Marshall University Math Colloquium
November 19, 2014
Chagas disease is a major health problem in rural South and Central America where an estimated 8 to 11 million people are infected. It is a vector-borne disease caused by the parasite Trypanosoma cruzi, which is transmitted to humans mainly through the bite of insect vectors from several species of so-called “kissing bugs.” One of the control measures to reduce the spread of the disease is insecticide spraying of houses to prevent infestation by the vectors. However, re-infestation of homes by vectors has been shown to occur as early as four to six months after insecticide-based control interventions. In this talk, I will present re-infestation models that shed light on the effectiveness of the insecticide spraying. In particular, I will present both numerical explorations and some mathematical results. Comparison of the effectiveness of two spraying strategies namely; continuous and intermittent shows no statistically significant difference between the two strategies for small population size. For large population size, intermittent treatment is slightly more effective than continuous treatment. Another interesting result is the existence of a hysteresis-like phenomenon. This occurs when two different spraying rates lead to two different numbers of infested units at equilibrium. These results have potentially important implications for designing cost-effective control spraying strategies.