An Age-Dependent Model for Dengue Transmission: Analysis and Comparison to Field Data from Semarang, Indonesia

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.