ANALYsis OF INCIDENCE PATTERNS

Transcription

1 A COMPUTER MODEL OF WILDLIFE; EA.BIES EPIZOOTICS AND AN ANALYsis OF INCIDENCE PATTERNS by Charles Willard Smart Thesis submitted to th~ Graduate Fa<::,ulty of.the Virginia Polytehni TnstJtute and State Univ:ersity _ in andiday for the degree of MA.STER OF SCIENCE :,".: :. in.... WILDLIFE MANAGEMENT APPROVED: ~~~~~~~~~~~~~~~ Chairman, Robert H. Giles, Jr. Alfre\i D. S11llivan J. William shii'id{, Jr. Otober i970 Blaksburg, Virgi nia:

2 ,,... ~'.,' Pa&e'..'...., :. LIST: OF TABL~S, ~IS'i' OF FIGURES. '...,; LIST OF APPENDICES... -~: \D:. :. I!... '....vi.~... viii. ACKNOWLEDGEMENTS...I!'... :.,. -!I'..!... : 't+RODIJCTION T...-.~~--!" ' x11e J.labi'e~ P.roblem.!'. ~!t.....'..... :.. :~ ;;.. ~,. '!'. '... Wil41ife Spei~s ~fetei;..... ' ".... wiillife ';Reservoirs ~- ~.. :,;' 1'..... ';. 41!.,".. f.!.. '.... l..... :. ~..~:: ; '' i.'_.... : ' ~-1.!" ~... ~bies SY'mptoms in Wi1dli:Ee " 11.. Latent s~ptoms.. ~....:' ~..... :..,.. Inuh~ttonPeri.oasand pt.iration pf sy-mp~o1u~ ~~f~s,transrn~~sio~,. '.'......, :... ~ : Cyli ~hies. Inidene Spatial Relationships in Wildlife Rabies.. '.. Wildlife Rab:j.es R,eporti:rig.. wildlife.rabies Control : ' ,... ~._ ,... Models <i1ld Simulation.... "':... METHODS ~.. Analysis pf Rabies Repo;i:-ts...!II ~ :. : 'll ,6 18'.HJ l~ 20.. ' 2l 25 2.s -:. _:. :..:.. ; :., ;: Comp~te:r Si11l~~ation of.rabies Epidemiology Desriptiol} of GASP Sim\llation Language : D~finition and General Appx:oa:h. to Simulation... with GASP, '.. :,_.,

3 iii Page GASP Simulation Proedures Simulation of Rabies Epidemiology - Program Desription 34 Desription of Rabies Simulation Subprograms 35 Data Input. Dynami Modifiation. RESULTS Analysis of Rabies Reports Report Site. Mapping.. Clllllulative Time Patterns Overall Temporal and Spatial Relationships Computer Simulation of R<:lbies Epidemiology Unontrolled Epidemi Rabies Control by Trapping. Rabies Control Utilizing Chemosterila.nts Rabies Control by Vaination DISCUSSION Analysis of Rabies Reports. 80 Computer Simulation of Rabies Epidemiology 81 Model Testing 81 Information Gaps 82 Sample Simulation Results 82 The Expense of Simulation 84 Expansion of the Model. SUMMARY LITERATURE CITED 89

4 iy APPENDIX V;I:TA Page

5 LIST OF TABLES Table I. Rabies inubation periods in seleted animal speies '..... ' Page 14 IL III. IV. v. VI. VII. Periods of linial rabies syinpfoms in seleted animal speies '! Surmnary of rabieslaboratory report$ used for analyses of time and spae relationships of inidenes in wildlife speies Definition of an elevator system in a bui1dingand its entities and attributes... Possible attributes of a simulation event.. Initial population parameters for a sample simulation Time in days required for.rabid members of speies (I) to ome into ontat with a member of speies ( J) VIII. Time in days required for a member of speies (J) to find the body of a rabid member of speies (I) 60 IX. x. XI. Probabilities of suseptible members of speies (J) ontrating rabies if attaked by a rabid member of speies (I) displaying syinptoms (K). Probabilities of transmissionmode (1) being U$ed by a member of speies (I), shq_wing syinptoms (K)., in ontating membe!'s of speies (J).. Probabilities that speies (I) will be eaten by spei.es. (J) Q _ v

6 LIST OF FIGURES Figure '1. Generalized GASP simulation program Main program Subroutine EVNTS Subroutine SYMPTM Subroutine CONT CT Subroutine DEAD Subroutine PRDATN Subroutine REPROD Subroutine OUTPUT Subroutine ENDSIM Cumulative rabies reports by week from four ounties studied , Temporal separations between eah possible ombination of rabies reports, by-ouhty Spatial separations between eah possible ombination of rabies reports, by ounty Number of animals dying per week under a strategy of no ontrol Number of animals infeted.per week under a strategy of no ontrol Number of infetive foxes present per week under a no-ontrol strategy Number of animals dying per week under a strategy of fox trapping Number of animals infeted per week under a strategy of fox trapping Number of infetive foxes present per week under a strategy of fox trapping vi

7 vii Figure Number of animals dying per week under a strategy of fox sterilization.. Number of animals infeted per week under a strategy of fox sterilization.... Number of infetive foxes present per week under a strategy of fox sterilization.... Number of animals dying per week under a strategy of fox vaination... Number of animals infeted per week under a strategy of fox vaination

8 LIST OF APPENDICES Appendix I. Program for analysis of rabies reports. 98 II. GASP II wildlife rabies simulator III. Important rabies model variables and aumulators. 120 IV. Data input speifiations for non-gasp variables. 124 viii

9 ACKNOWLEDGEMENTS This study was niade possible by funds provided by the Nationai. S.iene Foundation, the Virginia Cooperative Wildlife Researh Unit, and the Division of Forestry and Wildlife Sienes, Virginia Polytehni Institute and State University. I would like to express by sinere appreiation to Dr. Robert :a. Giles, Jr., Assoiat:e Professor of Wildlife Management, who ontributed valuable guidane and enouragement throughout this Study. Thanks are also due to.dr. Alfred D~. Sullivan, Assistant Professor of Statistis, Forestry and Wildlife, and to Dr. J. William Shmidt, Jr., Assistant Professor of Industrial Engim~ering, who served as members of my ommittee and provided helpful advie onerning. tehnial aspets 0 this study. Reognition ;is due to Rose. Exterminator Company, Troy, Mihigan for his ontinued interest in this projet and to for his valuable support., National Communiable Disease Center, Atlanta, Georgia I am indebted to for his aid in the initial formulation of a omputer-based rabies model and to for his.assistane with tehnial problems. I appreiate the aid and suggestions of my fellow graduate students, in partiular and Speial reognition goes to my wife,, wh,o supplied au1p1e enouragement and aided in data analysis an.l typing. Thanks are also due to, anl. who typed the final draft of this manusript. ix

10 INTRODUCTION "Rabies is an aute infetious disease aused by a filterable virus" (Johnson 1959a: 405). It is "primarily an infetion or the anine rae but may affet any of the warm blooded animals. Seondarily it is a disease of man" (Ke ls er 1955: 250). The history of rabies in domesti speies is long and well doumented. Kelser (1955: 250) ited reports of rabies as early as the 13th entury B.. in Europe. Spangler (1966:1) alled the disease "one of the oldest, one of the most dangerous, and one of the most stubborn plagues of both man and animal." THE RABIES PROBLEM The importane of rabies annot be overemphasized. Aha (1966: 140) reported 2407 human rabies deaths in the western hemisphere from 1954 to Sikes (1967:4) noted 1964 rabies deaths in the world from 1962 to 1963, but estimated that twie that number went unreported. But the danger of human deaths is not as important as the eonomi onsequenes of rabies. Held et al. (1967:1017) reported that 30,000 persons annually reeive the expensive immunization treatment, 200 in Virginia alone (Marx and Swink 1963:173). Livestok deaths, however, aount for the greatest eonomi losses. During the first half of 1969 at least 269 farm animals were lost to rabies in the United States. Virginia lead the nation in attle rabies for this period with.50 reported lossed (Baker 1969). These figures do not reflet the total impat of rabies upon livestok, however. Parker.(1961:278) felt that many ases of livestok rabies are simply not reported due to the expense and diffiulty of pakaging and shipping the heads of large animals for laboratory examination. The total l

11 2 eonomi loss in livestok, then, may be several times that indiated by laboratory onfirmations. Wildlife Rabies Several authors (Merriam 1966; Friend 1968:82) have reognized the positive relationship between rabies deaths in domesti animals and rabies epizootis in loal wildlife. Prior (1969: 1) ited rabies as a publi health problem, an agriultural problem, and a wildlife problem. The latter problem is beoming inreasingly important. The existene of rabies in North Amerian wildlife prior to the arrival of the white man is unertain. Verts (1967:149) thought that if it did exist it was probably prevalent in the members of the Canidae, due to their irumpolar distribution. The ear.lies t reords of animq.l rabies in the United States are from an epidemi in dogs in Virginia in 1753 (Johnson 1959a: 406). Gier (1948: 143) reported a fox rabies epizooti in Massahusetts in 1812 and Johnson (195% :270) stated that the earliest reports of rabies in the spotted skunk were from California in Up until the last deade, before vaine ame into widespread use, rabies ontinued to be onsidered primarily a disease of domesti dogs. Wildlife rabies is urrently a problem in Europe (Serakowa 1968) and in Vietnam (Baker 1967:7-8). In reent years researhers have begun to reognize the inreasing importane of wildlife rabies (Tierkel 1954: l; Steele 1967: 264), Washburn (1966:4) noted the onversion of rabies from an urban to a rural problem. National statistis reveal that wildlife has aounted for the most rabies ases for at least nine onseutive years (Baker 1968: 1) and the same trend ontinues (Baker 1969: 1). The inidene of rabies in wildlife speies

12 3 appears to have inreased as vaination programs have beome more ef feti vein ombatting the disease in domesti dogs (Sikes and Tierkel 1960:1). Tierkel (1954:1) stressed the importane of three wildlife-man rabies relationships. The first, wildlife transmission of rabies to man by diret ontat, ours infrequently. However, Washburn (1966: 4) has pointed out the inreased probability of this danger in the near future with the urrent inreases in leisure time and inreases in ontat between the Amerian publi and wildlife speies. The seond relationship, rabies transmission from wildlife to domesti speies to man, is of more immediate onern to publi health workers. This route is well doumented (Friend 1968; Serakowa 1968) and is the basis for the third signifiant aspet of wildlife rabies, eradiation. Eradiation of rabies in domesti animals and man ultimately depends upon the ontrol of the disease in wildlife speies. Rabies Eradiation D. H. Spangler (1966:1) in his address to the 1966 National Rabies Symposium artiulated the need for the omplete eradiation of rabies. He felt that eradiation of any disease is superior to mere ontrol. It is the "best protetion" we an have, he said, and is now eonomially feasible. Through tehnology and researh man has onquered a large number of one-s rious diseases inluding bruellosis, foot-and-mouth disease, vesiular exanthema, glanders, yellow fever, typhoid, diptheria, and polio (Spangler 1966: l; Washburn 1966: 5-6). If these diseases ould be eradiated the.re is little reason why energies might not now be turned to the omplete elimination of rabies. Through strit quarantine and ontrol measures, 36 ontries, islands, and territories are now reported as entirely free of rabies (Baler 1968:6). It seems probable that the United States

13 4 ould be added to this list if publi support an be mustered for a researh and eradiation program. Suh a program must be national in sope (Spangler 1966:1). Besides publi eduation, most authorities feel that researh is the first and most important step in an eradiation sheme (Washburn 1966:5). Meyer (1955:2), in disussing the ontrol of zoonoses, felt that eradiation is ''muh less a problem of wiping out overt disease than of learning the usual habits of infetive agents and then dealing with what are often ineradiable mammalian, bird, or arthropod resevoirs. 11 With the investigation of wildlife vaination tehniques as suggested by Marx (1966: 120) and Washburn (1966:5), these resevoirs may no loriger remain inonquerable. Nelso,n ( 1966) listed the urrent needs in rabies researh. These inlude more effetive tehniques for reduing the population of suseptible animals, figures for the proper degree of redution, the study of a latent arrier state, and researh onerning the effets of density stressr A SYSTEMS APPROACH TO RABIES The basis of an effetive understanding of the epidemiology of any disease is a omprehensive view of the entire omplex of fators affeting its dissemination. Rabies is no exeption. Detailed knowledge of only a few fators, suh as etiology or pathogenesis, is not enough. Ultimate effetiveness of ontrol strategies will depend upon an eologial viewpoint, a holisti approah enompassing not only the fators affeting disease, but also their interrelationships. In short the study of disea,se must be the study of a system, a term defined by Watt (1968) as "an inter-. loking omplex of proesses haraterized by many reiproal ause-effet pathways. 11 The status of our urrent knowledge of rabies is relatively

14 5 firm in the realm of domesti animals and man. Vaination and ontrol programs have been most effetive in reduing rabies inidene in this setor. Wildlife rabies and its relationship to domesti rabies are, however, areas in whih sientists are omparatively ignorant. Complete rabies ontrol will depend upon the analysis of this disease system and its related proesses as a unified whole. System analysis aording to Hayne (1969 :120) must start with the onstrution of a model large and omplex enough to adequately desribe the system in question. The first step in the analysis of the disease system, of rabies, then, should be the onstrution of a. omprehensive model. Eologists have long been utilizing the proess of modeling in their s tudies. However, the resulting models have been, for the most part, mental abstrations of reality. These foster an intuitive understanding of the omplex interations of the natural world, but often lak the onreteness of preise quantifiation neessary for authoritative analysis. In reent years the tehniques of modeling and simulation by means of the eletroni omputer have been vastly improved. The tremendous bookkeeping apaity of the omputer makes it the ideal devie for simulation. Large files of information an be quikly examined for the stat us of many fators. The effets of status hanges on variables of interest may easily be omputed. This entire proess may be repeated over many short periods. Computer modeling i$ often a more desirable method of analysis than is experimentation with atual omponents of a system in question, suh as rabies. It is less expensive and nondestrutive of atual system elements. Little risk to humans or to eosys tern. omponents is involved a.s a result of improper or speulative. deisions. The modeling proess does

15 6 not take as long as would the experiments required to yield the same information 9 1 utilizing only minutes of omputer time as opposed to days or years of experimentation. The effets of extreme situations; diffiult to reprodue in reality, are easily simulated by omputer. Of.ourse it may not be possible to examine satisfatorily all faets of a system by omputer simulation alone. Field experiments and verifiation of results go hand in hand with model building and are the foundation of improved data inputs. Abstrat models possess two inherent values. The first, and most obvious, is their preditive value.. Hypothetial situations may be arranged and sys tern performane may be observed for eah set of situation speifiations. The seond value of modeling is perhaps the more important. The very at of designing a omputer model of a system is a valuable disovery proeps. The neessity of simplifying and abstrating the proesses and elements omprising a system and mathematially desribing their interations often leads to new insights of relationships never before onsidered. The elimination of extraneous omplexity often reveals fats previously hidden to the experimenter. It is with this seond value in mind that the experimenter hose to approah the study of wildlife rabies by means of simulation. The objetives of this study were twofold. The first was to examine reords of reported rabies inidenes in eologially divergent areas and thereby establish a graphial model of the temporal and spatial patterns, if any, whih haraterize wildlife epidemis. The seond objetive was to inorporate this information and the sum of. urrent knowledge onerning wildlife rabies into a viable, omputer.,-based simulation of the disease ''s dynamis. Suh a model might provide a most useful to o1 for the deision-maker involved - in the exeution of optimum rabies researh and ontrol strategies.

16 LITERATURE REVIEW Rabies is an enephaliti viral disease of endothermi animals (Johnson 1959a:405). (Matsumoto 1962: 199). The virus itself is double-walled and elongated It is. 250 to 400 rnillimirons in diameter, having surfae projetions about 100 Angstrom units in length (Almeida et al. 1962: 14S:-149). Johnson (1959a: ) stated that the virus is resistant to antibiotis, but is quikly destroyed by strong aids or bases, fonnalin, and sunlight. Charateristi inlusion boqies, termed Negri bodies, are onsidered diagnosti (Rhodes and van Rooyen 1962: 401). WILDLIFE SPECIES AFFECTED Verts (1967:145) stated that rabies is restrited to mammals under natural onditions. It is most ommonly reported in members of the Mustelidae, Canidae, Proyonidae, Vespertilionidae, and Molossidae. The disease is most ommonly reported in the striped skunk (Mephitis mephi tis) (Verts 196 7). It does affet spotted skunk (Spilogale putorius) populations, but not to the same degree (Johnson 1959b ;25}. The next most ommonly reporteq wildlife family with rabies is the Ganidae.,Raush (1958:247), in a study of Alaskan rabies, reported the disease in the red fox (Vulpes fulva), the arti fox (Alopex lagopus), and the timber wolf (Canis lupus). The oyote (Canis latran.:s) is oasionally reported as infeted in the western United States (Baker 1968). Prior (1969 :31) reported the gray fox (Uroyon inereoargenteus) as the speies primarily affeted in Virginia. Together the skunks and the foxes have aounted for over 80 perent of the total wildlife rabies reports in the United States (Baker 1968: 1). 7

17 8 Bat rabies is assuming inreasing importane in the United States. :First reported in 1953 (Venters et al. 1954:18), bat rabies has been on.-.. firmed in 25 of the 40 known speies (Constantine 1965 :252). Baer and Bales (1967) stated that rabies virus may be disseminated by hemataphagous, frugi vorous, an.l insetivorous bats. Other speies. whih are oasionally reported as rabid are the oelot (Felis pardalis), oppossum (Didelphis marsupialis), raon (Proyon. lotor), bobat (Lynx rufus), badger ('I'axidae ta:ims), woodhuk (Marmota monax), gopher (Citellus spp.), and oati (Nasua naria) (Baker 1968). Toro (1996: 131) reported the mongoose (Viverridae) as a major reservoir in Puerto Rio. Ballantyne and O'Donoghue (1954) reported rabies in aribou (Rangifer spp.) and weasels (Mustela erimina). In addition Baker (1967) has noted rabies in various speies of deer, rabbits, and small rodents. WILDLIFE RESERVOIRS. The exat nature of the wildlife reservoirs of rabies is relatively unknown. Johnson (1966 :29), in disussing wildlife reservoirs, thought that the long-term wildlife host of rabies would be a speies whih did not ordinarily assume a role in epidemi outbreaks. Verts (1967: ) on the other hand, stated that reservoir speies ould be major partiipants in epizootis and might be expeted to display ative.rabies symptoms.... The speies onsidered to be the major rabies reservoirs in the ~United States are bats (all speies), the striped skunk, red and gray foxes, and the ermine. These speies at as hosts in distint enzooti areas, the fox being the major vetor in the East, the skunk in the entral states, and I I both speies serving as the reservoir in the West (Steele, personal ommuniation 1970)..Johnson. (1959a:405) suggested that the "permanent hosts" of rabies are members of the Mustelidae.

18 9 Several researhers. (Sanderson et al :92; Verts ~967:145) have onsidered and rejeted the possibility of. rabies being perpetuated by a multispeies omplex in any one area. They stated that the eologial and behavioral barriers between. s;peies durin,g interepizooti periods, the mehania.l barriers to transmission, and the attenuation of virus after several passes through the s~e speies rule out s;uh a possibility. Both Prior (1969:39) and Held et al. (1967) named the fox (red arid gray) as the primary reservoir in.the southeastern United States. The striped skunk is onsidered the major rabies reservoir in CaJ,.i..., fornia (Johnson 1966:28), and in the Midwest (Tierkel 1958: 445, 1959:196; Verts 1967: 169). Several authors (Sulkin 1962: ; S:i,kes 1967:2) have statedthat one or more speies of pats may serve as a wildlife rabies reservoir. Pawan (1936: ) found vampire bats to be asymptomati rabies.~arriers in Central and South Ameria. The bats were able to transln!t the virus over extended time periods. Fredikson and Thomas (1965: 497) attempted unsuessfully to orrelate fox rabies with th'7 pre4ominane of bat aves in. Tennessee. The role of bats as a.reservoir speies is, however, ontrover-.. s.ial. Many authors hold the opinion that bat rabies, at least in North Ameria, is independent of other wildlife speies (Constantine 1967a:885; Friend 1968:92). Raoons, although suseptible to rabies, apparently do not serve as a reservoir for other speies (Sikes 1967:2; Verts 1967:156; Friend 1968:9Q). The bite of a rabid raoon will often fail to ause rabies in another animal and it is hypothesized that this speies may denature or ina~ivate the virus in some way (Steele, person;;il ommuniation 1970)~

19 10 Rodents appar~ntly do not serve as a rabies vetor. Winkler (1966: 36) stated that rodents "are not partiularly suseptible to rabies infe-, tion" and, when infeted; do not normally.show virus in their salivary glands. Tierkel (1959:198) found no evidene of rabies in over 1000 ro-,, dents olleted in epizooti areas of New York and Georgia. No arthropod vetors have been established. Bell et al. (1957:282) foµnd that the virus lasted only a short time in tiks. A number of authors (Marx 1966; Verts and Storm 1966) have held the opinion that wildlife rabies reports may be biased and unrepresentative of the. atual degree of involvement of ertain speies as reservoirs. Johnson (1959b : ) stated that minks and weasels! may be more important in rabies epizootiology than reports indiate.. Weasels are one of the few. speies onunon to all endemi areas and may be the long-term rabies host' even though the frequeny with whih this speies is reported is not high (Johnson 1966:29). The disreteness of enzooti rabies areas of foxes versus skunk.s is still unexplained. Population levels of either speies appear unrelated to the speies whih serves as a reservoir (Parker 1961:274; Parker and Wilsnak 1966:33-34; Friend 1968:95). Tentative explanations of the.ge~ graphial predominane of one speies ra,ther than another inlude eologial or behavioral isolation of the speies in question (Verts and Stor.m 1966: 420; Verts 1967:156; Friend 1968:93) and variable speies suseptibility to different virus strains or doses (Sikes and Tierkel 1960 :272; Prio_r 1969: 39), Sikes and Tierkel (1960) presented evidene that foxes infeted with small doses of rabies virus would possess saliva of insuffiient infetivity to affet skunks, but ould transmit the disease to other

20 '..,,' ', ~ : I <' '. foxes. Sikes (1962: 1046) stat d that the greater infetivity Qf skunk saliva might qmpletely overwhelm foxes arid make them in~ffet.ive as arriers. Prior (1969 :40).suggested that; red foxes to rabi.es and produe a mor virulent virus than d9 gl;'<ly foxes The saliva of a red foxwould.bemore likely than that pf agra,y fox to ini~ tiate.a rabies infetion in a striped skunk, a relatively insuseptible speies. For this reason the red fox is the mor.e li~ely of the.twq spe,-.. ies to be assoiated with t"fie striped skw.nk in rabies epizootis. RABIES SYMPTOMS IN WILDLIFE ' Conventional disease texts reognize t'wo types qf rapie13 symptoms, in animals. The "fµrioµs'' onditiqn is h.araterized, by a~iti:ttiqn and (lggressiveriess, as opeosed to the relative ina.tiv:ity of the "pari.lytf'! ondition (Kelser 1955 :26~). 'fhe symptoms are variable, hqwever,.and intermediate forms afe, reo~n.ized (Rihards :4).. Different mani.. ' festations of.ral:>ies. are related primarily to. (he hqs:t $p.eies (yert:;s. 1967:147), Ra:bidskunk9 are often ha~.;iterized by thliiirextremely a~-:',gressiye behavipr (Rihards 1957 :4; Ver ts 1967 :~68)~ In early stages of sym~tom~., striped skunks.are onfused and lethargi... ' ~Xpf:!l mµsk is inhibited (Verts 1967:168.:..169). They are ative at any hour.. and r;t:ot notu:rna:l~. as under no'rma.1 ond:i;tion$ '(Parl5-er 1961:274}.. Symptoms ip bat spe.ies. are mor~.variable. Bfier and Bales (1967)< noted a wiie variety of symptoms in Mexian freetail bats ang foµnd tl,<j,ss~fiatiol'j. diffiult. LATENT SYMPTOMS Verus (1967:14a-149) reognized four' possible o'qtses of tahie:s in ', ' -. '. '. naturally infeted animals. Besides death. o;uring several days after <a

21 12 "nonna:l" inubation period and the omplete absene of symptoms or virus, he listed two hroni stages. The virus may.beome latent; only to be reativated by external stimuli at a later date. Or.the infeted a:nim;il may :lisplay no symptoms, but produe infetive saliva for a period of several months. Bell (1965) haraterized hronit rabies in dogs as fall~ ing into one of.four ategories: 1) delayed onset.of symptoms 2) linial symptoms, followed by reovery 3) linial disease of long duration 4) apparently healthy arrier state He ited evidene of one or more of these ategories being onfinned i.n experimental rats and rabbits, bats, skunks, foxes, and man., Taylor and Knowelden {1964:lll) reognized three types of disease arriers,.,. onvalesent, healthy, and intennittent. Asymptomati arrier states have been demonstrated in bats (;Pawan 1936; Sulkin et al. 1960; Sulkin 1962) and experimental animals (Fishman and Ward 1968: 137). Johnson (1966: 27) found that the virus of ertain skunks produed asymptomati infetions in adult mie. Reovery from ra"" bies has been reorded (Johnson 1959a:410; Merhant and Paker 1961:796), even in man (Kraut 1966:224), and might lead to the seond arrier state ited by Bell (1965). Reativation of latent rabies infetions is thought by some (Verts 1967: ) to be the key to rabies perpetuation inwildlife during interepizooti periods. The role of stress and trauma in preipitating I disease symptoms is generally well doumented (Turner 1960; Rhodes and van Rooyen 1962:81). Rabies-speifi literature is also filled with evidene

22 ~ '. '. suggesting the role of rowding and ompetiti;m stfes)'l. in atiyation of '. - - '.. latent rabies infetions/.. (Belll96S:l71; Johnson l9q5:823; Soa.ve 1964: 268). Sulkin e1: al. (1960: 613) found tha.t ra.qi~s yirus W(ls in aroused bats, but not i.n h;i.bernating individuals. Moore (1970: 168) hypothesized that development.. of p:reviously 1,mdemonstrat.ed rabies symptoms in a naturally infeted 'bat of aptivity..... INCUEATIONPERIODS AND DUR.ATIONOFSYMP'.fOMS Kelser (1955:262) statel that the. 1.~ngth of r(lbies ~riubation in animals was related to the spe:i_es of.jhe vi:tus donor the loation and extent of wou11ds, the quarit::i;ty of virus the virulene of that virus. ~ '. -. Sikes (1962:104'.l) likewis.e found an orrelation between the quantity of yirus injeted and..the length inubation period i:p. experimental ani111als. Johnson (l959b:273), in re""'. ferring to wildlife speies, related le:p.gth of virus illubation to the mode of transmission. As m,entloned. earlier, prolonged inubatio11 rnay result of reativation of latent virus (l<oprowski 195.2:963). For purposes of modeling wildlife rabies epidemiqlogy. the. disease literature w.::i,s si;arhed in order to obtain reliable.estimates.6f the limits and distributions of inubation and syl!lptom duration.in the speies to be onsidered. The results are presented in Tables I and IT. y:irus may appear in saliva before the atual display toms. Baer and Bales (1967:85) found rabies v:!-rus iri the freetail bats up to 12 days prior to the onset of symptoms. 1043,.-1044) reported virus in skunk saliva up to 5 days before and after the appearane of symptoms.

23 14 Table I. Rabies inub~tion periods in seleted animal speies. Speies Referene Inubation Period (days) minimum maximum median Dog Fox Johnson (1948) S:i,J,<es (l962) Fox. Parker & Wilsnak (1966) Fox Steele (1967) Ski.ink.. Parl<er & Wilsnak. (1966) 14 Vampire bat. Pa\Van (1936) 9 Mexian freetail bat :Baer. Bale~ (1967) 14 Big brown bat. Moore & Raymond (19 70) 395 i

24 15 Table IL Periods of linial rabies symptoms.in seleted animal speies. Speies Referene Duration of Symptoms (days) minimum maximum median Dog Fox Skunk Johnson (1948). Parker & Wilsnak Parker & Wilsnak (1966) (1966) Mexian freetail bat.baer & Bales (1967) 4 11

25 16 RABIES TRANSMISSION Bite transmission has traditionally been assumed to be the major mode of rabies dissemination in mammalian speies (Johnson 1959a:405; Verts 1967: ). However, reent evidene has suggested that this route is not ompletely responsible for the perpetuation of interepizooti rabies infetions in wildlife populations (Verts 1967 :171). Tierkel (1959:191) found that only 54 to 90 perent of laboratory animals dying from rabies arried rabies virus in their salivary glands. Other tis-- sues have been found to be affeted by the disease (Johnson 1966:29). Besides bite transmission of rabies, urine transmission of the virus is a distint possibility (Jol:mson 1959a:417), espeially in bats (Steele, personal ommuniation 1970). Rabies transmission by ingestion of the virus has beendemonstrated and ould be a fator in natural populations. Johnson (1959a: ) stated that rabies virus infetivity is retained for 1 to 2 weeks in animal tissues exposed to air at room temperature. Kelser (1955:277) and Johnson (1959b:273) have reported evidene of rabies transfer from mother to young by milk. Serakowa (1969) onfirmed food-borne rabies infetions in experimental animals and suspeted abrasions of the lips, gums, or ' ' intestinal trat to be the means of viral entry. However, Soave (1966: 45-46) and. Fishman and Ward (1968:136) demonstrated infetion from ingested virus in the absene of oral abrasions. Infetion by means of oral routes required large doses of virus, as would be arried in the brains of wild speies (Fishman and Ward 1968:136). Aerosol transmission of rabies by means of urine and saliva droplets in bat aves has been reported and is onsidered a possible means of viral

26 17 transfer from bats to other wildlife (Constantine 1962:289; MLean, personal ommuniation 1969). Constantine (1967b) was able to demonstrate rabies infetion in a large number of wildlife speies aged in bat aves, inluding the opossum, a speies relatively resistant to the disease. Verts (1967:155), however, held that the requisite onditions for aerosol transmission our too infrequently to make it a major soure of wildlife infetion. Winkler (1966) indiated that bats. may ontrat rabies through aerosol transmission, but Baer and Bales (1967: 87) and Sulkin et al. (1960) indiated that the insetivorous speies are relatively insuseptible to intranasal infetion, exept by large I doses of virus. The possibility of in utero transfer of rabies from a mother to her young has been onfirmed by investigations (Remlinger 1919:378; Verts 1967: ). Konradi (1916:37-46) wrote that in utero transmission was possible, but that the rabies virus would be modified in the proess. Sims et al. (1963:25) have demonstrated in _!.ltero rabies transfer in bats, as have Bell et al. (1965) in white mie. Infetivity rates for natural transmission modes have not been determined, but it appears that not all individuals exposed to rabies ontrat infetion. Sikes (1962:1046) found antibodies produed in only 1 of 12 skunks and 4 of 12 foxes experimentally infeted, Ver.ts (1967: ) noted seasonal differenes in the sex ratios of rabid skunks, leading him to hypothesize the role of stress in inreasing the suseptibility to infetion. Tierkel (1959:193) stated that, in general, older animals were less suseptible to rabies infetion than juveniles.

27 18 CYCLIC RABIES INCIDENCE Shoening (1956:201) stated that rabies is a density dependent disease, the prevalene of whih is diretly related to the density of suseptible hosts. Numerous authors have related the seasonal peaks of rabies inidene to population peaks in foxes (Raush 1958:255; Marx and Swink 1963:172; Friend 1968:71) and in skunks (Parker 1961: ; Verts 1967: ). However, Verts (1967) wrote that other fators were involved in rabies peaks beause, even though skunk populations were at a high point, the rowding effets of winter lumping were at a minimum. Serakowa (1968) noted a rabies peak in European foxes during April and May, oiniding with the inreased stresses of estrus in females. Friend (1968: 82-93) demonstrated a peak inidene in New York foxes in late winter and early spring, a period of inreased movement arid food gathering. He. also reorded a lesser peak in the fall while family dispersal was ourring. Johnston and Beauregard (1969: ) noted two rabies peaks in Ontario red foxes. One ourred in females during Marh, oiniding with parturition. The other involved juvenile males and took plae in early fall, while this group was under the stress of dispersal. Sanderson et al. (1967:92) hypothesized the role of the stresses of latation and pregnany in the inreased suseptibility of female striped skunks. Peaks in bat rabies have been assoiated with the fatigue and stress of migration (Constantine 1967a:873; Friend 1968:92; Prior 1969:42). Johnston and Beauregard (1969:367) noted a three-year rabies yle in Ontario foxes. Prior (1969:31) suggested that suh yles might be attributed to rab1-es immunity aquired by the young from their mother.

28 19 The degree of immunity would derease with eah suessive litter, but several generations might pass before a population ould regain a high degree of suseptibility. In their disussion of disease yles Taylor and Knowelden (1964: 265) suggested different explanations based on the pattern of inidene. "Periodi reurrene" of a disease, normally at intervals of more than one year, was attributed to the density of suseptible individuals. Seasonal fators of stress.were presented as a possible explanation for disease peaks separated by approximately one year. SPATIAL RELATIONSHIPS IN WILDLIFE RABIES It has been demonstrated that rabies inidenes are not spread homogeneously over large land areas. They appear to be, in fat, lustered about ertain foi (Verts 1967 :164; Serakowa 1968). Little is known about the eologial reasons for the lustered patterns of inidene whih result. The movements of rabid wildlife are also relatively unstudied. Gier (1948:150) thought that rabid foxes.probably do not travel far.after de..., veloping rabies symptoms. He onluded that rapid spread of the disease would not be the result of only a few infeted individuals. Rabid skunks may travel up to three quarters of a mile or farther (Parker 1961:275). Storm and Verts (1966: ) stated that the movements of rabid skunks were not signifiantly different from those of noninfeted individuals of -similar age and sex. WILDLIFE RABIES REPORTING National rabies statistis are ompiled from animal inidene reports issued by individual state health departments. The researher

29 20 using suh reports as a basis for determining P!'ltterns of rabies ini"".'. ' ! dene should be aware of t:.he biases to whih they are subjept r'.,' Meyer (1955:4) stated that rural disease reporting depend1;> largely 1. upon the initiative of the individual owners of affeted an~mals. Con- '. $tantine (1967a:885) felt that reporting fre.iuepy with ~espet to wild-... life rabies is proportional to human p~pulation density. Prior (1969 :' 34) disagreed, asserting that the influene of individuaj. health offier13 would mask the effet of population density on reporting frequeny;... Wildlife rabies reporting is exellent in suddenly prominent.rabies areas (Parker 1961: 278), b.ut drops as the disease be,omes "old hat". ' Marx (1~66:119) ited loal news media as playing an. important.. role in.,,.... r!!lbies reporting. Parker (1961:278) disussed repor:ting bias with respet to speies. He stated that skunks, due to their t.mpleasant odor, were less likely than other wildlife speies to be submitted for 1abora""..... tory examination Wildlife are not submitted unless rather positiv symptoms have been demonstrated. The result is a relatively higher per-. entage of positive laboratory onfirmations in wildlife speies than in domesti animals (Prior 1969: 36"'.'.37). WILDLIFE RABIES CONTROL Aording to Meyer (1955:23), rabies ontrol in rural areas may be aomplished by two means,... supervised killing of wildh.fe to redue animal-to-animal ontats and.preinfetion vaination of domesti animals. With respet to wildlife population redution, Shnurrenberger et al. (1964:165) stated that "arithmeti redutions" in the density of. wildlife should. result in a "geometri redution of ontat probability." Assuming that this priniple does hold and that population redution is

30 21 helpful, a ertain knowledge of the proper degree of redution is neessary (l'ierkel 1954:1). Population redution may not be as effetive in the ontrol of wildlife rabies as was on;e thought. Marx (1966) indiated that Virginia's fox trapping program appears ineffetive and Nelson (1966) warned of instanes where trapping has been shown to stimulate reprodution. Rabies ontrol options other than trapping are open to ontrol agen:- ies. They inlude population redution by means of ontrolled poisons, hemosterilants, and wildlife rabies vaination (MLean, personal ommuniation 1969). All of these areas are relatively unexplored, however. Rabies ontrol requires intensive appliation of the seleted tehniques. The eonomi requirements of wildlife rabies ontrol, espeially. in wilderness areas, may make it impratial at the present time (Raush 1958: ). Unwise ontrol measures applied without thorough knowledge of their onsequenes may adversely affet deliate natural ommunities. Constantine (1967b:29) has warned of the severe eologial reperussions whih may result from the indisriminate destrution of bat aves as reservoirs of rabies vetors. MODELS AND SIMULATION The exploration of omputer modeling and its appliation to researh in industry and the sienes is a relatively new field, having been possible only with the reent advent of omputer systems of suitable storage apaity. In the few deades of the development of omputer simulation tehniques appliations to a number of fields have been oneived. These inlude urban planning (Wilson 1968; Forrester 1969), industrial engineer.- ing (Pritsker and Kiviat 1969; Pritsker and Burgess 1970), mediine (Meier et al. 1964; Priban 1968), general eology (Garfinkel 1962; Watt

31 ), forestry (O'Regan et ai. 1965; Newnham 1967); and fisheries management (Southward 1968). Orutt et al. (1961) used. an IBM 704 omputer to model the soial and eonomi strut.ure of Amerian om mere in minute detail.. Waggoner ani Ho-rsfall (1969) have written a. FORTRAN IV simula:tor of plant disease. The simulation of the managemerit of white-tailed deer herds by means of omputer has reently been explored (Hayne 1969; Riffe 1970). Davis (1967) onstrµted a general mathematial model, of deer herd management by the use of dynami linear p rogramming tehniques. Watt (19()8) disussed a ~ide variety of eologial omputer in~dels of popu:l.ation dynamis, dispersal, predation, anq disease. A omprehensive review.ofmodern omputer simulation tehniques is available in referenes by Churhi;nan et al (1957) and Naylor >et al. (1966). The earliest reorded attempts at modeling disease were made by William Farr in 1840 as ited by Bailey (1957:7-8); Farr suessfully fitted a normal urve to da:ta onerning the quarterly smallpox 4eath rate in England~. In he used the same urve-fitting tehnique to predit the ourse of a rinderpest outbreak in attle, but met little suess. The observed and predited urves were bell-shaped, but dis-. played little agreement. The basis of most future disease modeling work,,.. was provided by Hamer (1906).' He demonstratel that, in general, the ourse of an epidemi depended upon the number of SUl:!Ceptible individuals in a population and the ontat rate between infetives and suseptibles. The redution of susep~ibles by disease and slow subsequent inreases in the size of this group were presented as a possible ex'planation for the yli disease ourrene. Bailey (1957:8) ited the work of Soper

32 23 (1929) who attempted to explain reurrent epidemis. Soper's analysis was deterministi in nature, not allowing for variations due to hane. Bartlett (1957). used stohasti proesses for the same purpose~ and ahieved results agreeing more losely to atual data. Stohasti tehniques off er an added degree of omplexity to disease simulation. Bailey (i957:10) named MKendrik (1926) and Green"."' wood (1931) as early pioneers in stoha,sq. epidemi modeling. Bartlett (1957) presented a stohasti model of measles. Watt (1968: ) has. written a FORTRAN program whiq desribes the general disease model of Kermak and MKendrik (1927). His prog+am allows for additional fators inluding: 1) immigration and emigration 2) variable infetivity rates due to weather 3) up to four speies of animals 4) stohasti assumptions.... Reent mathematial models formea.suring the rate of spread of hypothetial epidemis to fixed groups of individuals have been onst.ruted by Raskey (1957) and Beker (1968). A omplete review of historial models used in the siene of epidemiology is presented by Bailey (1957) and Bartlett (1960). Rabies reservoirs ha.ve been demonstrated in several wildlife speies, notably skunks, foxes, and bats. Rabies inubation periods and symptoms are highly variable, but it has been hypothesized that a latent form of the disease is responsible for its interepizooti maintenane. The bite route is the major mode of virus transmission, but other methods are possible under onditions of-rowding and stress. Wildlife rabies ontrol

33 24 has been studied little and onsists of stopgµp, emergeny illeasures. Models of other infetious diseases have been suessful:j_y onstruted and have been most valuable in detennini~g researh and ontrol strategies. A similar model of rabies epidemiology might also serve to indiate priorities for suh strategies.

34 METHODS Two distint approahes were undertaken to desribe wildlife rabies epizootis. The first method used was to analyze health. department reords of onfi:qned rabies reports in several ounties where the disease had reahed epidemi proportions. The objetive of this approah was to desribe temporal and spatial relationships between rabies inidenes in wildlife populations. A. omparison of these patterns for similarities or di~fferenes between eologially dissimilar areas was intended to more losely pinpoint the fat9rs affeting the spread of rabies. A seond approah to the study of wildlife rabies was to onstrut a stohasti model of the disease, a simulation adapted to the eletroni digital omputer. Even above the preditive value of suh a model would be its value as an important heuristi devie for rabies study. With this heuristi objetive in mind, a simuli;ltion sheme was designed to be as general in nature as possible~ It was onstruted so that a minimum of reprogramm.ing woul;l be neessary in expan;ling the simulation to aommodate more wildlife speies, other possible transmission modes, modified inubation periods, or iteratively hanging probabilities. ANALYSIS OF.. RABIES. REPORTS Complete listings of positive laboratory rabies reports were obtained from three Virginia ounties (Bedford, Nelson, and Washington) seleeted for their high rabies inidene~ These reports were olleted. by staff of the Virginia Department of Publi Health under the supervision of Mr. John R. Bek, Bureau of Sport Fisheries and 25

35 26 Wildlife, Di vision of Wildlife Servies. They inluded the date and plae at whih the rabid animal was found, the name of the person submitting the speimen, and the species of the animal infeted. In addition, data from Imperial County, California, were obtained from the National Communiable Disease Center for analysis as a high rabies area of a vastly different eologial nature. Table III summarizes the ontent of these reports. The initial step in the analysis of the patterns of reported rabies inidenes for eah ounty was the plotting of eah rabies ourrene on a map and visual examination of the spatial arrangement of reports. Seondly, time patterns were analyzed on a traditional epidemiologi basis, the umulative perentage of the total rabies ases reported per week being graphed by ounty. Finally the time and spae relationships between reports were analyzed simultaneously by ounty, in an attempt to demonstrate signifiant patterns of "subsequent" and "preedent" reports as first explored by Shnurrenberger (1968). The times (days) and distanes (miles) from eah report to every other report ourring at a later date were reorded, then punhed on IBM ards. By means of a FORTRAN IV program (Appendix I) the relationship of every possible pair of reports was assigned a ategory based on the separation between them in time and distane. After every possible ombination of two reports had been lassified, the number of ombinations falling within the spatial and temporal separation limits of eah ategory were tabulated for eah ounty. The resulting figures

36 27. Table III. Summary of rabies laboratory reports used for analyses of time and spae relationships of inidenes in wildlife speies. County State Inlusive Dates No. Positive Reports Bedford Virginia to Nelson Virginia to Washington. Virginia to Imperial California to

37 28 were used in the onstrution of t,10 graphs for the display of the. patterns of time and distane separations between reports for the four areas studied. These graphs assumed the form of frequeny distributions, the dependent variables being the perentage of the total tabulations for eah ounty falling into eah time or distane separation lass. COMPUTER SIMULATION OF RABIES EPIDEMIOLOGY The simulation language seleted for the modeling of rabies epidemiology was GASP II (Pritsker and Kiviat 1969). The investigator had reently ompleted oursework with one of the authors of this language and was more familiar with this simulation tehnique than any other. At the time of this study the required GASP sub routines were operational in the V.P. I. omputing sys tern and easily aessible. Desription of GASP Simulation Language GASP II is a generalized ativity simulating program written in FORTRAN IV. Originally designed and doumented with referene to engineering appliations, it is non-speifi enough to be useful in the modeling of a wide variety of systems, e.g., rabies epidemiology. GASP II onsists of approximately 20 subprograms whih serve to advane time during the simulation, store and retrieve required information, monitor simulation progress, ollet and report measurements of system performane, and generate random variables. A omplet_e desription of the program and its onepts is presented by Pritsker and Kiviat (1969). The following desription will serve only to familiarize the reader with GASP

38 29 proedures siffiiently for understanding the rabies simulation. Definitions and General Approah to Simulation with GASP By simulation the programmer seeks to model a system or some part of reality whih is of interest. The system may be viewed as being omposed of entities and proesses. Entities are any physial parts of a system, suh as people, animals, or mahinery. Proesses are viewed best as the ativities in whih entities may engage and the means by whih entities may interat. Eah entity of a system is haraterized by a set of attributes. Attributes are harateristis of an entity whih may be quantified. Table IV illustrates an example of an elevator system. It may be seen that eah entity of the system is haraterized by a set of values (attributes). The attributes of any entity need not desribe it ompletely. They need only to be detailed enough to yield a simulation suffiiently realisti to meet the programmer 1 s requirements. An entity may be said to be in a partiular state when its attributes have speifi numerial values. The ation of an entity moving from one state to another is referred to as an ativity. An event takes plae at a point in time and either starts or ends an ativity. Events, like entities, have attributes. In fat, eah event must be haraterized by at least one attribute, the point in time at whih it is to our. Other event attributes may define the type of event and the attributes of entities affeted by this event. If "Elevator starts to travel" is an event whih may take plae in the system desribed in Table IV, it may have attributes suh as those listed in Table V.

39 30 Table IV. Definition of an elevator system in a building and its entities and attributes (from Pritsker and Kiviat 1969). Entities Attributes B~ilding Elevator Floor People Number of floorn. Distane between floors. Passenger apaity. Speed. Minimum stopping time at a floor, Current floor loation. Number of people waiting for ej,.evator. Probability that people will want to go to other floors given that they are on this floor. Arrival rate at building. Preferene for floors. Arrival rate of people on floor waiting to go up or down.