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Table 2 Syphilis model parameters notation and values

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

Parameters Description Values Source
\(\pi _{m}\) Recruitment rate into susceptible male population 0.3 [29]
\(\pi _{f}\) Recruitment rate into susceptible female population 0.45 [29]
\(\alpha _{f}\) Transmission probability of female with syphilis infection 0.2 [15]
\(\alpha _{m}\) Transmission probability of male with syphilis infection 0.5 [15]
\(\gamma _{m}\) Progression rate from male with primary syphilis to male with secondary syphilis infection 0.01 [15]
\(\gamma _{f}\) Progression rate from female with primary syphilis 0.627 [15]
ψ Average number of sexual partner per unit time to female with secondary syphilis infection 2 [19]
\(\beta _{m}\) Progression rate from male with secondary syphilis to male with latent syphilis infection 0.618 [15]
\(\beta _{f}\) Progression rate from female with secondary syphilis to female individual with latent syphilis infection 0.618 [15]
\(\varphi _{m}\) Rate of recovery from syphilis in infectious male 0.1 [29]
\(\varphi _{f}\) Rate of recovery from syphilis in infectious female 0.1 [29]
\(\sigma _{m_{1}}\) Treatment rate of male with primary stage syphilis 0.05 [29]
\(\sigma _{m_{2}}\) Treatment rate of male with secondary stage syphilis 0.1 [29]
\(\sigma _{m_{3}}\) Treatment rate of male with latent stage syphilis 0.2 [29]
\(\rho _{f_{1}}\) Treatment rate of female with primary stage syphilis 0.05 [29]
\(\rho _{f_{2}}\) Treatment rate of female with secondary stage syphilis 0.1 [29]
\(\rho _{f_{3}}\) Treatment rate of female with latent stage syphilis 0.2 [29]
μ Rate of natural death 5.48 × 10−5day−1 [42]
\(A_{1}\) Weight coefficients for both infectious male and female syphilis 31 [38]
\(B_{1}\) Relative cost for prevention and treatment in male and female individuals 0.5 [38]
\(B_{2}\) Relative cost for prevention and treatment in male and female individuals 0.4 Assumed
\(B_{3}\) Relative cost for prevention and treatment in male and female individuals 0.3 Assumed