 |
Center for Nonlinear Studies |
Part 1: Jessie Conrad - Mathematical analysis for a model to control Chagas disease: Fighting an infection with an infection- Chagas disease is a vector-borne disease that is endemic across the Americas. I will construct a mathematical model for two parasites, Trypanosoma cruzi and T. rangeli, that can cause Chagas disease. Recent research has found that if a host is first infected with with the non-pathogenic parasite T. rangeli, then the host will be protected from infection from the pathogenic parasite T. cruzi. Our two strain model allows us to explore this dynamic and analyze the dynamics of introducing T. rangeli into host populations to help control the spread of T. cruzi. We show that repeated introductions of T. rangeli could significantly reduce the prevalence of T. cruzi infection and help control the spread of Chagas disease. Part 2: Li Guan - How the distribution for the time since infection to recovery affects the course of an epidemic- Most mathematical models assume that rate that people recover from an infection is independent of the length of time they have been infected. Models with a constant rate of recovery from an infection result is an exponentially distributed waiting time. This can be a poor approximation for most diseases. We explore the qualitative and quantitative impact of including a more realistic distribution of the time from infection to recovery in mathematical models on the predicted course of an epidemic. A theoretical analysis of the equations and numerical simulations are used to demonstrate how the distributed incubation times have a strong impact on the dynamics of the epidemics. We quantify the magnitude of these uncertainties in both simulated and real epidemic datasets.
Host: Mac Hyman