This paper introduces a nonlinear dynamic model to study spatial and temporal dynamics of epidemics of susceptible-infected-removed type. It involves modeling the respective collections of epidemic states and syndromic observations as random finite sets. Each epidemic state consists of the number of infected individuals in an isolated population system and the corresponding partially known parameters of the epidemic model. The infectious disease could spread between population systems with known probabilities based on prior knowledge of ecological and biological features of the environment. The problem is then formulated in the context of Bayesian framework and estimated via a probability hypothesis density filter. Each population system under surveillance is assumed to be homogenous and fixed, with daily reports on the number of infected people available for monitoring and prediction. When model parameters are partially known, results of numerical studies indicate that the proposed approach can help early prediction of the epidemic in terms of peak and duration.