Global dynamics of a multiscale malaria model with two strains

This work examines the global dynamics of a two-strain malaria model proposed in a recent paper (Agusto, 2014). The global stability of the disease-free equilibrium when the basic reproduction number equals one, as well as the global stability of the resistant strain-only boundary equilibrium and coexistence equilibrium, have not been addressed in Agusto (2014). In fact, the model incorporates a factor that individuals infected with sensitive strain can transform into individuals infected with resistant strain, posing substantial challenges to global stability analysis. Notably, a key characteristic of this model is that the dynamics of humans and mosquitoes operate on different time scales. Consequently, we utilize the geometric singular perturbation theory to separate fast and slow dynamics, thereby obtaining global dynamics. Our results may offer deeper insights into the competitive exclusion and coexistence of two strains.