Abstract:
The paper presents the basic model for the transmission dynamics of West Nile
virus (WNV). The model, which consists of seven mutually-exclusive compartments
representing the birds and vector dynamics, has a locally-asymptotically
stable disease-free equilibrium whenever the associated reproduction number
(R0) is less than unity. As reveal in [3, 20], the analyses of the model show the
existence of the phenomenon of backward bifurcation (where the stable diseasefree
equilibrium of the model co-exists with a stable endemic equilibrium when
the reproduction number of the disease is less than unity). It is shown, that the
backward bifurcation phenomenon can be removed by substituting the associated
standard incidence function with a mass action incidence. Analysis of the
reproduction number of the model shows that, the disease will persist, whenever
R0 > 1, and increase in the length of incubation period can help reduce
WNV burden in the community if a certain threshold quantities, denoted by
Δb and Δv are negative. On the other hand, increasing the length of the incubation
period increases disease burden if Δb > 0 and Δv > 0. Furthermore, it
is shown that adding time delay to the corresponding autonomous model with
standard incidence (considered in [2]) does not alter the qualitative dynamics
of the autonomous system (with respect to the elimination or persistence of the
disease).
