Modeling Malaria Transmission and Control: An SIR–SI Framework with Three Optimal Intervention Strategies

Mojeeb AL-Rahman EL-Nor Osman; Mohammed Salaheldeen Abdelgader

Mojeeb AL-Rahman EL-Nor Osman Department of Mathematics and Computer Science, Faculty of Pure and Applied Sciences, International University of Africa, P.O. Box 2469, Khartoum, Sudan. College of Commerce and Business, Lusail University, Lusail, Qatar.
Mohammed Salaheldeen Abdelgader Department of Mathematics, Faculty of Mathematical and Computer Sciences, University of Gezira, Wad Madani, Sudan. Department of Mathematical Sciences, Collage of Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE.

Abstract

In this study, we developed and analyzed an SIR–SI malaria transmission model that accounted for partial immunity and re-infection within recovered human population. The basic reproduction number, R₀, was obtained via the next-generation matrix approach, and the local as well as global stability of the disease-free equilibrium (DFE) were investigated. Both analytical and numerical analyses demonstrated the occurrence of a backward bifurcation, whereby a stable DFE could coexist with a stable endemic equilibrium under certain parameter conditions. Numerical simulations validated the theoretical results and further examined the effects of three time-dependent optimal control strategies: bed-net usage u₁(t), antimalarial treatment u₂(t), and insecticide spraying u₃(t). Sensitivity analysis identified the human-to-mosquito transmission rate as a critical parameter influencing R₀. Model parameters describing mosquito biting behavior, natural mortality, and transmission rates were taken from published entomological and demographic sources, while the immunity-loss rate, recovery rate, and re-infection probability were estimated by fitting the model to WHO-reported cumulative malaria case data for the Democratic Republic of Congo, so the model was calibrated to regional epidemiological data rather than purely hypothetical. Simulation outcomes indicate that the integrated application of all three interventions yields the most significant and sustained reductions in human and mosquito infection prevalence, with the potential for disease eradication within a few years. These findings underscore the necessity of coordinated, multi-faceted intervention strategies for effective malaria control in high-burden regions, such as the Democratic Republic of Congo.

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