An age-dependent model for dengue transmission: Analysis and comparison to field data

Abstract Medical statistics reveal a significant dependence of hospitalized dengue patients on their age. We extend an ODE system governing dengue epidemics to a hyperbolic PDE system to incorporate age dependence. The equilibrium distributions are determined by the fixed points of the resulting integro-differential equation. The basic reproductive number is then characterized to define parameter regimes, where either only the disease-free or an endemic equilibrium exists. Using rather general and minimal assumptions on the population distribution and age-dependent transmission rate, we prove the existence of those equilibria. Furthermore, the convergence of an iteration scheme to either of the two equilibria in relation to the basic reproductive number is analytically shown. We then validate our model via parameter estimation using existing data from the city of Semarang, Indonesia.