Modelling vertical transmission in vector-borne diseases with applications to Rift Valley fever.

We present two ordinary differential equation models for Rift Valley fever (RVF) transmission in cattle and mosquitoes. We extend existing models for vector-borne diseases to include an asymptomatic host class and vertical transmission in vectors. We define the basic reproductive number, ℛ(0), and analyse the existence and stability of equilibrium points. We compute sensitivity indices of ℛ(0) and a reactivity index (that measures epidemicity) to parameters for baseline wet and dry season values. ℛ(0) is most sensitive to the mosquito biting and death rates. The reactivity index is most sensitive to the mosquito biting rate and the infectivity of hosts to vectors. Numerical simulations show that even with low equilibrium prevalence, increases in mosquito densities through higher rainfall, in the presence of vertical transmission, can result in large epidemics. This suggests that vertical transmission is an important factor in the size and persistence of RVF epidemics.