Mathematical modelling and optimal control of malaria transmission with antimalarial drug and insecticide resistance

This study presents a mathematical model to explore malaria transmission dynamics in the presence of antimalarial drug-resistant parasites and insecticide-resistant mosquitoes. The analytical findings demonstrate a stable disease-free equilibrium when the effective reproduction number is below one. For single-strain malaria infections, the endemic equilibrium may exhibit one, two or no solutions. The model is extended to incorporate three time-dependent controls: long-lasting insecticidal nets, antimalarial treatment and mosquito adulticides. Simulation results indicate that interventions excluding drug-resistant parasites and insecticide-resistant mosquitoes are ineffective. The most effective strategies combine insecticides targeting all vectors with treatments for all malaria cases, regardless of resistance. Efficiency analysis suggests implementing all three controls at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>≥</mml:mo><mml:mn>80</mml:mn><mml:mi>%</mml:mi></mml:math> efficacy for the maximum impact, while assessments of cost-effectiveness highlight the combination of long-lasting insecticidal nets and antimalarial treatment as a practical option in resource-constrained settings. Nonetheless, integrating all three measures is recommended for substantial malaria transmission reduction.