  Malaria is one of the deadliest infectious diseases globally, causing
hundreds of thousands of deaths each year. It disproportionately affects young
children, with two-thirds of fatalities occurring in under-fives. Individuals
acquire protection from disease through repeated exposure, and this immunity
plays a crucial role in the dynamics of malaria spread. We develop a novel
age-structured PDE malaria model, which couples vector-host epidemiological
dynamics with immunity dynamics. Our model tracks the acquisition and loss of
anti-disease immunity during transmission and its corresponding nonlinear
feedback onto the transmission parameters. We derive the basic reproduction
number ($\mathcal{R}_0$) as the threshold condition for the stability of
disease-free equilibrium; we also interpret $\mathcal{R}_0$ probabilistically
as a weighted sum of cases generated by infected individuals at different
infectious stages and different ages. We parametrize our model using
demographic and immunological data from sub-Saharan regions. Numerical
bifurcation analysis demonstrates the existence of an endemic equilibrium, and
we observe a forward bifurcation in $\mathcal{R}_0$. Our numerical simulations
reproduce the heterogeneity in the age distributions of immunity profiles and
infection status created by frequent exposure. Motivated by the recently
approved RTS,S vaccine, we also study the impact of vaccination; our results
show a reduction in severe disease among young children but a small increase in
severe malaria among older children due to lower acquired immunity from delayed
exposure.
