A Mathematical Analysis of the Impact of Immature Mosquitoes on the Transmission Dynamics of Malaria

Abstract

This study delves into the often-overlooked impact of immature mosquitoes on the dynamics of malaria transmission. By employing a mathematical model, we explore how these aquatic stages of the vector shape the spread of the disease. Our analytical findings are corroborated through numerical simulations conducted using the Runge–Kutta fourth-order method in MATLAB. Our research highlights a critical factor in malaria epidemiology: the basic reproduction number $$. We demonstrate that when $$ is below unity $$, the disease-free equilibrium exhibits local asymptotic stability. Conversely, when $$ surpasses unity $$, the disease-free equilibrium becomes unstable, potentially resulting in sustained malaria transmission. Furthermore, our analysis covers equilibrium points, stability assessments, bifurcation phenomena, and sensitivity analyses. These insights shed light on essential aspects of malaria control strategies, offering valuable guidance for effective intervention measures.