Theory and Modern Applications
Table 2 All parameters in system (6) and their interpretation
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 |