Theory and Modern Applications
Table 2 Syphilis model parameters notation and values
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 |