MATHEMATICALMODELINGOFMALARIATRANSMISSIONAND TREATMENT:ACASEOFCONFLICTZONES

Abstract

Malaria continues to be among the most pressing public health challenges globally, disproportionately affecting vulnerable populations in tropical and subtropical regions. The infection is spread through the bites of female Anopheles mosquitoes carrying the parasite, with high-risk groups including people with compromised immune systems and travelers to endemic areas. Despite extensive control efforts and the formulation of mathematical models that integrate essential biological and pharmacological components such as human immunity level, vector behavior treatment coverage and drug resistance, significant gaps persisted in understanding malaria transmission and treatment dynamics, particularly in conflict-affected zones. The study develops a mathematical model for malaria transmission and treatment in conflict zones capturing interventions such as full treatment and partial treatment. The model utilizes a system of ordinary differential equations (ODEs) to describe the progression describing malaria transmission and treatment over time, capturing transitions across different human and mosquito compartments. The positivity of solutions was established to ensure biological feasibility. The existence of a Disease-Free Equilibrium (DFE) was determined and found that no infection exist in human population. Stability analysis was conducted to assess the conditions under which malaria can be eliminated, while sensitivity analysis identified key parameters that significantly influenced transmission and treatment outcomes. Numerical simulations were performed using Mathematica and python software to validate the analytical results and examine the effects of control measures under varying conditions. The findings provided insights into the effectiveness of treatment strategies and interventions aimed at reducing malaria transmission and mortality in conflict zones. The study also offered evidence-based recommendations applicable to similar health constrained environments.