Abstract
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 R 0 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.
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De Koeijer, A. A. (1993). Effects of PDV-virus infection on a susceptible population of harbour seals (Phoca vitulina). Masters thesis, Theoretical biology, Leiden University.
De Swart, R. L., P. S. Ross, L. J. Vedder, H. H. Timmerman, S. H. Heisterkamp, H. Van Loveren, J. G. Vos, P. J. H. Reijnders and A. D. M. E. Osterhaus (1994). Impairment of immune function in harbor seals (Phoca vitulina) feeding on fish from polluted waters. Ambio 23, 155–159.
De Swart, R. L. (1995). Impaired immunity in seals exposed to bioaccumulated environmental contaminants. PhD thesis, Erasmus University Rotterdam.
Diekmann, O., A. A. de Koeijer and J. A. J. Metz (1996). On the final size of epidemics within herds. Canad. Appl. Math. Quart. 4, 21–30.
Dietz, R., M. P. Heide-Jørgensen and T. Härkönen (1989). Mass deaths of harbor seals in Europe. Ambio 18, 258–264.
Grenfell, B. T., M. E. Lonergan, and J. Harwood (1992). Quantitative investigations of the epidemiology of phocine distemper virus in European common seal populations. Science of the Total Environment 115, 15–29.
Hall, A. J., R. R. Law, D. E. Wells, J. Harwood, H. Ross, S. Kennedy, C. R. Allchin, L. A. Campbell and P. O. Pomeroy (1992). Organochlorine levels in common seals (Phoca vitulina) which were victims and survivors of the 1988 phocine distemper epizootic. Science of the Total Environment 115, 145–162.
Harada, Y., H. Ezoe, Y. Iwasa, H. Matsuda and K. Sato (1995). Population persistence and spatially limited social interaction. Theor. Pop. Biol. 48, 65–91.
Harwood, J. and A. Hall (1990). Mass mortality in marine mammals: its implications for population dynamics and genetics. Trends Ecol. Evol. 5, 254–257.
Harwood, J., S. D. Carter, D. E. Hughes, C. E. Bell, J. R. Baker and H. J. C. Cornwell (1989). Seal disease predictions. Nature 339, 670.
Heide-Jørgensen, M. P. and T. Härkönen (1992a). Epizootiology of the seal disease in the eastern North Sea. J. Appl. Ecol. 29, 99–107.
Heide-Jørgensen, M. P., T. Härkönen and P. Åberg (1992b). Long-term effects of epizootic in harbor seals in the Kattegat-Skagerrak and adjacent areas. Ambio 21, 511–516.
Kennedy, S. (1990). A review of the 1988 European seal morbillivirus epizootic. Vet. Rec. 127, 563–567.
Kermack, W. O. and A. G. McKendrick (1927). Contributions to the mathematical theory of epidemics, part I. Proc. Royal Soc. A116, 700–721.
Lefèvre, C. and P. Picard (1993). An epidemic model with fatal risk. Math. Biosci. 117, 127–145.
Osterhaus, A. D. M. E. and E. J. Vedder (1988). Identification of virus causing recent seal deaths. Nature 335, 20.
Picard, P. and C. Lefèvre (1993). Distribution of the final state and severity of epidemics with fatal risk. Stochastic Processes and their Applications 48, 277–294.
Reijnders, P. J. H. and K. Lankester (1990). Status of marine mammals in the north sea. Netherlands J. Sea Res. 26(2–4), 427–435.
Ross, P. S., R. L. De Swart, P. J. H. Reijnders, H. Van Loveren, J. G. Vos and A. D. M. E. Osterhaus (1995). Contaminant-related suppression of delayed-type hypersensitivity and antibody responses in harbour seals fed herring from the Baltic Sea. Env. Health Persp. 103, 162–167.
Thompson, P. M. and D. Miller (1992). Phocine distemper virus outbreak in the Moray Firth common seal population: an estimate of mortality. Science of the Total Environment 115, 57–65.
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De Koeijer, A., Diekmann, O. & Reijnders, P. Modelling the spread of phocine distemper virus among harbour seals. Bull. Math. Biol. 60, 585–596 (1998). https://doi.org/10.1006/bulm.1997.0030
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DOI: https://doi.org/10.1006/bulm.1997.0030