A model for Chagas disease with controlled spraying

Abstract

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.

Keywords:

• Chagas disease
• nonlinear ODE system
• Trypanosoma cruzi
• numerical simulations
• vector control
• insecticide spraying
• epidemic dynamics
• dynamical systems

AMS Subject Classification :

• 34A12
• 92B05
• 34A34

Acknowledgements

We thank Prof. Darrell Schmidt for the references to the Nicholson blowflies mathematical model, Ms April Clark for multiple literature searches and help in determining initial parameters in earlier versions of the model, Mr Qi Lu and Prof. Harvey Qu for their contributions to earlier versions of the model and estimates of the parameters, Mr McBride for his editorial help, and Prof. Serge Kruk and Mr Michael DuChene for setting up the web interface. We also thank the reviewers for their helpful suggestions.