From Dynamical Processes to Likelihood Functions, An Application to Internet Surveillance Data for Influenza Like Illnesses

Basic stochastic processes, like the SIS and SIR epidemics, are used to describe data from an internet based surveillance system, the InfluenzaNet. Via generating functions, in some simplifying situations there can be analytic expressions derived for the probability. From this likelihood functions for parameter estimation are constructed. This is a nice application in which partial differential equations appear in epidemiological applications without invoking any explicitly spatial aspect. All steps can eventually be bridged by numeric simulations in case of analytical difficulties [1, 2].