Threshold and stability results for a malaria model in a population with protective intervention among high‐risk groups

Abstract

We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non‐immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated.

First Published Online: 14 Oct 2010