Mathematical Modeling and Analysis of the Vertical and Horizontal Transmission Dynamics of Syphilis with Treatment Intervention

Abstract

We developed in this study a mathematical model of the transmission dynamics of Syphilis, which takes into account both vertical and horizontal transmission and the effect of treatment as a control measure. The basic reproduction number   was calculated to represent the persistence and eradication conditions of the disease. The results of the analysis show that the disease free equilibrium is locally asymptotically stable for  , globally stable for  and that a stable endemic equilibrium is established for . The parameters whose values had a positive sensitivity index increased the transmission of Syphilis, such as contact and transmission rate, while the parameters whose values had a negative sensitivity index reduced the transmission of Syphilis, such as the treatment rate, etc. Numerical simulations also revealed that if the treatment rate is increased, the burden of Syphilis to the population is greatly reduced. This highlights the importance of treatment interventions in interrupting and maybe stopping the spread of Syphilis in human populations.