A Mosquito-Borne Disease Model with Non-exponentially Distributed Infection and Treatment Stages

Abstract

Most epidemiological models for mosquito-borne disease assume exponentially distributed residence times in disease stages in order to simplify the model formulation and analysis. However, these models do not allow for accurate description of the interaction between drug concentration and pathogen load within hosts. To improve this, we formulate a model by considering arbitrarily distributed sojourn for various disease stages. The model formulation is presented using two proven equivalent approaches: integral equations and partial differential equations. Analysis of the model includes the existence of equilibrium solutions and stability, which are shown to be dependent on whether the control reproduction number {mathcal {R}}_c is less or greater than 1. It is also shown that, when the general distributions are replaced by gamma distributions, the system of integral equations can be reduced to a system of ODEs, which has some non-trivial characteristics which are only captured by non-exponential distributions for disease stages.