A mathematical model for Chagas disease transmission with neighboring villages

Chagas disease has been the target of widespread control programs, primarily through residual insecticide treatments. However, in some regions like the Gran Chaco, these efforts have failed to sufficiently curb the disease. Vector reinfestation into homes and vector resistance to insecticides are possible causes of the control failure. This work proposes a mathematical model for the dynamics of Chagas disease in neighboring rural villages of the Gran Chaco region, incorporating human travel between the villages, passive vector migration, and insecticide resistance. Computational simulations across a wide variety of scenarios are presented. The simulations reveal that the effects of human travel and passive vector migration are secondary and unlikely to play a significant role in the overall dynamics, including the number of human infections. The numerical results also show that insecticide resistance causes a notable increase in infections and is an especially important source of reinfestation when spraying stops. The results suggest that control strategies related to migration and travel between the villages are unlikely to yield meaningful benefit and should instead focus on other reinfestation sources like domestic foci that survive insecticide spraying or sylvatic foci.