  Medical statistics reveal a significant dependence of hospitalized dengue
patient on the patient's age. To incorporate an age-dependence into a
mathematical model, we extend the classical ODE system of disease dynamics to a
PDE system. The equilibrium distribution is then determined by the fixed points
of resulting integro-differential equations. In this paper we use an extension
of the concept of the basic reproductive number to characterize parameter
regimes, where either only the disease-free or an endemic equilibrium exists.
Using rather general and minimal assumptions on the population distribution and
on the age-dependent transmission rate, we prove the existence of those
equilibria. Furthermore, we are able to prove the convergence of an iteration
scheme to compute the endemic equilibrium. To validate our model, we use
existing data from the city of Semarang, Indonesia for comparison and to
identify the model parameters.
