Structured Population Models for Vector-Borne Infection Dynamics

Abstract

Dynamical systems provide an appropriate framework to examine whether, where and when a vector species and/or a vector-borne pathogen can establish and spread. Such systems often contain time lags to reflect the transition times from one physiological stage to the next, or from one geographic location to others. We present a brief introduction to dynamical systems generated by delay differential equations with varying delay. We focus on those delay differential equations which are reduced from structured population partial differential equation models, and we discuss the implicit assumption that needs to be made to permit this reduction process. We demonstrate the model formulation from tick population and tick-borne disease infection dynamics, and from bird migration and avian influenza spread dynamics. We show how model parameters, especially time-varying development delays, can be informed from laboratory experiments, field studies and surveillance data, and how these parameters are integrated to a single threshold parameter, the basic reproduction number, to quantify when population establishment and disease persistence are likely.