\(\lambda _{M}^{\alpha }\)

The recruitment rate of mosquitoes (assumed susceptible)

\(\mu _{M}^{\alpha }\)

The natural death rate of mosquitoes

\(\lambda _{B}^{\alpha }\)

The recruitment rate of birds (assumed susceptible)

\(\mu _{B}^{\alpha }\)

The natural death rate of birds

\(\varPsi _{B}^{\alpha }\)

The migration rate of birds

\(d_{B}^{\alpha }\)

The WNVinduced death rate of birds

\(\lambda _{H}^{\alpha }\)

The recruitment rate of humans (assumed susceptible)

\(\mu _{H}^{\alpha }\)

The natural death rate of humans

\(d_{I}^{\alpha }\)

The WNVinduced death rate of humans

\(d_{H}^{\alpha }\)

The death rate of hospitalized humans

\(\beta _{1}^{\alpha }\)

The probability of WNV transmission from an infected bird to a susceptible mosquito

\(\beta _{2}^{\alpha }\)

The probability of WNV transmission from an infected mosquito to a susceptible bird

\(\beta _{3}^{\alpha }\)

The probability of WNV transmission from mosquitoes to humans

\(b_{1}^{\alpha }\)

The per capita bitting rate of mosquitoes on the primary host (birds) and \(b_{1}^{\alpha }=\frac{b^{\alpha }N_{B}}{N_{B}+N_{H}}\)

\(b_{2}^{\alpha }\)

The per capita bitting rate of mosquitoes on the humans and \(b_{2}^{\alpha }=\frac{b^{\alpha }N_{H}}{N_{B}+N_{H}}\)

\(b^{\alpha }\)

The average bitting rate of mosquitoes

\(\alpha _{\omega }^{\alpha }\)

The rate of development of clinical symptoms of WNV

\(r^{\alpha }\)

The natural recovery rate

\(\tau ^{\alpha }\)

The treatmentinduced recovery rate

\(\gamma ^{\alpha }\)

The hospitalized rate of infectious humans
