Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations

1.  This paper explores the concept of the critical community size for persistence of infection in wildlife populations. We use as a case study the 1988 epidemic of phocine distemper virus in the North Sea population of harbour seals, Phoca vitulina. 2.  We summarize the available data on this epidemic and use it to parameterize a stochastic compartmental model for an infection spreading through a spatial array of patches coupled by nearest-neighbour mixing, with replacement of susceptibles occurring as a discrete annual event. 3.  A combination of analytical and simulation techniques is used to show that the high levels of transmission between different seal subpopulations, combined with the small annual birth cohort, act to make persistence of infection impossible in this harbour seal population at realistic population levels. The well known mechanisms by which metapopulation structures may act to promote persistence can be seen to have an effect only at weaker levels of spatial coupling, and higher levels of host recruitment, than those empirically observed.

[1]  P. Pomeroy,et al.  The descriptive epizootiology of phocine distemper in the UK during 1988/89. , 1992, The Science of the total environment.

[2]  W M Schaffer,et al.  The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[3]  R. Dietz,et al.  Retrospective of the 1988 European seal epizootic , 1992 .

[4]  I. Robinson,et al.  Anti-canine distemper virus antibodies in common and grey seals , 1992, Veterinary Record.

[5]  J. Gaspard Deterministic and Stochastic Models , 1991 .

[6]  S. P. Ellner,et al.  Measles as a case study in nonlinear forecasting and chaos , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[7]  O. Diekmann,et al.  On the final size of epidemics within herds , 1995 .

[8]  A. Hall Morbilliviruses in marine mammals. , 1995, Trends in microbiology.

[9]  T. Härkönen,et al.  Epizootiology of the seal disease in the eastern North Sea , 1992 .

[10]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[11]  T. Härkönen,et al.  Comparative life histories of East Atlantic and other harbour seal populations , 1990 .

[12]  C. Goodhart Did virus transfer from harp seals to common seals? , 1988, Nature.

[13]  B. McConnell Seals in Orkney , 1985 .

[14]  Odo Diekmann,et al.  How does transmission of infection depend on population size , 1995 .

[15]  B. McConnell,et al.  New approaches for field studies of mammals: experiences with marine mammals , 1989 .

[16]  P. Thompson,et al.  SEROLOGIC STUDY OF PHOCINE DISTEMPER IN A POPULATION OF HARBOR SEALS IN SCOTLAND , 1992, Journal of wildlife diseases.

[17]  P. Thompson,et al.  Winter Foraging by Common Seals (Phoca Vitulina) in Relation to Food Availability in the Inner Moray Firth, N.E. Scotland , 1991 .

[18]  Mark Bartlett,et al.  Deterministic and Stochastic Models for Recurrent Epidemics , 1956 .

[19]  J. Heesterbeek,et al.  The saturating contact rate in marriage- and epidemic models , 1993, Journal of mathematical biology.

[20]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[21]  Ilkka Hanski,et al.  Single‐species metapopulation dynamics: concepts, models and observations , 1991 .

[22]  M. Blixenkrone-Møller Biological properties of phocine distemper virus and canine distemper virus. , 1993, APMIS. Supplementum.

[23]  T. Härkönen,et al.  REBUILDING SEAL STOCKS IN THE KATTEGAT-SKAGERRAK , 1988 .

[24]  A. Osterhaus,et al.  Morbilliviruses in aquatic mammals: report on round table discussion. , 1995, Veterinary microbiology.

[25]  A. Trudgett,et al.  Demonstration of antibodies in archival sera from Canadian seals reactive with a European isolate of phocine distemper virus. , 1992, The Science of the total environment.

[26]  James H. Brown,et al.  Turnover Rates in Insular Biogeography: Effect of Immigration on Extinction , 1977 .

[27]  B. Liess,et al.  Morbillivirus infections of seals during the 1988 epidemic in the Bay of Heligoland: III. Transmission studies of cell culture-propagated phocine distemper virus in harbour seals (Phoca vitulina) and a grey seal (Halichoerus grypus): clinical, virological and serological results. , 1990, Zentralblatt fur Veterinarmedizin. Reihe B. Journal of veterinary medicine. Series B.

[28]  Bryan T. Grenfell,et al.  Chance and Chaos in Measles Dynamics , 1992 .

[29]  Andrew D. Barbour The duration of the closed stochastic epidemic , 1975 .

[30]  Odo Diekmann,et al.  The force of infection in populations of varying size: a modelling problem , 1995 .

[31]  P. Thompson,et al.  Phocine distemper virus outbreak in the Moray Firth common seal population: an estimate of mortality. , 1992, The Science of the total environment.

[32]  ON THE ASYMPTOTIC SIZE AND DURATION OF A CLASS OF EPIDEMIC MODELS , 1995 .