An Age-Structured Mathematical Model of Malaria Transmission Dynamics With Imperfect Vaccination in the Context of Partial Differential Equations

Malaria remains one of the leading causes of morbidity and mortality worldwide, particularly in tropical and subtropical regions. In 2024 alone, the WHO African Region reported approximately 265 million cases and 579,000 deaths. To address this persistent public health challenge, we developed a novel age-structured mathematical model for malaria transmission, formulated using partial differential equations that explicitly incorporate the effects of imperfect vaccination. We first established the existence and uniqueness of the model solutions and demonstrated that they remain non-negative and bounded, thereby confirming the model’s mathematical and epidemiological well-posedness. The basic reproduction number was derived using the next-generation matrix approach. Employing a Lyapunov functional method, we proved that when R0 1, the endemic equilibrium is globally asymptotically stable, signifying disease persistence within the population. Sensitivity analysis revealed that increases in the transmission rate and waning rate of vaccine-induced immunity lead to an increase in R0, while higher disease-induced mortality, vaccination, and recovery rates reduce R0. A key contribution of this study lies in the calibration of the model using empirical data from the Ilu Ababor Zone Health Office in Oromia, Ethiopia, which significantly improves the estimation of critical transmission parameters. Finally, numerical simulations were conducted to illustrate and validate the main theoretical results.