Mathematical modeling of viral epidemics: A review

Mathematical models to describe transmission and propagation of diseases have gained momentum over the last hundred years. Formulated mathematical models are currently applied to understandthe epidemiology of various diseases including viral diseases viz Influenza, SARS, measles, etc. With the emergence of advanced computing tools, designing mathematical models and generating simulations (numerical solutions) have become feasible. There is an enormous scope for using mathematical models in studying epidemiology of viral diseases through transmission dynamics of outbreaks and in evaluating or predicting the effects of interventions and vaccinations. The influenza pandemic of 2009 and the recent Ebola epidemics of 2014-15 have generated renewed interest in mathematical modelling of epidemics. Here we present a review of the various mathematical models and their applications in the study of virus driven epidemics.