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Table 3 Sensitivity indices of \(\mathcal {R}_{0}\) to parameters for the lymphatic filariasis model, evaluated at the parameter values given in Table 2

From: Mathematical analysis of a lymphatic filariasis model with quarantine and treatment

\(\mathcal {R}_{0}\)
Parameter \(\Upsilon _{p}^{\psi }\) Sensitivity index
Λ h \(-\frac {1}{2}\) -0.5
μ v \(\frac {1}{2} \left (\frac {\alpha _{v}}{\alpha _{v}+\mu _{v}}-3\right)\) -1.36013
Λ v \(\frac {1}{2}\) 0.5
κ \(\frac {1}{2} \kappa \left (\frac {\theta }{\theta \kappa +\mu _{h}}-\frac {1}{\mu _{h}+\kappa +n \varphi }\right)\) 0.462806
β 1 1
φ \(-\frac {n \varphi }{2 \left (\mu _{h}+\kappa +n \varphi \right)}\) -0.466545
n \(-\frac {n \varphi }{2 \left (\mu _{h}+\kappa +n \varphi \right)}\) -0.466545
𝜗 h \(\frac {1}{2}\) 0.5
𝜗 v \(\frac {1}{2}\) 0.5
α h \(\frac {\mu _{h}}{2 \left (\alpha _{h}+\mu _{h}\right)}\) 0.0000819193
α v \(\frac {\mu _{v}}{2 \left (\alpha _{v}+\mu _{v}\right)}\) 0.360131
θ \(\frac {\theta \kappa }{2 \theta \kappa +2 \mu _{h}}\) 0.49613
  1. The parameters are ordered from most to least sensitive for each \(\mathcal {R}_{0}\)