Mathematical Modelling of Syphilis Transmission Dynamics: Impacts of Mass Media Report, Risky Sexual Behavior and Treatment

Abstract Syphilis is one of the deadly sexually-transmitted diseases. This paper studied the impacts of sexual behavior, mass media report and treatment of infected individuals on the dynamics of syphilis transmission. The analytical and numerical analyses of the model are presented. The disease free equilibrium of the model is both locally and globally asymptotic stable when the associated reproduction number is less than unity.  Analysis of the Reproduction number shows that it is not possible to control syphilis disease transmission if the rate of individuals practicing risky sexual behavior is high. Furthermore, the treatment of late (latent and tertiary) syphilis infection is beneficial to the infected individuals, but has no impact in the lowering of the reproduction number. This study suggests that the effective control strategy of syphilis must focus on lowering the number of individuals practicing risky sexual behavior and applying higher treatment rates for early syphilis infections. Furthermore, the media function should address the issues regarding safe sexual behavior. Keywords: Syphilis, sexually transmitted infection, Risky sexual behavior, Mass medi

Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection

In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls