Using math to fight Chagas Disease

Researchers in the Department of Mathematics and Statistics have developed a mathematical model for Chagas disease, a tropical parasitic disease. This group has recently published a report in the journal PLoS ONE about A Model for Chagas Disease with Oral and Congenital Transmission (8(6): e67267). The lead author is Daniel Coffield, a Mathematics Professor at the University of Michigan-Flint, who obtained his PhD in Applied Mathematical Sciences from Oakland University in 2009, working with Professor Anna Spagnuolo. Professors Spagnuolo and Meir Shillor supervised the four student coauthors in the Department of Mathematics and Statistics Research Experience for Undergraduates program, funded by the National Science Foundation. One of the students, Alexandra Zetye, is an OU student who won honorable mention for the Barry Goldwater Scholarship last year. Below is the beginning of the introduction to the paper (references removed). For those who want to read the entire paper, note that all Public Library of Science (PLoS) papers are open access, so no subscription is needed to download the paper online.

"Chagas disease is caused by infection with the parasite Trypanosoma cruzi and is a major source of suffering throughout Latin America. The disease leads to organ deformity and early death in about one third of the 8–10 million individuals infected. Vector transmission by reduviids is largely responsible for the spread of T. cruzi, with some particular species specialized in domestic infection cycles. Other modes of transmission include blood tranfusions, organ transplants, oral transmission, and congenital transmission [from mother to embryo or fetus].

Although various drugs are under development and testing, current control of the transmission of Chagas disease remains largely based on vector control and blood-bank screening. In particular, the Southern Cone Initiative was implemented in the 1990s with the goal of interrupting the transmission of Chagas disease in South American countries through insecticide spraying and blood screening. This program has led to a dramatic decrease in transmission in several countries in South America, with some regions now reporting a considerable drop in infections from Triatoma infestans, the primary vector, and transmission virtually at zero. Additional control measures are treatment for acute Chagas disease and for congenital transmission cases. While insecticide spraying for Chagas vectors has led to a significant decrease in new infections, improved housing, better drugs, and an effective vaccine are needed. In particular, T. cruzi infection is likely to remain endemic in sylvatic hosts despite spraying efforts and neither insect control nor current drug treatment is optimal for this disease because of the long life span of infected human hosts, triatomine insecticide resistance, and the ease with which protozoans develop drug resistance.

Mathematical models for studying Chagas disease dynamics with seasonal insecticide spraying were presented in. In this work, we enhance the model in [their previous publication], adding the effects of congenital transmission in infected humans and infected dogs and excluding spraying. We also account for oral transmission by allowing the domestic mammals to consume the vectors, as observed experimentally... The predation term involves a density-dependent consumption rate in the form of a Holling Type II response… There are other likely routes of oral transmission in domestic mammals such as ingesting feces-contaminated food and water or licking feces-contaminated fur. Though the vector consumption is derived on the basis of the animals preying on the vectors, the consumption term can still in some sense account for these other modes since the consumption is dependent on the vector density.

The primary aim of this work is to investigate the significance of the following modes of disease transmission relative to vector biting: 1) oral transmission due to predation, and 2) congenital transmission. In particular, we want to know if these transmission modes play a significant role in human infection and have implications for disease control."