Spatiotemporal Patterns of Disease Spread: Interaction of Physiological Structure, Spatial Movements, Disease Progression and Human Intervention

Abstract

In this article we review some recent literature on the mathematical modelling of vector-borne diseases with special reference to West Nile virus and with particular focus on the role of the developmental stages of hosts in determining the transmission dynamics, the effectiveness of different approaches to controlling the vector and the spatial spread of an epidemic. A possible model incorporating the developmental stages of avian hosts is discussed which consists of equations for infective and susceptible juvenile and adult hosts and infected adult vectors. Conditions for the system to evolve to the disease free state are presented. These elucidate the role of, for example, the various death rates involved. We also review a mathematical model which incorporates culling the vector at either the larval or the adult stage and the effectiveness of the two approaches is compared. Conditions are given that are sufficient for eradication and this leads insights into the required minimum frequency of culling. Very infrequent culling is no better than no culling at all and can actually increase the time average of the number of infected vectors. We also review a reaction-diffusion extension of the model which can be used to estimate the speed at which an epidemic moves through space. Finally, we review some recent work on the use of patch models of a West Nile virus epidemic. These models are arguably easier to relate to surveillance data which is organised according to administrative regions or landscape. The patch model is used to study the situation when the dispersal of birds is not symmetric.