Mathematical modelling of malaria: Population-scale dynamics, vaccination, and evolution

Malaria transmission and persistence depend critically on the interaction between parasite dynamics, human immunity, and epidemiological feedbacks. I will review recent work with collaborators developing and analysing structured PDE models spanning both population and within-host scales. At the population level, we couple vector–host epidemiology with the acquisition and loss of anti-disease immunity. Bifurcation analysis reveals the changing structure of endemic equilibria as transmission intensity rises, and our exploration of vaccination strategies, motivated by the RTS,S vaccine, highlights how seasonal transmission profiles may impact interventions. We also investigate multiple potential causes of backward bifurcation in this model. At the within-host level, we examine how parasites allocate resources between proliferation and transmission stages under immune pressure. Using an age‑of‑infection–structured model, we characterize immune-driven clearance thresholds and analyse parasite investment strategies, contrasting constant versus time-varying allocation rules. Our results indicate that adaptive immunity can impose a survival-reproduction tradeoff that explains why malaria parasites cannot evolve ever faster within-host multiplication. Together, these studies illustrate how immunity and feedbacks across scales shape malaria outcomes and inform intervention strategies.