Modelling the spread of phocine distemper virus among harbour seals

Data presented in earlier publications on the 1988 epizootic among seals in North West Europe show a pattern that is somewhat inconsistent with the predictions of the standard mathematical model of epidemics. We argue that for animals living in herds or colonies, such as seals, the mutual contact behaviour is such that models for the transmission of infectious diseases should be applied with special care for the distinction between numbers and densities. This is demonstrated by using a mechanistic description of the contacts among seals, which leads to a slightly different formulation of the model. Results of the analysis of this formulation are more in line with the data. The model introduced here can be applied to epidemics among all kinds of animals living in herds and in fact to any species with constant local density, independent of the total population size (i.e., occupying a variable area). Application of the traditional formulation, using different parameters for herds of different sizes, will give equally good results for non-lethal diseases. However, especially for diseases with a low R0 and high death rates, such as the phocine distemper virus (PDV) disease, the two model formulations give quite different results. Further analysis of the model is performed to determine the most important factors influencing such an epidemic. The survival of infected animals turns out to have a disproportionately great influence on the intensity of the epidemic. Therefore in the case of the PDV epizootic we conclude that marine pollution may not only have contributed to the high death rates, but, if so, it has intensified the epizootic as well.