Assessing the invasion speed of triatomine populations, chagas disease vectors evaluación de la velocidad de invasión de poblaciones de vectores triatominos de la enfermedad de chagas

Abstract

Spraying insecticides to control triatomine populations, the vectors of Chagas disease, does not prevent the disease’s reemergence in infested areas. Mathematical models try to explain this reemergence in terms of the factors underlying sylvatic transmission of the parasite Trypanosoma cruzi. The presence of reservoir hosts such as woodrats is essential to the infection’s geographical spread. This study models a vector-host system using integrodifference equations to incorporate dispersal as well as hostvector interactions. These equations capture, simultaneously, the three processes taking place between successive generations: demography, infection and spatial dispersal. Travelling waves, the solutions of the integrodifference equations thus derived, allow one to calculate numerically the invasion speed of the disease. Neubert-Caswell’s theorem can then be applied to calculate the analytical invasion speed.

On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease

“…Mathematical modeling stand a good tool to gain insights into 6092 N. DIB-BAGHDADLI, R. LABBAS, T. MAHDJOUB AND A. MEDEGHRI these processes [21]. These approach used, for example, ordinary differential equations [15], partial differential equations [24] and integro-difference equations [20], [18]. Other studies based on scientific calculus were also used as cellular automaton [23], [5] and agent-based model [6], [9].…”