Fast and Slow Dynamics of Malaria and the S-gene Frequency∗

A mathematical model incorporating both malaria epidemics and human population genetics of the sickle-cell gene is studied. Singular perturbation techniques are used to separate the dynamics of the model into two timescales with a faster time-scale for the epidemics and a slower time-scale for the change in gene frequencies. A complete analysis of the dynamics on the slow manifold is conducted, which provides insights into how malaria epidemics may have an impact on the maintenance of the sickle-cell gene in a population where malaria is prevalent.