A Double Age-Structured Model for Within-Host Malaria Dynamics: Coupling RBC Lifespan and Infection Age

Malaria is one of the most prevalent diseases spread by mosquitoes in tropical and subtropical areas. In this study, we present an age-structured mathematical model for the within-host dynamics of Plasmodium falciparum malaria, employing a dual age-structured partial differential equation (PDE) incorporating chronological age, a for uninfected red blood cells (RBCs) and infected RBCs by their infection age, s . We provide a thorough mathematical analysis, such as well-posedness, equilibrium points, basic reproduction number R0, and critical delay. The disease-free equilibrium (DFE) is locally asymptotically stable for any delay τ≥0 whenever R0 1, the DFE loses stability. Furthermore, the system entered a Hopf interval as τ passed through its critical value τc, leading to oscillations and limit cycles around the endemic equilibrium point (EEP). Moreover, we conducted an uncertainty and sensitivity analysis using Monte Carlo methods and Sobol sensitivity analysis, and we found that high uncertainty in R0, given the current knowledge of parameter values, indicates high heterogeneity. Even with the substantial uncertainty reflected in the wide 95% CI, only about 15.7% of simulations produced R0