# Mathematical Models for Chagas Disease

## Authors

• Meir Shillor Oakland University

## Abstract

We present mathematical and computational results for a model for the dynamics of Chagas disease. It is caused by the parasite T. cruzi that is transported by the vectors
Triatoma infestans, and affects millions of humans and domestic mammalsВ  throughout rural areas in CentralВ  and South America.В  The chronic disease causes mortality
and severe morbidity.В  To control the disease spread periodic insecticide spraying of theВ В village houses is used and also bank blood screening.

The basic model for the disease dynamics consists of four nonlinearВ В ordinary differential equations for the populations of the vectors and of infected vectors,В В humans, and domestic animals. It has time-dependent periodic coefficients to accountВ for seasonality, and was developed in [1]. The mainВ motivation for the model was to optimize the insecticide spraying schedules. The model was extended to take into account congenital transmission in both humans
and domestic mammals as well as oral transmission in domestic mammals [2].В In particular, oral transmission provides an alternative to vector biting as an infection
В route for the domestic mammals, who are key to the infection cycle.В  This may lead toВ В high infection rates in domestic mammals even when the vectors have a low preferenceВ В for biting them, and ultimately results in high infection levels in humans.В В Another extension was to allow for random coefficients, reflectingВ  the uncertainty in their values.В В The simulations show that the variations in some of the model parameters lead toВ В considerable variations in the numbers of infected humans and domestic mammals.

[1] A.M. Spagnuolo, M. Shillor, G.A. Stryker,
A model for Chagas disease with controlled spraying,
J. Biological Dynamics 5(4)(2010) 299--317.

[2] D.J. Coffield Jr., E. Mema, B. Pell, A. Pruzinsky, M. Shillor, A.M. Spagnuolo, and A. Zetye, A Model for Chagas Disease with vector consumption and transplacental transmission, to appear in PLOS.

## Author Biography

### Meir Shillor, Oakland University

Department of Mathematics and Statistics, Professor