Nonlinear filtering of myxomatosis based on hormonal control of flea reproduction by the rabbit

A 4-dimensional nonlinear system of ordinary differential equations was recently constructed by Antonelli and Seymour to model the European rabbit viral disease known as myxomatosis. This model is based on the documented Rothschild's effect, that is, on the hormonal control of flea reproduction by the rabbit. Our model incorporates density dependent rabbit reproductivity and total caloric intake over time. Three nonlinear filtering problems are considered here in which the signal process is always the entire 4-dimensional system but where the observations processes are, least squares estimation of the number or density of rabbits, estimation of flea numbers, and simultaneous estimation of rabbit densities and total caloric intake, respectively. Extensive use is made of H. Kunita's backward Stratonovich calculus and stochastic partial differential equations theory to obtain exact solution measures of the Zakai equation for these three problems