transmission are considered to account for the different characteristics of each strain type.
We vary the horizontal transmission ability of the invasive strain and run simulations for an equivalent time period of 30000 days (82 years). We fi nd that the horizontal transmission potential of the invasive strain must be about 1.5 times as great as the other in order for over 50% of the runs to end with the invasive strain dominating. However, in the ODE model, the horizontal transmission of the invasive need only be 1.056 times that of the other strain. We also determine from the ODE model that considering three modes of transmission and no migration of vectors into the region being modeled, it is impossible for the two strains to coexist.
Marcel Munoz Figueroa,
Xavier Martinez Rivera,