Optimal control analysis of malaria and its associated complications

Abstract

Malaria is an infectious disease caused by a Plasmodium parasite. It remains one of the most life-threatening vector-borne diseases worldwide. The disease burden is further exacerbated by life-threatening complications which poses a significant challenge to healthcare systems, where treatment capacity is often saturated. This study advances previous malaria modelling research by explicitly incorporating malaria-induced complications into an optimal control framework with a realistic saturated treatment function that captures healthcare resource limitations. It specifically addresses the problem of designing cost-effective intervention strategies that minimise both the number of infections and the associated complications under resource constraints. To solve this, we applied stability and bifurcation analyses to establish threshold conditions for disease persistence. The study then extended the model into an optimal control framework using Pontryagin’s minimum principle. The results show that saturated treatment significantly reduces recovery. Numerical simulations demonstrate the time-dependent control strategies significantly influence malaria dynamics across different parameter scenarios. Effectiveness analysis indicates that simultaneous implementation of multiple control measures is the most efficient strategy to reduce the malaria burden. Prioritising outpatient treatment combined with insecticide spraying provides an economically viable approach, particularly in resource-limited settings.