Optimal control of a two-group malaria transmission model with vaccination

Malaria is a vector-borne disease that poses major health challenges globally, with the highest burden in children less than 5 years old. Prevention and treatment have been the main interventions measures until the recent groundbreaking highly recommended malaria vaccine by WHO for children below five. A two-group malaria model structured by age with vaccination of individuals aged below 5 years old is formulated and theoretically analyzed. The disease-free equilibrium is globally asymptotically stable when the disease-induced death rate in both human groups is zero. Descarte's rule of signs is used to discuss the possible existence of multiple endemic equilibria. By construction, mathematical models inherit the loss of information that could make prediction of model outcomes imprecise. Thus, a global sensitivity analysis of the basic reproduction number and the vaccination class as response functions using Latin-Hypercube Sampling in combination with partial rank correlation coefficient are graphically depicted. As expected, the most sensitive parameters are related to children under 5 years old. Through the application of optimal control theory, the best combination of interventions measures to mitigate the spread of malaria is investigated. Simulations results show that concurrently applying the three intervention measures, namely: personal protection, treatment, and vaccination of childreen under-five is the best strategy for fighting against malaria epidemic in a community, relative to using either single or any dual combination of intervention(s) at a time.