Mathematical Modeling of the Transmission Dynamics of Syphilis Disease Using Differential Transformation Method

Mbachu Hope Ifeyinwa

doi:10.11648/j.mma.20200502.11

Abstract

In this work, we developed a mathematical model for the transmission dynamics of the Syphilis disease under some assumptions made. The method of differential transformation is employed to compute an approximation to the solution of the non-linear systems of differential equations for the transmission dynamic of the disease model. The differential transformation method is a semi-analytic numerical method or technique, which depends on Taylor series and has application in many areas including Biomathematics. The disease-free equilibrium of the syphilis model is analyzed for local asymptotic stability and the associated epidemic basic reproduction number R<sub>0</sub> is less than unity. It is also known that the global dynamics of the disease are completely determined by the basic reproduction number. Sensitivity analysis is performed on the model’s parameters to investigate the most sensitive parameters in the dynamics of the disease, for control and eradication.

Highlights

A mathematical model is a description of a system using mathematical concepts and language
Mathematical modeling in epidemiology provides understanding of the mechanisms that influence the spread of a disease and it suggests control strategies
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions

Summary

Introduction

A mathematical model is a description of a system using mathematical concepts and language. Mathematical modeling in epidemiology provides understanding of the mechanisms that influence the spread of a disease and it suggests control strategies. Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. The modeling of infectious diseases is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic, [3]. Often when engineers analyze a system to be controlled or optimized, they use a mathematical model, [4]. They can help to identify where there may be problems or pressures, identify priorities and focus efforts. Other relevant papers consulted include the following: [1, 5,6,7,8, 10, 11]

Model Formulation

Assumption of the Model

Parameters and Symbols

Schematic Diagram of the Model Below is the schematic diagram of the model

Application of Differential Transformation Method

Mathematical Analysis of the Model

Sensitivity Analysis

Summary

Conclusion

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