Modelling the dynamics of bluetongue disease and the effect of seasonality

We present mathematical models for the midge-borne disease bluetongue, with cattle and sheep as hosts. The models take the form of delay differential equations and incorporate the incubation time of bluetongue in cattle, sheep and midges, and also the larval developmental time of midges. Recovery in cattle and sheep is also included. Both an autonomous and a periodic model are considered, to take account of seasonality. For both models we present conditions for the disease-free state to be linearly stable, and a detailed interpretation of those conditions. The results of simulations are also presented. Important findings include the need for prompt diagnosis of latent infection and appropriate action before the animal turns infectious, and the need for measures that reduce insect bites.