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Medical statistics reveal a significant dependence of hospitalized denguepatient on the patient's age. To incorporate an age-dependence into amathematical model, we extend the classical ODE system of disease dynamics to aPDE system. The equilibrium distribution is then determined by the fixed pointsof resulting integro-differential equations. In this paper we use an extensionof the concept of the basic reproductive number to characterize parameterregimes, where either only the disease-free or an endemic equilibrium exists.Using rather general and minimal assumptions on the population distribution andon the age-dependent transmission rate, we prove the existence of thoseequilibria. Furthermore, we are able to prove the convergence of an iterationscheme to compute the endemic equilibrium. To validate our model, we useexisting data from the city of Semarang, Indonesia for comparison and toidentify the model parameters.

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