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Table 6 Sensitivity indices for chronic productive virus population \(\pmb{V_{2}^{*}}\)

From: Andronov-Hopf bifurcation and sensitivity analysis of a time-delay HIV model with logistic growth and antiretroviral treatment

Parameter Index
\(T_{\mathrm{max}}\) \(\frac{R_{0} SI(T_{1}^{*}|T_{\mathrm{max}})}{R_{0}-1}-\frac{\Lambda T_{\mathrm{max}}SI(T_{1}^{*}|T_{\mathrm{max}})+rT_{1}^{*}T_{2}^{*}}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
Λ \(\frac{R_{0} SI(T_{1}^{*}|\Lambda)}{R_{0}-1}+\frac{\Lambda T_{\mathrm{max}}(1-SI(T_{1}^{*}|\Lambda))}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
r \(\frac{R_{0} SI(T_{1}^{*}|r)}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}-\Lambda T_{\mathrm{max}}SI(T_{1}^{*}|r)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
\(d_{T}\) \(\frac{R_{0} SI(T_{1}^{*}|d_{T})}{R_{0}-1}-\frac{\Lambda T_{\mathrm{max}}SI(T_{1}^{*}|d_{T})}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
\(d_{L}\) \(-\frac{R_{0} SI(T_{2}^{*}|d_{L})}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|d_{L})}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
a \(-\frac{R_{0} SI(T_{2}^{*}|a)}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|a)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
c \(-\frac{R_{0} SI(T_{2}^{*}|c)}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|c)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
k \(- \frac{R_{0} SI(T_{2}^{*}|k)}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|k)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}-1\)
N \(-\frac{R_{0} SI(T_{2}^{*}|N)}{R_{0}-1} +\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|N)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
\(n_{rt}\) \(-\frac{R_{0} SI(T_{2}^{*}|n_{rt})}{R_{0}-1} +\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|n_{rt})}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}+\frac{n_{rt}}{1-n_{rt}}\)
\(n_{p}\) \(-\frac{R_{0} SI(T_{2}^{*}|n_{p})}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|n_{p})}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)
η \(-\frac{R_{0} SI(T_{2}^{*}|\eta)}{R_{0}-1}+\frac{r T_{1}^{*} T_{2}^{*}SI(T_{2}^{*}|\eta)}{\Lambda T_{\mathrm{max}}+rT_{1}^{*}T_{2}^{*}}\)