“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."
“This work studies a mathematical model for the dynamics of Chagas disease, a parasitic disease that affects humans and domestic mammals throughout rural areas in Central and South America. It presents a modified version of the model found in Spagnuolo et al. [A model for Chagas disease with controlled spraying, J. Biol. Dyn. 5 (2011), pp. 299-317] with a delayed logistic growth term, which captures an overshoot, beyond the vector carrying capacity, in the total vector population when the blood meal supply is large. It studies the steady states of the system in the case of constant coefficients without spraying, and the analysis shows that for given-averaged parameters, the endemic equilibrium is stable and attracting. The numerical simulations of the model dynamics with time-dependent coefficients are shown when interruptions in the annual insecticide spraying cycles are taken into account. Simulations show that when there are spraying schedule interruptions, spraying may become ineffective when the blood meal supply is large. “
Matthew Toeniskoetter was an Oakland University student who won the Louis R. Bragg Graduating Senior Award from the Department of Mathematics and Statistics.
He is now a graduate student in the Mathematics Department at Purdue University.
Andrea Thatcher is currently a graduate student in Applied Mathematics at Arizona State University.
Benjamin Wood graduated from Michigan State University’s Professional Master of
Science Program in Industrial Mathematics in May 2012. He is currently employed at Global
Business Services Emerging Leaders Associate at Nielsen in Tampa, Florida.
Lindsey Kingsland won the Concordia University - Irvine President’s Academic Showcase award ($1,000) in 2012
for best project, based on the Chagas disease work from the REU program. She used the money to
go to Haiti and she is currently a grade 6 – 12 Science and Mathematics teacher at Liberty
Academy School in Haiti.
A team of undergraduates working with Profs. Shillor and Spagnuolo use mathematics to study the spread of Chagas Disease.
Created by Brad Roth (firstname.lastname@example.org) on Friday, January 4, 2013 Modified by Brad Roth (email@example.com) on Monday, January 14, 2013 Article Start Date: Friday, January 4, 2013