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Table 2 All parameters in system (6) and their interpretation

From: Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

Parameter Interpretation
\(\lambda _{M}^{\alpha }\) 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 WNV-induced 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 WNV-induced 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 treatment-induced recovery rate
\(\gamma ^{\alpha }\) The hospitalized rate of infectious humans