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 |