Age-Structured Malaria Model: Modeling, Analysis, and Control With Temperature–Humidity Effects

We develop an age-structured malaria transmission model coupling human demographic structure with temperature- and humidity-dependent mosquito life-history parameters across all aquatic and adult vector stages, calibrated from field data collected at TIDRC, Jimma University, Ethiopia. Well-posedness of the resulting system, which involves a dynamic rather than demographically fixed total human population, is established via integrated semigroup theory on a nondensely defined operator domain. The next-generation operator yields R0T,H in closed form as an explicit function of both climate variables, peaking at T≈25.9°C, H≈63.5%R0=7.308 and exceeding unity for T∈22,31°C regardless of humidity. Bifurcation analysis of the age-structured PDE system produces exact closed-form bifurcation coefficients C1 and C2; backward bifurcation, with its associated bistability and elimination threshold below unity, requires disease-induced mortality to substantially exceed natural human mortality. Sensitivity analysis identifies mosquito egg deposition and adult mortality as the dominant drivers of R0. An optimal control problem with five intervention strategies is analyzed via the Pontryagin maximum principle; simulated interventions show indoor residual spraying can achieve elimination alone at moderate coverage, while insecticide-treated nets are the most cost-effective single measure. These results clarify how climate and vector demography jointly shape malaria risk and provide a rigorous mathematical foundation for age-targeted control prioritization.