Abstract: A state space model is developed for a system of nonlinear differential equations with observations consisting of nonlinear functions of the state variables. This is applied to modelling gonorrhea transmission in a heterosexual population. Variable transformations are used to keep the incidence rates in the interval zero to one and the unknown parameters in the proper ranges. A refinement of the model allows adaptively varying contact rates. The Kalman filter is used to calculate an approximate likelihood, and nonlinear optimization is used to obtain approximate maximum likelihood estimates.
Key words and phrases: State space models, nonlinear differential equations, Kal- man filter, epidemics, adaptive estimation.