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Theory and Modern Applications

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