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

TL;DR

This paper develops an age-dependent mathematical model for dengue transmission using PDEs, analyzes its equilibria, and validates it with field data from Semarang, Indonesia.

Contribution

It introduces an age-dependent PDE model for dengue, extending classical models, and provides analytical and numerical methods for equilibrium analysis and validation.

Findings

Model captures age dependence in dengue transmission.

Existence of disease-free and endemic equilibria proven.

Model aligns with field data from Semarang.

Abstract

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.