An SIR Model of Influenza with the Effects of Treatment and Vaccination

Abstract

We produced an SIR model of influenza which is a global infectious disease, by using Caputo fractional derivative. In this model, we separated S and I into different groups. Separation is made according to the group of people in S who get vaccinated and are protected from influenza, also people in S who get vaccinated but are not protected besides people in S who do not get vaccinated. Furthermore, infected people are separated as treated and untreated people in I. We did stability analysis of the model and produced the basic reproduction number. We emphasized the importance of influenza vaccine and treatment for infected people by varying the values of the parameters and was shown with graphics.