Mathematical Analysis of Plasmodium Falciparum Malaria Transmission Dynamics with Assessment the Effectiveness of Drug and Insecticide Resistance

Abstract

This study presents a deterministic compartmental model to investigate Plasmodium falciparum malaria transmission dynamics under the combined effects of drug and insecticide resistance, explicitly incorporating asymptomatic infections to better capture silent transmission pathways. The population is divided into five classes: susceptible (S), exposed (E), asymptomatic (I₁), symptomatic (I₂), and recovered (R), alongside vector two classes, susceptible (U) and infectious (W). The model is proven to be mathematically and biologically well-posed, the basic reproduction number (R₀) is derived via the next-generation matrix method (NGM), and a sensitivity analysis is conducted to identify the parameters that significantly influence transmission. Numerical simulations demonstrate that escalating resistance drastically intensifies disease propagation, whereas integrated multi-pronged interventions successfully suppress transmission and ensure disease containment.