Vector-borne diseases and the basic reproduction number: A case study of African horse sickness

The basic reproduction number, R(0), can be used to determine factors important in the ability of a disease to invade or persist. We show how this number can be derived or estimated for vector-borne diseases with different complicating factors. African horse sickness is a viral disease transmitted mainly by the midge Culicoides imicola. We use this as an example of such a vector-transmitted disease where latent periods, seasonality in vector populations, and multiple host types may be important. The effect of vector population dynamics which are dependent on either host or vector density are also addressed. If density-dependent constraints on vector population density are less severe, R(0) is more sensitive to vector mortality and the virus development rate. Host-dependent vector dynamics change the relationship between R(0) and host population size. Seasonality can either increase or decrease the estimate of R(0), depending on the lag between the peak of the midge population and the infective host population. The relative abundance of two host types is a factor in the ability of a disease to invade, but the strength of this factor depends on the differences between the hosts in recovery from infection, mortality and transmission. Removal of a reservoir host may increase R(0).