A meta-population model of malaria with asymptomatic cases, transmission blocking drugs, migration and screening.

We consider a two-Patch malaria model, where the individuals can freely move between the patches. We assume that one site has better resources to fight the disease, such as screening facilities and the availability of transmission-blocking drugs (TBDs) that offer full, though waning, immunity and non-infectivity. Moreover, individuals moving to this site are screened at the entry points, and the authorities can either refuse entry to infected individuals or allow them in but immediately administer a TBD. However, an illegal entry into this Patch is also possible. We provide a qualitative analysis of the model, focusing on the emergence of endemic equilibria and the occurrence of backward bifurcations. Furthermore, we comprehensively analyse the model with low migration rates using recent refinements of the regular perturbation theory. We conclude the paper with numerical simulations that show, in particular, that malaria can be better controlled by allowing the entry of detected cases and treating them in the better-resourced site rather than deporting the identified infectives and risking them entering the site illegally.