An optimal control model for malaria transmission incorporating asymptomatic and symptomatic infections with a nonlinear force of infection

Abstract

The study presents a mathematical model of malaria parasite spread among humans and mosquitoes that accounts for both symptomatic and asymptomatic human infections, as well as a non-linear force of infection represented by saturated incidence rates. Upon formulation, a positivity test is performed to assess the biological significance of the model. The model’s endemic and disease-free equilibria are also established. The basic reproduction number is computed, and the existence and stability of equilibria are analyzed using the Routh–Hurwitz criterion. Bifurcation analysis reveals a backward bifurcation. A sensitivity analysis of the reproduction number, supported by PRCC plots, identifies key influential parameters. Based on these results, the malaria model is updated to include three controls: insecticide-treated bed nets, treatment of infected individuals, and insecticide use. An optimal control problem is then formulated and analyzed via Pontryagin’s Maximum Principle, and solved using forward–backward sweep methods. The results indicate that the combined strategy—integrating all three controls—is the most effective, leading to the elimination of both symptomatic and asymptomatic malaria cases.