Estimation of the Malthusian parameter in an stochastic epidemic model using martingale methods

Data, on the number of infected, gathered from a large epidemic outbreak can be used to estimate parameters related to the strength and speed of the spread. The Malthusian parameter, which determines the initial growth rate of the epidemic is often of crucial interest. Using a simple epidemic SEIR model with known generation time distribution, we define and analyze an estimate, based on martingale methods. We derive asymptotic properties of the estimate and compare them to the results from simulations of the epidemic. The estimate uses all the information contained in the epidemic curve, in contrast to estimates which only use data from the start of the outbreak.