Global approximate solution of SIR epidemic model with constant vaccination strategy

Providing a global semi-analytical method has the advantage of offering a global and accurate solution to the epidemic model, which can help in studying and controlling the spread of the disease. Unlike numerical methods such as the Runge-Kutta-Fehlberg method, global semi-analytical methods can provide an explicit expression of the solution over the entire time period, including obtaining the peak time, which is crucial information for understanding disease spread. In this paper, a global semi-analytical method based on the two-point Pade approximants for solving the SIR epidemic model of childhood diseases is presented. The objective of this study is to examine the temporal dynamics of a childhood disease when a preventive vaccine is present. For this purpose, we have first derived the solution of the SIR model of childhood diseases in terms of series expansions for small and large values. Then, the theory of two-point Pade approximations is used to provide the global approximate solution. The peak time related to this model is also obtained via these global approximants. Furthermore, in order to show the efficiency of our study, some graphs have been given to compare our results with those obtained using the classical Pade approximations and the numerical Runge-Kutta-Fehlberg method.

Automated summary

This paper presents a global semi-analytical method based on two-point Pade approximants for solving the SIR epidemic model of childhood diseases. The method provides an explicit analytical solution over the entire time period, including the peak time, which is crucial for understanding disease spread. The efficiency of the method is demonstrated by comparing the results with classical Pade approximations and the numerical Runge-Kutta-Fehlberg method.