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Table 3 Sensitivity indices of syphilis model \(\mathcal{R}_{0}\)

From: Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Parameter Description Sensitivity Index
\(\pi _{m}\) Recruitment rate into susceptible male population 1
\(\pi _{f}\) Recruitment rate into susceptible female population 1
\(\alpha _{f}\) Transmission probability of females with syphilis infection 0.5
\(\alpha _{m}\) Transmission probability of males with syphilis infection 0.5
\(\gamma _{m}\) Progression rate from male with primary syphilis to male with secondary syphilis infection 0.042548
\(\gamma _{f}\) Progression rate from female with primary syphilis 0.37906
ψ Average number of sexual partner per unit time to female with secondary syphilis infection 1
\(\beta _{m}\) Progression rate from male with secondary syphilis to male with latent syphilis infection −0.39089
\(\beta _{f}\) Progression rate from female with secondary syphilis to female individual with latent syphilis infection −0.0000013015
\(\sigma _{m_{1}}\) Treatment rate of males with primary stage syphilis −0.45322
\(\sigma _{m_{2}}\) Treatment rate of males secondary stage syphilis −0.0027407
\(\rho _{f_{1}}\) Treatment rate females with primary stage syphilis −0.25536
\(\rho _{f_{2}}\) Treatment rate of females with secondary stage syphilis −0.044735