Modelling wildlife rabies: Transmission, economics, and conservation

Abstract Rabies is a fatal zoonotic disease of mammals; it exacerbates the uncertainty of conserving populations of some threatened mammals (TM). Modelling affords an inexpensive, a priori way of studying key parameters of wildlife rabies transmission, rabies management economics, and TM conservation. Numerous models of rabies transmission have been published. Linear density dependent models predicted that a threshold density ( K T  ⩽ 1.0), possibly attained by culling or contraception, would eliminate an epizootic through reduced contacts among host animals. Density independent models predicted less advantage of culling and contraception in rabies control due to limited contacts among territorial host animals. Recent stochastic, mixed models offer novel predictions about the role of culling, fertility control, and oral rabies vaccination (ORV) in disease management. Use of a “threshold successful contact” rate ( C T ) as a parameter in these models predicts that density reduction of host animals will enhance ORV campaigns in non-TM contexts via more efficient bait delivery and vaccination. Economic analyses of medical, public health, and veterinary costs have shown post-exposure prophylaxis (PEP) and increased pet vaccinations (PV) to be major rabies-caused expenses during and after epizootics in North America. No modelling efforts have examined either the benefits-costs of rabies management strategies to conserve TM or the use of ORV, per se , to conserve TM – an omission due in part to the lack of methodologies for properly valuing TM (potential savings) and the expense or lower priority of using ORV for TM protection. This paper: (1) describes key aspects of rabies-transmission models in wildlife, (2) posits the use of C T to predict disease persistence, (3) reviews selected ORV strategies, economic studies, and benefit–cost models associated with the use of ORV as a means of rabies control in non-TM situations, (4) discusses implications of these models to the conservation of TM, and (5) recommends five steps to improve modelling of rabies transmission (wildlife disease in general), rabies-control economics, and TM conservation.

[1]  M. Kieny,et al.  Large-scale eradication of rabies using recombinant vaccinia-rabies vaccine , 1991, Nature.

[2]  A. Mantovani,et al.  Le controle de la rage selvatique dans le nord-est de l'Italie , 1982 .

[3]  N. Tordo,et al.  Antigenic and genetic divergence of rabies viruses from bat species indigenous to Canada. , 2001, Virus research.

[4]  G. Smith The role of the Badger (Meles meles) in rabies epizootiology and the implications for Great Britain , 2002 .

[5]  David W. Macdonald,et al.  Rabies and Wildlife: A Biologist's Perspective , 1980 .

[6]  J. Blanton,et al.  Rabies surveillance in the United States during 2006 Public Veterinary Medicine: Public Health , 2007 .

[7]  M. Aubert Costs and benefits of rabies control in wildlife in France. , 1999, Revue scientifique et technique.

[8]  Bruce C. Lubow,et al.  Fitting population models to multiple sources of observed data , 2002 .

[9]  Campbell Jb Oral rabies immunization of wildlife and dogs: challenges to the Americas. , 1994 .

[10]  L. E. Peterson,et al.  Eliciting expert opinion using the Delphi technique: identifying performance indicators for cardiovascular disease. , 1998, International journal for quality in health care : journal of the International Society for Quality in Health Care.

[11]  R. Zerbe,et al.  Benefit-cost analysis in theory and practice , 2002 .

[12]  R. Sterner,et al.  Relative Factor Costs of Wildlife Rabies Impacts in the U.S. , 2004 .

[13]  J. Gog,et al.  Disease in endangered metapopulations: the importance of alternative hosts , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[14]  M. Begon,et al.  A clarification of transmission terms in host-microparasite models: numbers, densities and areas , 2002, Epidemiology and Infection.

[15]  N. Barlow The ecology of wildlife disease control : simple models revisited , 1996 .

[16]  J. Ballou ASSESSING THE RISKS OF INFECTIOUS DISEASES IN CAPTIVE BREEDING AND REINTRODUCTION PROGRAMS , 1993 .

[17]  T. Sidwa,et al.  Evaluation of oral rabies vaccination programs for control of rabies epizootics in coyotes and gray foxes: 1995-2003. , 2005, Journal of the American Veterinary Medical Association.

[18]  E. E. Holmes,et al.  Are Diffusion Models too Simple? A Comparison with Telegraph Models of Invasion , 1993, The American Naturalist.

[19]  R. Putman Mammals as pests. , 1990 .

[20]  M. Meltzer,et al.  The cost of rabies postexposure prophylaxis: one state's experience. , 1998, Public health reports.

[21]  R. May,et al.  Population Biology of Infectious Diseases , 1982, Dahlem Workshop Reports.

[22]  D. Swerdlow,et al.  Rabies surveillance in the United States during 2004. , 2005, Journal of the American Veterinary Medical Association.

[23]  Kathleen A. Smith,et al.  Cost of distributing oral raccoon-variant rabies vaccine in Ohio: 1997-2000. , 2002, Journal of the American Veterinary Medical Association.

[24]  G C Smith,et al.  Models of Mycobacterium bovis in wildlife and cattle. , 2001, Tuberculosis.

[25]  M. Meltzer,et al.  DIRECT AND INDIRECT COSTS OF RABIES EXPOSURE: A RETROSPECTIVE STUDY IN SOUTHERN CALIFORNIA (1998–2002) , 2007, Journal of wildlife diseases.

[26]  T. Selhorst,et al.  Emergency vaccination of rabies under limited resources – combating or containing? , 2005, BMC infectious diseases.

[27]  H. B. Batista,et al.  Studies on antigenic and genomic properties of Brazilian rabies virus isolates. , 2005, Veterinary microbiology.

[28]  T. Strine,et al.  Rabies surveillance in the United States during 1994. , 1995, Journal of the American Veterinary Medical Association.

[29]  Andrew P. Dobson,et al.  EXPOSING EXTINCTION RISK ANALYSIS TO PATHOGENS: IS DISEASE JUST ANOTHER FORM OF DENSITY DEPENDENCE? , 2005 .

[30]  R. May,et al.  Population biology of infectious diseases: Part II , 1979, Nature.

[31]  C. Struchiner,et al.  Fuzzy Dynamical Systems in Epidemic Modeling , 2000 .

[32]  R. Ostfeld,et al.  Spatial epidemiology: an emerging (or re-emerging) discipline. , 2005, Trends in ecology & evolution.

[33]  David L Smith,et al.  Predictive Spatial Dynamics and Strategic Planning for Raccoon Rabies Emergence in Ohio , 2005, PLoS biology.

[34]  Rowland R Kao,et al.  The role of mathematical modelling in the control of the 2001 FMD epidemic in the UK. , 2002, Trends in microbiology.

[35]  C. Marks,et al.  Distribution and density estimates for urban foxes (Vulpes vulpes) in Melbourne: implications for rabies control , 1999 .

[36]  R. Anderson Immunization in the field , 1991, Nature.

[37]  Laurence V. Madden,et al.  Some methods for eliciting expert knowledge of plant disease epidemics and their application in cluster sampling for disease incidence , 2002 .

[38]  Roy M. Anderson,et al.  Population dynamics of fox rabies in Europe , 1981, Nature.

[39]  M. Eidson,et al.  Public Health Impact of Reemergence of Rabies, New York , 2002, Emerging infectious diseases.

[40]  J. V. Straaten Challenges and Pitfalls of Cost-Benefit Analysis in Environmental Issues , 1998 .

[41]  M. Leslie,et al.  Compendium of Animal Rabies Prevention and Control, 2004. , 2004, Journal of the American Veterinary Medical Association.

[42]  David W. Macdonald,et al.  An integrated disease management strategy for the control of rabies in Ethiopian wolves , 2006 .

[43]  N. Tordo,et al.  Host Switching in Lyssavirus History from the Chiroptera to the Carnivora Orders , 2001, Journal of Virology.

[44]  D. Smith,et al.  Results of an oral rabies vaccination program for coyotes. , 1998, Journal of the American Veterinary Medical Association.

[45]  David L. Bergman,et al.  Population Monitoring in Support of a Rabies Vaccination Program for Skunks in Arizona , 2003, Journal of wildlife diseases.

[46]  G. Casey,et al.  Experimental rabies in skunks: oral, nasal, tracheal and intestinal exposure. , 1979, Canadian journal of comparative medicine : Revue canadienne de medecine comparee.

[47]  L Tischendorf,et al.  Chance and risk of controlling rabies in large–scale and long–term immunized fox populations , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[48]  R. Rosatte,et al.  RACCOON AND SKUNK POPULATION MODELS FOR URBAN DISEASE CONTROL PLANNING IN ONTARIO, CANADA , 2001 .

[49]  D. Macdonald Rabies and wildlife: a conservation problem? , 1993, The Onderstepoort journal of veterinary research.

[50]  K. Fagerstone Wildlife Fertility Control , 2002 .

[51]  Fishbein Db,et al.  Rationale and prospects for rabies elimination in developing countries , 1994 .

[52]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[53]  P. Boffetta Molecular epidemiology. , 2000, Journal of internal medicine.

[54]  An Integral for a Reaction-Diffusion System , 1991 .

[55]  G. Gettinby,et al.  Positive and negative effects of widespread badger culling on tuberculosis in cattle , 2006, Nature.

[56]  M. Artois,et al.  Radio-pistage de renards enrages , 1982 .

[57]  U. Breitenmoser,et al.  [Rabies-free status of Switzerland following 30 years of rabies in foxes]. , 2000, Schweizer Archiv fur Tierheilkunde.

[58]  A. Benyoussef,et al.  LATTICE THREE-SPECIES MODELS OF THE SPATIAL SPREAD OF RABIES AMONG FOXES , 1999, adap-org/9904005.

[59]  Monetary Valuation Methods for Economic Analysis of the Benefit-Costs of Protecting Rare Wildlife Species from Predators , 2002 .

[60]  A. King,et al.  Rabies virus variants and molecular epidemiology in Europe. , 2004 .

[61]  Graham C. Smith,et al.  Demography of two urban fox (Vulpes vulpes) populations , 1987 .

[62]  J. B. Campbell Oral rabies immunization of wildlife and dogs: challenges to the Americas. , 1994, Current topics in microbiology and immunology.

[63]  Mick G. Roberts,et al.  Mathematical models for microparasites of wildlife , 1995 .

[64]  D. Slate,et al.  Oral Rabies Vaccination: A National Perspective on Program Development and Implementation , 2002 .

[65]  G. Hess Disease in Metapopulation Models: Implications for Conservation , 1996 .

[66]  Wiktor L. Adamowicz,et al.  What's it Worth? An Examination of Historical Trends and Future Directions in Environmental Valuation , 2004 .

[67]  G. Baer The natural history of rabies , 1978, Medical History.

[68]  H. McCallum,et al.  How should pathogen transmission be modelled? , 2001, Trends in ecology & evolution.

[69]  B T Grenfell,et al.  Individual-based perspectives on R(0). , 2000, Journal of theoretical biology.

[70]  M. Meltzer Assessing the costs and benefits of an oral vaccine for raccoon rabies: a possible model. , 1996, Emerging infectious diseases.

[71]  D. Haydon,et al.  Integrating Epidemiology into Population Viability Analysis: Managing the Risk Posed by Rabies and Canine Distemper to the Ethiopian Wolf , 2002 .

[72]  F. Steck,et al.  Assessment of fox control in areas of wildlife rabies. , 1981, Bulletin of the World Health Organization.

[73]  Eduardo Massad,et al.  Fuzzy gradual rules in epidemiology , 2003 .

[74]  D. Slate,et al.  ORAL RABIES VACCINATION: REDUCING ECONOMIC UNCERTAINTY VIA RESPONSE SURFACE ANALYSIS , 2003 .

[75]  C. Rupprecht,et al.  Phylogenetic relationships of Irkut and West Caucasian bat viruses within the Lyssavirus genus and suggested quantitative criteria based on the N gene sequence for lyssavirus genotype definition. , 2005, Virus research.

[76]  F. Cliquet,et al.  Rabies and rabies-related viruses: a modern perspective on an ancient disease. , 2004, Revue scientifique et technique.

[77]  M. Aubert Control of rabies in foxes: what are the appropriate measures? , 1994, Veterinary Record.

[78]  R. B. Stewart,et al.  ELIMINATION OF RABIES FROM RED FOXES IN EASTERN ONTARIO , 2001, Journal of wildlife diseases.

[79]  K. Bögel,et al.  Recovery of reduced fox populations in rabies control. , 2010, Zentralblatt fur Veterinarmedizin. Reihe B. Journal of veterinary medicine. Series B.

[80]  S. Harris,et al.  Flexible spatial organization of urban foxes, Vulpes vulpes, before and during an outbreak of sarcoptic mange , 2000, Animal Behaviour.

[81]  G. Gettinby,et al.  Effects of culling on badger meles meles spatial organization: implications for the control of bovine tuberculosis , 2005 .

[82]  J. Loomis,et al.  A willingness-to-pay function for protecting acres of spotted owl habitat from fire , 1998 .

[83]  M. G. Smith,et al.  Mass human exposure to rabies in New Hampshire: exposures, treatment, and cost. , 1996, American journal of public health.

[84]  R. Rosatte,et al.  EMERGENCY RESPONSE TO RACCOON RABIES INTRODUCTION INTO ONTARIO , 2001, Journal of wildlife diseases.

[85]  M. Aubert,et al.  Elimination of terrestrial rabies in Western European countries. , 2004, Developments in biologicals.

[86]  G. Smith Modelling rabies control in the UK : the inclusion of vaccination , 1995 .

[87]  M. Begon,et al.  Transmission dynamics of a zoonotic pathogen within and between wildlife host species , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[88]  Parker Rl,et al.  Pathogenesis of skunk rabies virus: quantitation in skunks and foxes. , 1966 .

[89]  C. Rupprecht,et al.  Rabies in Endangered Ethiopian Wolves , 2004, Emerging infectious diseases.

[90]  K Dietz,et al.  Characteristics of the spread of a wildlife rabies epidemic in Europe. , 1976, Bulletin of the World Health Organization.

[91]  L. Miller,et al.  IMMUNOCONTRACEPTION AS A WILDLIFE MANAGEMENT TOOL : SOME PERSPECTIVES , 1998 .

[92]  M. Smreczak,et al.  Rabies control in wildlife with oral vaccination in Poland , 2005 .

[93]  D. Slate,et al.  Status of oral rabies vaccination in wild carnivores in the United States. , 2005, Virus research.

[94]  P. White,et al.  Contact rates between possums revealed by proximity data loggers , 2005 .

[95]  A. Fooks,et al.  Wildlife rabies control policy in Great Britain. , 2006, Developments in Biologicals.

[96]  Andrew P. Dobson,et al.  Ecology of Infectious Diseases in Natural Populations: Frontmatter , 1995 .

[97]  M. Efford,et al.  THE EFFECT OF MANIPULATING POPULATION DENSITY ON THE PROBABILITY OF DEN-SHARING AMONG COMMON BRUSHTAIL POSSUMS, AND THE IMPLICATIONS FOR TRANSMISSION OF BOVINE TUBERCULOSIS , 1998 .

[98]  D. Macdonald,et al.  The red fox (Vulpes vulpes) in Saudi Arabia: loose‐knit groupings in the absence of territoriality , 1999 .

[99]  F. Meslin,et al.  Rationale and prospects for rabies elimination in developing countries. , 1994, Current topics in microbiology and immunology.

[100]  William G. Cochran,et al.  Experimental Designs, 2nd Edition , 1950 .

[101]  J. Bingham Canine Rabies Ecology in Southern Africa , 2005, Emerging infectious diseases.

[102]  A. Wandeler Oral immunization against rabies: afterthoughts and foresight. , 2000, Schweizer Archiv fur Tierheilkunde.

[103]  R. Tinline,et al.  Postexposure Treatment and Animal Rabies, Ontario, 1958-2000 , 2002, Emerging infectious diseases.

[104]  Anders Johansen,et al.  Spatio-temporal self-organization in a model of disease spreading , 1994 .

[105]  Graham C. Smith,et al.  A mathematical model for the control of diseases in wildlife populations: culling, vaccination and fertility control , 2002 .

[106]  D. Slate,et al.  ECONOMIC ANALYSIS OF A LARGE SCALE ORAL VACCINATION PROGRAM TO CONTROL RACCOON RABIES , 2000 .

[107]  S. Cleaveland Historical Perspectives of Rabies in Europe and the Mediterranean Basin , 2006, Tropical Animal Health and Production.

[108]  M. Jay,et al.  Rabies in a vaccinated wolf-dog hybrid. , 1994, Journal of the American Veterinary Medical Association.

[109]  R. Parker,et al.  Pathogenesis of skunk rabies virus: quantitation in skunks and foxes. , 1966, American journal of veterinary research.

[110]  Peter Caley,et al.  The effects of reducing population density on contact rates between brushtail possums: implications for transmission of bovine tuberculosis , 2002 .

[111]  Piran C. L. White,et al.  Encounters between red foxes (Vulpes vulpes): implications for territory maintenance, social cohesion and dispersal , 1994 .

[112]  J. Childs,et al.  Rabies surveillance in the United States during 2002. , 2003, Journal of the American Veterinary Medical Association.

[113]  M. Artois,et al.  Transmission et pathogénie chez le renard roux de deux isolats à dix ans d'intervalle du virus de la rage vulpine , 1990 .

[114]  R. Engeman,et al.  An economic assessment of the potential for predator management to benefit Puerto Rican parrots , 2003 .

[115]  G. Smith,et al.  MODELING CONTROL OF RABIES OUTBREAKS IN RED FOX POPULATIONS TO EVALUATE CULLING, VACCINATION, AND VACCINATION COMBINED WITH FERTILITY CONTROL , 2003, Journal of wildlife diseases.

[116]  Jean S. Smith,et al.  Epizootic canine rabies transmitted by coyotes in south Texas. , 1994, Journal of the American Veterinary Medical Association.

[117]  P. Bacon,et al.  Population Dynamics of Rabies in Wildlife , 1985 .

[118]  K. Stöhr,et al.  Progress and setbacks in the oral immunisation of foxes against rabies in Europe , 1996, Veterinary Record.

[119]  V. Dato,et al.  Benefits and costs of using an orally absorbed vaccine to control rabies in raccoons. , 1992, Journal of the American Veterinary Medical Association.