A spatio-temporal epidemic model for influenza: A Case Study of the 1988-1989 Epidemic in Japan

A mathematical model is built for influenza or other similar disease epidemics in a multi-region setting. The model is an extended type of chain-binomial model applied to a large population (Cliff et al., 1981), taking into account interregional infection by interregional contacts of people. If the magnitude of the contact is presented by simple distance-decay spatial interaction or the most primitive gravity model, a conventional gravity-type epidemic model (Murray and Cliff, 1977; Thomas, 1988) is deduced. Given the number of infectives and susceptibles, the chain-binomial model predicts the number of infectives in the next period with binomial probability distribution. Available data are, however, weekly cases per reporting clinic in each prefecture reported by the surveillance project, characterized by continuous variation; the data could be a surrogate index for rates of infection. The author modified the model to use rates of infectives and susceptibles, and used a normal approximation of binomial distribution. With the maximum-likelihood method, this model can be calibrated. The specification of the model is as follows:.