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Table 2 Variables and parameters in the R0 equation, following [44]

From: Evaluating the risk for Usutu virus circulation in Europe: comparison of environmental niche models and epidemiological models

Parameter Value
Mosquitoes
 Mortality rate \(m_{M}\) \(m_{M} \left( T \right) = 0.00025T^{2} - 0.0094T + 0.10257\)
\(T\): daily mean temperature
 Biting rate \(\kappa\) \(\kappa \left( T \right) = \frac{0.344}{{1 + 1.231{ \exp }\left( { - 0.184\left( {T - 20} \right)} \right)}}\)
 Product of biting rate (\(\kappa\)) and transmission possibility from mosquitoes to birds (\(P_{M}\)) \(\beta_{M}\) \(\beta_{M} \left( T \right) = P_{M} \kappa \left( T \right)\)
\(P_{M}\) = 1
 Percentage of non-hibernating mosquitoes \(\delta_{M}\) \(\delta_{M} = 1 - \frac{1}{{1 + 1775.7{ \exp }\left[ {1.559\left( {D - 18.177} \right)} \right]}}\)
\(D = 7.639arcsin\left[ {{ \tan }\left( \epsilon \right){ \tan }\left( \varphi \right) + \frac{0.0146}{{{ \cos }\left( \epsilon \right){ \cos }\left( \varphi \right)}}} \right] + 12\)
\(\epsilon = 0.409sin\left( {\frac{{2\pi \left( {d - 80} \right)}}{365}} \right)\)
\(D\): daytime length,\(\epsilon\): declination, \(\varphi\): geographic latitude
 Exposed—infected/infectious rate \(\gamma_{M}\) \(\gamma_{M} \left( T \right) = 0.0093T - 0.1352\), \(T \ge 15^{^\circ }\)
\(\gamma_{M} \left( T \right) = 0\), \(T < 15^{^\circ }\)
 Susceptible mosquito population \(S_{M}\) Dynamic value, see Additional file 3
Birds
 Mortality rate \(m_{B}\) 0.0012
 Removal rate: fraction of infected birds either recovering or dying \(\alpha_{B}\) 0.182
 Exposed—infected/infectious rate \(\gamma_{B}\) 0.667
 Product of biting rate (\(\kappa\)) and transmission possibility from birds to mosquitoes (\(P_{B}\)) \(\beta_{B}\) \(\beta_{B} \left( T \right) = P_{B} \kappa \left( T \right)\)
\(P_{B}\) = \(0.125\)
 Susceptible black bird population \(S_{B}\) Dynamic value, see Additional file 3
 Environmental capacity \(K_{B}\) see Additional file 3