A Mathematical Model Of Syphilis Transmission In An Msm Population

Keywords

34D23; 92D30; Disease control; Global stability; Reproduction number; Sensitivity; Syphilis

Abstract

Syphilis is caused by the bacterium Treponema pallidum subspecies pallidum, and is a sexually transmitted disease with multiple stages. A model of transmission of syphilis in an MSM population (there has recently been a resurgence of syphilis in such populations) that includes infection stages and treatment is formulated as a system of ordinary differential equations. The control reproduction number is calculated, and it is proved that if this threshold parameter is below one, syphilis dies out; otherwise, if it is greater than one, it is shown that there exists a unique endemic equilibrium and that for certain special cases, this equilibrium is globally asymptotically stable. Using data from the literature on MSM populations, numerical methods are used to determine the variation and robustness of the control reproduction number with respect to the model parameters, and to determine adequate treatment rates for syphilis eradication. By assuming a closed population and no return to susceptibility, an epidemic model is obtained. Final outbreak sizes are numerically determined for various parameter values, and its variation and robustness to parameter value changes is also investigated. Results quantify the importance of early treatment for syphilis control.

Publication Date

7-1-2016

Publication Title

Mathematical Biosciences

Volume

277

Number of Pages

59-70

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.mbs.2016.03.017

Socpus ID

84964895320 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84964895320

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