Schematic flowchart of the model. The boxes (compartments) depict the variables: X = uninfected vector eggs, Y = infected vector eggs, Sv = susceptible vectors, Lv = vectors in the extrinsic incubation period, Iv = infectious vectors, Sh = susceptible hosts, Lh = latently infected hosts, Ih = infectious hosts, R = recovered and immune hosts. The solid-line arrows depict the flow out of and into compartments. Dashed line depict the influence of infectious vectors and infectious hosts on the flow from susceptible to latent infection and extrinsic incubation period. Next to the arrows are the parameters determining that flow or influence: h(t) = hatching rate at time t, b(t) = biting rate at time t, c = egg batch size, ζ = per egg vertical transmission probability, ϕv = transition rate of vector from extrinsic incubation period to infectious state, μv = mortality rate of vector, Λv = per bite transmission from one infected individual of host to a susceptible vector, Λh = the host specific per bite transmission from a vector to a host, ϕh = transition rate of host from the latent state to the infectious state, γ = recovery rate of host.