The SIR model when S(t) is a multi-exponential function

The SIR model can be expressed mathematically either as a system of nonlinear ordinary differential equations or as a nonlinear Volterra integral equation. In general, neither of these can be solved in closed form. In this book, it is shown that if S(t) is approximated by finite sum of exponential functions, or a logistic function which is an infinite sum of exponential functions, then we can have closed form solution. Also we will formulate a method to determine R0 the basic reproductive rate of an infection. The method we used here is an alternative and better way of studying the SIR model from the ususal way numerical method.