(Journal of Dynamics and Differential Equations (Springer), 2004) Feng, Zhilan; Yi, Yingfei; Zhu, Huaiping
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 time-scales 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.
Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We study a metapoulation model which explicitly incorporates the local population dynamics of two competing species. Singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to much more complex outcomes than simple patch models that do not include explicit local dynamics.