Analysis of a Malaria Transmission Model with Vaccination Proportion and Vaccine-Induced Immunity

Abstract

This study presents a mathematical model to describe the transmission dynamics of malaria in a highly endemic region, with a focus on vaccination and vaccine-induced immunity as primary control measures. By determining the basic reproduction number (R0), we evaluate the impact of these interventions on malaria-free and malaria-persistent equilibria. Our analysis shows that the malaria-free equilibrium is locally asymptotically stable when R01 and unstable otherwise. Numerical simulations demonstrate that increasing vaccination coverage and improving vaccine-induced immunity significantly reduce R0. A sensitivity analysis using partial rank correlation coefficients highlights the influence of key parameters, such as the mosquito-to-human transmission rate and mosquito birth and death rates, on malaria transmission. These findings underscore the potential of integrated strategies, combining vaccination with other interventions, to manage malaria effectively in highly endemic regions.

Keywords

• malaria
• transmission
• basic reproduction number
• stability
• vaccine