Epidemic Evolution: Multiple Analytical Solutions for the SIR Model

While there are many models of epidemic evolution perhaps the basis for such models finds itself in the lumped behavior expressed through the so-called SIR model (Susceptible, Infectious, Recovered) from which spring many related models. This paper discusses multiple analytic solutions to that equation including those that are available in closed analytic form and those for which at least one final integral has to be done numerically, so-called quasi-analytic solutions. The solutions are intrinsically time-dependent of course. The hope is that such an investigation will lead to a better understanding of when and how models can be of use in studying the dynamical evolution of diseases including, perhaps, the great influenza pandemic of 1918 together with later pandemics and epidemics not excluding the Covid-19 pandemic of the present day.