A model for Chagas disease with controlled spraying

Chagas disease is a vector-borne parasitic disease that infects mammals, including humans, through much of Latin America. This work presents a mathematical model for the dynamics of domestic transmission in the form of four coupled nonlinear differential equations. The four equations model the number of domiciliary vectors, the number of infected domiciliary vectors, the number of infected humans, and the number of infected domestic animals. The main interest of this work lies in its study of the effects of insecticide spraying and of the recovery of vector populations with cessation of spraying. A novel aspect in the model is that yearly spraying, which is currently used to prevent transmission, is taken into account. The model's predictions for a representative village are discussed. In particular, the model predicts that if pesticide use is discontinued, the vector population and the disease can return to their pre-spraying levels in approximately 5–8 years.