Epidemics 4 (2012) 211218

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Epidemics

j our na l ho me p age: www.elsev ier .com/

Local p mburrow

B.V. Schm c, J.a Faculty of Vetb Norwegian Vec Centre for Eco

a r t i c l

Article history:Received 18 JuReceived in reAccepted 17 DAvailable onlin

Keywords:Plague persistYersinia pestisMetapopulatioHotspots (mic

rsiniag for

servorable ecomes theot anpestisred fourve

cannot solely be explained by the existence of hotspots, and therefore other hypotheses, such as survivalin multiple host species, and persistence in eas or in the soil should be considered as well.

2013 Elsevier B.V. All rights reserved.

Introductio

The perspoorly undcaused thre2007; Gagethe diseasethroughoutStenseth, 2periods of tithe re-emerof more tha2010). Howwhich haveent absence(Davis et al

The etioterium ableform the laron its host

Corresponversity of Oslo

E-mail add1 These auth

1755-4365/$ http://dx.doi.on

istence and local re-emergence of bubonic plague iserstood. Bubonic plague is a ea-borne zoonosis thate pandemics in the past millennium (Bertherat et al.,

and Kosoy, 2005; Keeling and Gilligan, 2000). Currently, is still present in foci of wildlife rodent populations

the Americas, Africa and Asia (Salkeld et al., 2010;008). The disease can disappear from foci for longme before re-emerging. An example of this behaviour isgence of plague in Madagascar in 1991 after an absencen 60 years (Duplantier et al., 2005; Neerinckx et al.,ever, in the plague foci of Kazakhstan, Central Asia,

been monitored since 1949, shorter periods of appar- are more common, typically lasting about four years

., 2007b; Heier et al., 2011).logic agent of bubonic plague is Yersinia pestis, a bac-

to infect over 200 species of mammals, of which rodentsgest group (Gage and Kosoy, 2005). The effect of Y. pestisvaries; epizootics lead to high mortality in prairie dog

ding author at: Centre for Ecological and Evolutionary Synthesis, Uni-, Oslo, Norway.ress: Boris.Schmid@gmail.com (B.V. Schmid).ors contributed equally to this work.

populations (Biggins et al., 2010; Stapp et al., 2004), while blackrats (Rattus rattus; Duplantier et al., 2005), and great gerbils (Rhom-bomys opimus), the main host in Kazakhstan, are quite resistant tothe disease, although a substantial amount of genetic variation inresistance is alleged to exist within the gerbil population (Gage andKosoy, 2005; Ergaliyev et al., 1990a).

In this paper we will focus on the great gerbils in Kazakhstan.Speculation on how the bacterium is able to repeatedly re-emergein Kazakhstan after years of apparent absence has been ongoing forover half a century. A common suggestion on how the bacteriumcould persist in the region while appearing absent in its main host,is that during these times of absence it resides in alternative hosts orin hibernating eas (Eisen and Gage, 2008; Gage and Kosoy, 2005;Wimsatt and Biggins, 2009). Another suggestion is that the bac-terium continues to be present in the gerbils, but at a prevalencethat is too low to be picked up by the existing plague surveil-lance efforts (Davis et al., 2007b). Alternative hypotheses for plaguepersistence are survival of the bacterium in the soil (Ayyaduraiet al., 2008), in dead hosts (Easterday et al., 2011), or within liv-ing hosts during phases of decreased virulence of the bacterium(Wimsatt and Biggins, 2009). Finally, an intriguing possible mech-anism for plague persistence is that the bacterium survives duringinter-epizootic periods in small sub-regions which retain condi-tions favourable to its persistence, in so-called hotspots, plaguerefugia, or microfoci (Fedorov, 1944 as quoted in Davis et al., 2007b;Biggins et al., 2010; Hanson et al., 2006).

see front matter 2013 Elsevier B.V. All rights reserved.rg/10.1016/j.epidem.2012.12.003ersistence and extinction of plague in as, Kazakhstan

ida,c,,1, M. Jessea,1, L.I. Wilschuta, H. Viljugreinb,

erinary Medicine, Utrecht University, The Netherlandsterinary Institute, Norwaylogical and Evolutionary Synthesis, University of Oslo, Norway

e i n f o

ne 2012vised form 16 October 2012ecember 2012e 28 December 2012

ence

nrofoci)

a b s t r a c t

Speculation on how the bacterium Yeregion in Kazakhstan has been ongointheories is that plague persists in its rein which the conditions remain favouPrebalkhash region as a whole have ba metapopulation model that describminimum size of an individual hotspregion that would be required for Y. the combined area of hotspots requihave been missed by existing plague slocate /ep id emics

etapopulation of great gerbil

A.P. Heesterbeeka

pestis re-emerges after years of absence in the Prebalkhash half a century, but the mechanism is still unclear. One of their host (the great gerbil) in so-called hotspots, i.e. small regionsfor plague to persist during times where the conditions in thee unfavourable for plague persistence. In this paper we use

dynamics of the great gerbil. With this model we study thed the combined size of multiple hotspots in the Prebalkhash

to persist through an inter-epizootic period. We show thatr plague persistence is so large that it would be unlikely toillance. This suggests that persistence of plague in that region

212 B.V. Schmid et al. / Epidemics 4 (2012) 211218

To test whether such hotspots are a viable mechanism throughwhich plague can locally persist, we constructed and studied a spa-tial model based on the Prebalkhash plague focus in Kazakhstan.The model is a metapopulation model, in which each subpopula-tion consist2007a), witis to determa single hoan average the case wour objectivSize for singHeesterbeegreat gerbilto persist w

Backgroun

Biology of th

The PrebKazakhstanet al., 2007bof lake Balksikotrau plaand form than arid conbelow 20Precipitatioand the vegspecies (Ad

The maigerbil, R. oprows and adthem to surand Ghosh,features in chambers a2007; Prakavaries betwDavis et alchanges in occupied by100% (Davifamily groutheir immaduce 13 litoffspring infemale offspet al., 2005)

Fleas of atus, but adto feed on dominant vCoptopsyllagerbils predhottest monet al., 1963 are active inea genera year, and thby eas. Wwhile the l2007), the selves, due

the blood of the gerbil during a bacteremia (Perry and Fetherston,1997; Burdo, 1965). Infected eas can transmit the infection toother gerbils almost directly (through so-called early-phase trans-mission; Eisen et al., 2007), or through active regurgitation of the

ia fro

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mod, deaion, atep, tined

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(i.e. and t

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in ases oboves of a single great gerbil burrow system (Davis et al.,h its own infection dynamics. The objective of this studyine the minimum size needed for plague to persist in

tspot, or in a set of multiple hotspots, for the time ofinter-epizootic period (4 years, Davis et al., 2004). Inhere we study the minimum size of a single hotspot,e is analogous to determining the Critical Communityle homogeneously mixing populations (Diekmann andk, 2000), i.e. the critical metapopulation size of the

burrow system in Kazakhstan that is needed for Y. pestisithout invoking additional mechanisms.

d and model

e gerbils in the Prebalkhash region

alkhash region is the largest of the 10 plague foci in (Lowell et al., 2007). A well-studied sub-region (Davis; Kausrud et al., 2007) of this focus is located south-easthash, and consists of the Bakanas, Akdala and Sarye-ins. These plains together cover 150 km by 300 km,e study area to which our results apply. It experiencestinental climate with temperatures frequently fallingC in winter, and reaching more than 35 C in summer.n is less than 200 mm per year (Kausrud et al., 2007),etation cover is sparse, with a low diversity of plantdink et al., 2010).n plague host in the Prebalkhash region is the greatimus, a social burrowing rodent. Great gerbils live in bur-just their daily activity pattern to the season, enablingvive in the harsh climate (Kausrud et al., 2007; Prakash

1975). Burrows are relatively permanent and elaboratethe landscape, consisting of multiple entrances, foodnd nesting rooms (Addink et al., 2010; Kausrud et al.,sh and Ghosh, 1975). Their density in the Prebalkhasheen 2 and 7 burrows per hectare (Addink et al., 2010;., 2004). As a result of climatic, seasonal and annualpopulation size, the local fraction of burrows that is

a gerbil family uctuates between almost 0% to nearlys et al., 2004; Samia et al., 2011). Great gerbils live inps of typically one adult male, one or more females andture offspring (Randall et al., 2005). Adult females pro-ters each year, between April and September, with 47

each litter. All of the male and approximately half of thering migrate from the nest within 18 months (Randall.ll life stages predominantly reside in the burrow detri-

ult eas will also reside on gerbils for an hour a daytheir blood (Burroughs, 1947; Eisen et al., 2007). Theectors of Y. pestis are eas of the genera Xenopsylla and

(Rapoport et al., 2010). Adult Xenopsylla eas feed onominantly from spring to autumn, except during theths of summer, and hibernate through winter (Bibikovaas quoted in Samia et al., 2007). Adult Coptopsylla eas

autumn and winter (Ji-You, 1986). Some of the otherthat live within the burrows are active throughout theus the gerbils are effectively continuously parasitized

hen eas feed on the blood of a plague-infected gerbilatter is undergoing a bacteremic episode (Eisen et al.,eas become infected with the plague bacteria them-to the high concentrations of plague bacteria present in

bacter1914).

TheburrowjuveniacterizRandaroute ifeedinforagin2005; the dession ofoutbreregiondance the necbil famfractiothe bution wspreadmaticaresearcof thesmining(Reijni

Model

Theulationin spacreectsity of2010).ulationthe spegreat gand emodelone ofered/imto reinperiod

Theof birthdisperstime sdetermdetailswhichbils (i.gerbils1959),gerbilstion.

Theat timgerbilsproceslisted am the ea foregut into the gerbil (Bacot and Martin,

e two possible routes for the transfer of plague between gerbils and their eas. The rst is through infectedbils that migrate to another burrow. Migration is char-y its low frequency (once or twice in the life of a gerbil;al., 2005), and its relatively long distance. The secondough infected eas that drop off a gerbil after a bout ofile that gerbil is visiting another burrow during their

tivity, or as part of their social behaviour (Randall et al., et al., 2007b, 2008). If a large fraction of the burrows inystem is occupied by gerbil families, then the transmis-ue between burrows is more efcient, and a local plaguen result in an epizootic period in the whole Prebalkhashis et al., 2004). Davis et al. (2004) showed that the abun-hold for plague epizootics can indeed be expressed asry fraction of burrows that needs to be occupied by ger-

(or more precisely, the product of burrow density andoccupied burrows; Davis et al., 2008). In this regard,

and its possible occupants can be seen as a subpopula- a larger metapopulation (Davis et al., 2007a), and theague between the burrows can be characterized mathe-

a percolation phenomenon (Davis et al., 2008). Recents shown that besides gerbil occupancy, the ea burdenrbils also appears to be an important factor in deter-

percolation of plague through the Prebalkhash regiont al., 2012).

iption

ad of plague is studied in a spatially explicit metapop-el, whose subpopulations (the burrows) are structured

a regular square lattice. Such a lattice is assumed tover-dispersed distribution and relatively constant den-il burrows in the Prebalkhash region (Addink et al.,etapopulation model is based on an existing metapop-

del (Jesse et al., 2008), which has been tailored to meets of gerbil ecology. The model describes a population ofs living in burrows, and within each burrow the gerbilsre assumed to mix homogeneously. The gerbils in therience SIRS-type infection dynamics, and can thus be inollowing states: susceptible (S), infectious (I) or recov-ne (R). Recovered gerbils are only temporarily immuneon by plague, and regain susceptibility after a certainon et al., 2006; Park et al., 2007).el uses a discrete-time approximation of the processesth, recovery, and migration of gerbils, the process of eand the process of gerbil infection by infected eas. Eachhe number of births, etc., per burrow is stochastically

by discrete probability distributions (see Table 1 forhe distributions used). The time step is set to ve days,sponds to the typical incubation time of plague in ger-ing from S to I), and the minimal infectious period of

going from I to R) (Rivkus et al., 1973; Shmuter et al.,hus provides an upper limit in the model on how quicklyin the model can move through various stages of infec-

ber of gerbils per epidemiological state in a burrow x denoted by Sx(t), Ix(t), Rx(t) and the total number of

burrow x is given by Nx(t). The different gerbil and eaccur within each timestep in the order that they are. The order is articial, because all these processes are

B.V. Schmid et al. / Epidemics 4 (2012) 211218 213

Table 1All reported rates are per time step, and where a range is indicated, the rate changes according to a sine function (see Fig. 1). I: Randall et al. (2005). II: Korneyev (1968),Rudenchik (1967), Prakash and Ghosh (1975), Randall et al. (2005), and Frigessi et al. (2005). III: Biologically reasonable estimates based on the net growthrates reported inFrigessi et al. (2005). IV: Estimated from plague survival rates of gerbils with different levels of innate resistance in Ergaliyev and Pole (1990) and Ergaliyev et al. (1990b,a).V: Begon et al. (2006) and Park et al. (2007). VI: Erring on the high side of the 6.4% estimated by Eisen et al. (2007).

Parameter Denition Values

Summer value

m Migration rate of gerbils Bin(Sx + Ix + Rx , p- Fraction of eas that disperse from each burrow per timestep [0.1, 0.3] b Birth rate of gerbils Pois(), 0, 0du Death rate of uninfected gerbils Bin(Sx + Rx , p), p

Parameter Denition

dI Death rate of infected gerbilsr Recovery rate of infected gerbilsg Rate of loss of immunity in gerbils h Transmission chance from ea to gerbil, per infected ea per day T Time step of model

continuous in reality. However, in a discrete model it is necessary toimpose an order of events, such that the probabilities of e.g. dyingor recovering, are consistently applied to the correct number ofindividuals, and to ensure that biological constraints such as theminimal incubation time of infected individuals are respected. Themodel can be written as a set of stochastic difference equations:

Sx(t + 1) = Sx(t) + bNx(t) duSx(t) Sx(t)+ gRx(t) mSx(t) + MS(x, t), (1)

where b is a seasonal per capita birth rate, du is the death rate foruninfected gerbils, g the rate at which gerbils lose their immunity,m the per csusceptiblemigration ret al., 2005)tions, whosTable 1 for

Fig. 1. Simplidynamics. Foumodel. Gerbil disperse fromactivities (blueuninfected gerthe implemenmodel assumeon the 1st of Areferences to cof the article.)

The probinfected ththe model b

= 1 (1 where h is ttion to the gof infected age numberassumptionthe availabminus the cby any of th

T = 5 modred g

1) = 1) =

the pted g

aliyeent

probactiod toeter ma

and d hot balkigessapita migration rate, and Ms(x, t) gives the number of gerbils migrating into burrow x. The birth, death, andate are seasonal in reality (Frigessi et al., 2005; Randall, and are implemented as discrete probability distribu-e parameter values vary during the year (see Fig. 1 anddetails).

(whereThe

recove

Ix(t + Rx(t +whereof infecby Ergimplemwith abe a frroundeparamare sumFig. 1,

Thethe Preogy (Fred model implementation of seasonal effects on the gerbil populationr gerbil parameters have seasonal effects assigned to them in thebirth rate (green), migration rate (black), and the fraction of eas that

each burrow per timestep, as a result of gerbil foraging and social) have their peak rate during the summer season. The deathrate ofbils (red) has it peak rate during the winter season. Further details ontation of these seasonal effects are listed in the text and in Table 1. Thes a constant annual cycle, consisting of a 5 month summer, startingpril, followed by a 7 month winter season. (For interpretation of theolour in this gure legend, the reader is referred to the web version

Its seasonaquately desalternated bples of the birthrate ofautumn, buwhich is limpopulation cited in Frigbils is predoand fall, andeath of ththe winter ed) periodet al., 2005Sources

Winter value

), p [0, 0.033] 0 I0.1 II

.077] 0 III= 0.007 Bin(Sx + Rx , p), p [0.007, 0.044] III

Year-round value Sources

Bin(Ix , p), p = 0.086 IVBin(Ix , p), p = 0.52 IVBin(Rx , p), p = 0.037 V0.1 VI5 days

ability that a susceptible gerbil in a burrow becomesrough eabites from infected eas is approximated iny the equation

h)TIf (x,t)/Nx(t), (2)

he chance that a single infected ea transfers the infec-erbil during its daily feeding bout and If(t) is the numbereas in burrow x. The fraction If(x, t)/Nx(t) gives the aver-

of infected eas foraging on a gerbil at time t. Under the that the infected eas are uniformly distributed overle gerbils, the probability can be approximated as 1hance that a susceptible gerbil does not become infectede infected eas feeding on it during T consecutive days).el equations that govern the number of infected anderbils per burrow are:

Ix(t) + Sx(t) rIx(t) dIIx(t) mIx(t) + MI(x, t), Rx(t) + rIx(t) gRx(t) duRx(t) mRx(t) + MR(x, t),

(3)

er capita recovery rate is denoted by r and the death rateerbils by dI. Both parameters are based on observations

v and Pole (1990) and Ergaliyev et al. (1990a,b), and areed in the model as binomial probability distributionsability p of 0.52 and 0.086, respectively. Because cann, the number of newly infected gerbils ( Sx(t)) is

a natural number using a Bernoulli distribution. Thevalues, their probability distribution, and their sourcesrized in Table 1. The effects of seasonality are shown iniscussed in more detail below.summers and cold winters of the continental climate inhash region have a large impact on the local gerbil ecol-i et al., 2005; Stenseth et al., 2006; Kausrud et al., 2007).

l inuence on the local gerbil population can be ade-cribed by a 5 month summer period starting in spring,y a 7 month winter period (Frigessi et al., 2005). Exam-effect of seasonality on the gerbil population are the

gerbils, which is larger than zero between spring andt is zero during the winter months; their death rate,ited during the summer months, but kills 65% of the

during the winter months (Prakash and Ghosh, 1975 asessi et al., 2005). Similarly, migration of juvenile ger-minantly successful if migration occurs between springd is otherwise frequently associated with a prematuree migrating gerbil (Randall et al., 2005). Finally, duringseason, the gerbils have a shorter (but not well quanti-

of day-time activity (Prakash and Ghosh, 1975; Randall; Frigessi et al., 2005), foraging less outside (instead

214 B.V. Schmid et al. / Epidemics 4 (2012) 211218

depending more on stored food; Kelt, 2011), and thus interact lesswith neighbouring burrows. The exact shape of the relationshipbetween seasonality and many of the aspects of gerbil life in the Pre-balkhash region is not known, and therefore we have implementedthe impact sonal effectand winter,deathrate, mthat is applthat is appr0 that rdeclining afunction pein the Prebaate betweenthe model aand alwaysof spring (FApril.

We assuin temperabecause thedetritus of ta stable soutially bufferthat inter-asome degreplague (Stenare less welreduce ovein Stensethsistence wigerbils still of new gerb

There is rate or the there is disaof antibodieopted to coprocesses (model, the et al., 2006)

The modburrows spha. This is 0.844.84 bis a suitablareas wherea density of othreshold fo2010), whicsize of the sto 150 m 12000 m 20

We detions remaithe conditiounfavourabwithin a hotive to ventinteract withotspot. Unin a model tions with tboundariesthe hotspot

vailabDavis udencxpresw disents

h ason oratio), askhass in tIn the

to a withed torrow

the med tothat bns ofs). Ationquil

(Fright s of eulatil are

nd gr assume a constant number of 100 eas per gerbil, and thusmber of eas Nf(t) in a burrow at time t is given by 100Nx(t),

Nx(t) is the number of gerbils in burrow x at time t. ea population size within a burrow after the process ofpersal to neighbouring burrows is modelled as follows: rstocesses that inuence the number of gerbils per burrowantied. Subsequently, the ea population size per bur-

calculated from the number of gerbils in each burrow (seey above), and the fraction of these eas that are infectedlague is calculated based on the number of infected ger-esent in each burrow (see below, Eq. (4)). Finally, the eation of infected and uninfected eas within each burrow issed to neighbouring burrows, by means of the foraging andehaviour of gerbils (Randall et al., 2005; Davis et al., 2007b,

The model assumptions are that each burrow distributes a fraction (dependent on season, see Table 1 and Fig. 1) of its

neighbouring burrows within a Manhattan distance of tworegardless of the occupancy state or the number of neigh-of the burrow (burrows on the edge of a lattice have fewerof seasonality in the model by applying a simple sea- on four gerbil parameters that vary between summer

and are important for disease transmission (birthrate,igration rate, and foraging rate). The seasonal effect

ied in the model to these parameters is a constant rateopriate for that season, or a sine function with domaineaches a maximum halfway through the season beforegain (see Table 1 and Fig. 1 for a specication of ther parameter). Although the start of the summer seasonlkhash, and the extremity of the seasonality will uctu-

years with climate uctuations (Kausrud et al., 2010),ssumes no variation in the seasonality between years,

starts the 5 month summer season at the beginningrigessi et al., 2005), which we interpreted as the 1st of

me in this model that the effect of seasonal variationture and humidity on ea ecology can be neglected,se eas reside on the warm-blooded gerbils, or in thehe burrow microclimate (Ben Ari et al., 2011), and haverce of food (gerbil blood), and are thus at least par-ed from the effects of seasonality. It has been shownnnual uctuations in the temperature and humidity toe affect ea ecology and the ability of eas to transmitseth et al., 2006), but the effects on a seasonal timescale

l-described in the literature. If low temperatures indeedrall ea activity levels (Bibikova et al., 1963 as quoted

et al., 2006), then the effect would be that plague per-thin a burrow in winter would become less likely, asclear the disease at the same rate, but the infection rateils would be lower.no information available that indicates that the recoverydeath rate of infected gerbils depends on season, butgreement in the literature on whether the rate of decays that confer immunity to plague is seasonal. We havenservatively chose that as with the other within-bodyrecovery rate and death rate of infected gerbils) in theloss of immunity in the model is not seasonal (Begon.el describes the population of great gerbils living in

aced 50 m apart, resulting in a density of 4 burrows perat the higher end of the Prebalkhash density range ofurrows per hectare according to Davis et al. (2008), ande choice for the burrow density of putative hotspots:

the burrow density is high, will more frequently haveccupied burrows that is above the necessary percolationr plague transmission (Davis et al., 2008; Addink et al.,h facilitates the persistence of plague in the area. Thetudied lattices range from 3 3 burrows (corresponding50 m, or 2.25 ha) to 40 40 burrows (corresponding to00 m, 400 ha).

ne a hotspot as a small region in which the condi-n favourable for plague to persist during times wherens in the Prebalkhash region as a whole have becomele for plague persistence. We assume that gerbils livingtspot during an inter-epizootic period have little incen-ure outside the hotspot, as there will be few gerbils toh, and few foraging opportunities to exploit outside theder these circumstances, a hotspot can be representedsystem as an independent region, without any interac-he outside world. We therefore treat the burrows at the

of a modelled hotspot as having no neighbours outside: the gerbils in these burrows still migrate and forage

Fig. 2. Agerbils (1968; Rgerbils, ein burroexperim

as mucattenti

Mig(Fig. 2Prebalstanceshow. burrowstatus)assumvisit bu

In assumsize of fractioburrowpopulato an eburrowtion mperiodbil popsurvivaeas afurthethe nuwhere

Theea disthe prare qurow isdirectlwith pbils prpopuladispersocial b2008).uniformeas tosteps, bours le distance and frequency information on foraging and migration inet al., 2008; Randall et al., 2005; Begon et al., 2006) and eas (Korneyev,hik, 1967). Capture-recapture data on the daytime travel distance ofsed in metres (top x-axis) and in the corresponding distance expressedtance (bottom x-axis), based on the average burrow density on thesite.

the gerbils elsewhere in the hotspot, but divide theirver fewer burrows.n of the great gerbil is typically limited to 100500 m

capture-recapture experiments of R. opimus in theh region (Begon et al., 2006), and under similar circum-he Kyzylkum desert (Uzbekistan; Randall et al., 2005)

model, migrating gerbils are moved from their original randomly chosen burrow (independent of occupancyin 110 steps on the model grid. Migrating gerbils are

move instantly from one burrow to another and do nots or change infection status while migrating.odel, the ea population size within a burrow is

be in a quasi-steady state with the gerbil populationurrow (that is, prior to the ea-dispersal process, where

the ea population are exchanged with neighbourings eas have a short lifespan compared to gerbils, the eas within a burrow will generally quickly adjust in sizeibrium state that reect the number of gerbils in thatigessi et al., 2005; Krasnov et al., 2002). This assump-not be valid outside hotspot regions, specically duringxplosive growth and catastrophic collapse of the ger-on. However, within hotspots the conditions for gerbil

supposed to be more stable, and thus the number oferbils could generally be in this equilibrium state. We

B.V. Schmid et al. / Epidemics 4 (2012) 211218 215

neighbours). Furthermore, twice as many eas are distributed toburrows at a distance of one step, as are distributed to burrows ata distance of two steps. The resulting ea dispersion of this imple-mentation is similar to observed experimental results (Korneyev,1968; Rudeber of eas burrow thebecome infe

The innafrequency wduring an intion (KorneHigher levequency of bthe numbergerbil. Whedocumente2005), due tof the ea balkhash, Beliminate ththe bacteriais thereforeber of infecbeen appro

If (x, t) = 10

where If(x, t, Ix(t) the nis a phenomparameter vof infected prevalences2004; Ergal(Bibikova a

Results

We denremain favoconditions unfavourabconditions was a hotspostructed. Thplague extirates at whiInitial simuwith a high correspondbefore recowas introduthe start ofprevalence and peakedthe reporteburrows wi20% in the mmum plagu(Sviridov anwell reect

In roughin spring fatypically di(Fig. 3), wit

istogbasedwith aty in r

alf o entions

stumulametare d

tha is basimuimulion ttions

t size

r excluding simulations where plague failed to establishFig. 3), the relationship between plague persistence andt size becomes apparent: larger eld sizes lead to a largern of the simulations in which plague persisted for longers (Fig. 4). In about 5% of the hotspots of 40 40 burrowsa), plague persisted until March 1st of the subsequent year.er, for plague to persist within a single hotspot for multi-rs, the hotspots would have to be bigger, or the conditions

a hotspot would have to be more favourable then a gerbil of 10 gerbils per burrow, and a rate of loss of immunity ofred gerbils of 4.5 months.

density and loss of immunity

h an average gerbil density of 10 gerbils per burrow andrage loss of immunity of 4.5 months, the probability wasat plague could persist for a year or longer in any area ofa. At higher gerbil densities, and with a faster loss of protec-munity, multi-year persistence of plague became possible: adensity of 1824 gerbils per burrow, and a loss of protectiveity within 23 months, would lead to a probability of plagueing for more than 1 year of >1%, even in small areas of just

burrows (Fig. 5a). However, only at the largest simulatednchik, 1967 as quoted in Davis et al., 2007a). The num-per burrow after their dispersal is used to calculate per

probability that susceptible gerbils within the burrowcted by infected eas (Eq. (2)).te level of plague resistance of R. opimus determines theith which gerbils experience episodes of bacteremia

fection with plague, as well as the duration of the infec-yev, 1968; Rudenchik, 1967; Prakash and Ghosh, 1975).ls of innate plague resistance reduces both the fre-acteremia, and the infection duration, and thus lowers

of eas that are likely to become infected per infectedn infected, the rat ea Xenopsylla cheopis has a well-d median survival time of only 2 weeks (Lorange et al.,o starvation caused by a blockage formed in the foregutby Y. pestis. For the dominant ea species in the Pre-ibikova and Klassovskii (1974) report that these eithere plague bacteria in 23 weeks, or become blocked by

and die within 112 days. The number of infected eas expected to adjusts itself relatively quickly to the num-ted gerbils within each burrow. This relationship hasximated in the model by

0aIx(t)E, (4)

t) is the number of infected eas in burrow x at timeumber of infected gerbils in burrow x at time t, and Eenological constant for level of plague resistance. Thealues a = 0.11 and E = 0.4 are chosen to tune the numbereas such that the equation ts the observed plague

and plague-related death rate in gerbils (Davis et al.,iyev and Pole, 1990; Ergaliyev et al., 1990b,a) and easnd Klassovskii, 1974).

ed hotspots as small regions in which the conditionsurable for plague to persist during times where thein the Prebalkhash region as a whole have becomele for plague persistence. To study how favourable theithin a region need to be in order for that region to act

t, a spatially explicit metapopulation model was con-is model was used to repeatedly record the time untilnction for different hotspot sizes, gerbil densities, andch recovered gerbils lose their immunity against plague.lations were conducted for a small area of 100 burrows,average gerbil density of 10 gerbils per burrow (whichs to 40 gerbils per ha) and an average time of 4.5 monthsvered gerbils lost immunity (Park et al., 2007). Plagueced on time t = 0, which in the model corresponded to

springtime (April 1st). Under these conditions, plaguein gerbils was on average 11.15% during the outbreak,

at at most 6%. These prevalence levels are in line withd plague prevalence in the eld (Davis et al., 2004). Inth infected gerbils, plague prevalence in eas reachedodel, which corresponds to observations on the maxi-

e prevalence in eas in infected burrows in Kazakhstand Ilinskaya, 1967). In this regard, the model appears to

the prevalence of plague in the Prebalkhash focus.ly half the simulations, the initial introduction of plagueils to establish itself for a longer period of time, andes out within a month after a short epidemic periodhout spreading throughout the entire hotspot. In the

Fig. 3. H(25 ha), ulation immuni

other hout theconditwish toonly siin the therefofor lessresultsber of 1000 sextinctsimula

Hotspo

Afteitself (hotspofractioperiod(400 hHowevple yeawithindensityrecove

Gerbil

Witan ave40 timesteps), and an upper limit of 5000

(including those that went extinct early).

216 B.V. Schmid et al. / Epidemics 4 (2012) 211218

Fig. 4. Plague persistence as a function of eld size. Black lines denote the fractionof major plague outbreaks, from the start of the outbreak on April 1st in a given year,that persist until November 1st, December 1st, . . ., to March 1st the subsequent year,for different hotspot sizes. Gerbil density is 10 gerbils per burrow, and recoveredgerbils lose their immunity in on average 4.5 months.

hotspots (4there a smaan entire in

How many h

For hotsPrebalkhashto maintainthe bacteriuPrebalkhashfor the full dsist in the Plarge numbthe fact thaduring intethese hotsp

Fig. 6. Relative hotspot area in the study region that is necessary for plague per-sistence. Given the chance that plague persists for Y years in a single hotspot ofparticular size, the number of hotspots necessary to have a 95% chance that plaguepersists can be calculated, and the total hotspot area plotted as the percentage of thetotal area of the Bakanas, Akdala and Saryesikotrau plains. Plotted for hotspot sizesup to 400 ha, under high gerbil densities (23 gerbils/burrow), and a short period ofadaptive immunity (2 months).

, comnoue as

eter 2 mgle a

at leFig. 6sily pned sb-resh coeast

requer co

migal large number of gerbils in these hotspots compared to

Fig. 5. The conprobability of immunity, wh00 ha), and under the most favourable conditions wasll probability (0.1%0.5%) that plague would persist forter-epizootic period (>4 years, Fig. 5b).

otspots?

pots to be a mechanism of plague persistence in the region, it is not necessary that a single hotspot is able

plague for four consecutive years. During an epizootic,m will probably seed multiple hotspots throughout the, and only one of those hotspots would need to persisturation of the inter-epizootic period for plague to per-

rebalkhash region in general. However, although a veryer of hotspots could t within the Prebalkhash region,t plague was not detected by the surveillance effortsr-epizootic periods implies that the combined area ofots (which would contain a much higher density of

gerbilssmall e

If wparamnity inin a sinthat inyears (can eacombi(the subalkhain at lwouldtogethplagueunusutour plot in (a) shows the probability of plague persistence for one year in a metapopulaplague persistence for four years in a metapopulation of 40 40 burrows (400 ha). The x-ere a rate of 0.037 corresponds to an average duration of immunity of 27 time steps, i.e., 4pared to their surroundings; Frigessi et al., 2005) isgh to evade detection.sume the most favourable conditions of our testedrange (e.g. 23 gerbils per burrow and a loss of immu-onths), the probability that plague persists for Y yearsrea of size S can be transformed into a 95% probabilityast one of N hotspots of size S, plague persisted for Y). Doing so reveals that under these conditions, plagueersist for 1 year in hotspots that cover only 0.02% of theurface of the Bakanas, Akdala and Saryesikotrau plainsgion of 3.68 million ha (Davis et al., 2007b) of the Pre-nsidered in this study). However, for plague to persist1 hotspot during an inter-epizootic period of 4 yearsire a high number of large hotspots (300400 ha) thatver between 4.525% of these 3 plains (Fig. 6). Althoughht frequently be missed by sampling in a hotspot, thetion of 10 10 burrows (25 ha) and the contour plot in (b) shows theaxis in both plots shows the rate at which recovered gerbils lose their.5 months. On the y-axis the number of gerbils per burrow is shown.

B.V. Schmid et al. / Epidemics 4 (2012) 211218 217

the surrounding terrain would have been noted and documented.Under a more moderate set of parameters (lower gerbil density,longer duration of immunity), the total area of the study area thatwould have to act as a hotspot would only increase: if we repeatour calculatan immuniwould alreaof plague ho

Discussion

Based othat under fraction (>3a hotspot, ftence throuconditions fbalkhash reof gerbils thundoubtedl

The maithe winter plague are ics, as thereinfected e1975; Randnew gerbilssusceptibleduring the wbetween budata, we asschance of pmostly dueat the start persist unti

In the mhotspots woplague resipopulation inter-epizoof innate plthis assumpsurements models (Fisexample thria within owhether a lor detrimenon the balaplague tranpopulation rate.

There arplague pers

Dynamic ant of a hmove throthe next (et al., 199the infectbe very simsistence owithin-butle foragin

for plague persistence that occurs during the winter season instationary hotspots would likely apply to dynamic hotspots aswell.

Slow-down of plague dynamics in winter: the within-burrowtion ulate

inderbilof imumm, 200thesestageive th

hiberbilsinterstene tra

distag in t., 201ty threlatentlof inry rersist

pots pots.d be).

onclf inteouldle w). Hoant rmechs suril of h tobalkncy t

wled

wou for Qking

nces

E.A., Duse of ote Sejev, Aties in598.ai, S., -term287

.W., Mague b., Kla. Epizases 1ions for a gerbil density of 17 gerbils per burrow, andty that lasts 3 months, a 2-year inter-epizootic perioddy require that 32% of the Prebalkhash region consiststspots.

n the model simulations (Fig. 6), it has become clearnormal parameter conditions an unrealistically large2%) of the Prebalkhash region would have to act likeor hotspots to be the sole mechanism of plague persis-gh inter-epizootic periods. Even under very favourableor plague persistence between 4.5% and 25% of the Pre-gion would have to act like a hotspot. The high densityat need to be present for this in such hotspots wouldy have been noticed by the existing surveillance efforts.n bottleneck for plague persistence in the model isperiod (Fig. 3), during which the infection dynamics oflargely conned to the within-burrow plague dynam-

is no migration and less foraging by gerbils by whichas could spread to other burrows (Prakash and Ghosh,all et al., 2005; Frigessi et al., 2005). Furthermore, no

are born during winter, and thus the only source of news is recovered gerbils that lose their immunity to plagueinter months. Because of the lower levels of interactionrrows in winter (which, due to the lack of quantitativeumed to be 3-fold lower than in summer), the increasedlague persistence in larger simulated hotspots (Fig. 4) is

to the larger number of burrows with infected gerbilsof winter, which makes it more likely that plague willl spring in at least one of them.odel we assumed that the great gerbil population withinuld consist of gerbils with a uniform high level of innate

stance, because the prolonged exposure of the gerbilwithin a hotspot to plague (both during and betweenotic periods) would have likely selected for a high levelague resistance (Gage and Kosoy, 2005). In future work,tion could be tested by combining experimental mea-on plague vulnerability with plague infection dynamiccher et al., submitted for publication), to elucidate fore role of older gerbils in maintaining the plague bacte-therwise highly resistant gerbil populations. However,arger diversity in innate resistance would be benecialtal for plague persistence is not clear, and will dependnce between its positive effect on between-burrowsmission during winter, and its negative effect on thedensity of gerbils in general due to a higher mortality

e several other factors that could also be argued to affectistence by means of hotspots:

hotspots: unlike stationary hotspots, the dynamic vari-otspot would not be tied to a single location, but wouldugh the Prebalkhash focus from one favourable area toFedorov, 1944 as quoted in Davis et al., 2007b; Rohani7; Sherratt and Smith, 2008). However, during winterion dynamics of plague within a dynamic hotspot would

ilar to that of plague in a stationary hotspot, as the per-f plague during winter is predominantly determined byrrow disease dynamics, as there is no migration and lit-g activity (see Table 1). Therefore, the strong bottleneck

infecformsomeFor gloss the set al.that tive survafterin gein wpersi

Plagulonglivinet alsibiliin a frequport theoto pehotshotssprea2010

In cnism othey wand ro(Fig. 6domintional such athe soresearcthe Prefreque

Ackno

WeCentrefor ma

Refere

Addink, The Rem

Aikimbaliari593

AyyadurLong2865

Bacot, Aof pl

Begon, M2006Disedynamics presented in this metapopulation model ared as being independent of season. There are howeverications that this might be a too stringent assumption.s, Park et al. (2007) has reported an up to 5 times fastermunity in gerbils during the winter period than duringer period, although this nding is still disputed (Begon6). For Xenopsylla eas, Gage and Kosoy (2005) reports

eas might survive their plague infection in an inac- through winter. How frequently infected eas woulde winter, and whether these eas are still infectiousrnation is unknown. Both an increased loss of immunity

and an increased chance of survival for infected eas would have a positive effect on the chance of plaguece within a burrow through winter.nsfer between hotspots: plague can be transported overnces via infected eas carried by predators and birdshe Prebalkhash region (Aikimbajev et al., 2003; Heier1; Wimsatt and Biggins, 2009). This opens up the pos-at during an inter-epizootic period, plague can persistively small number of hotspots, if these hotspots arey re-infected by each other through long-distance trans-fected eas. Plague transfer between hotspots would induce the total number of hotspots needed for plague

through an inter-epizootic period, as newly infectedcompensate for the loss of existing plague-infected

A similar mechanism has been suggested for plaguetween prairie-dog towns in Colorado (Salkeld et al.,

usion, for plague hotspots to be the primary mecha-r-epizootic plague persistence in the Prebalkhash focus,

have to be so numerous and large that their existenceould be self-evident from plague surveillance effortstspots alone are therefore unlikely to have played aole in plague persistence in the Prebalkhash, and addi-anisms are needed if Y. pestis is to persist in this focus,vival in alternative host species, survival in eas, or ingerbil burrows. It is an interesting problem for future

analyze the ability of current surveillance practices inhash region to discover hotspots of the minimal size andhat we estimate to be necessary for plague persistence.

gment

ld like to thank our colleagues at the Kazakh Scienticuarantine and Zoonotic Diseases, Almaty, Kazakhstan,some of the Russian literature accessible to us.

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Local persistence and extinction of plague in a metapopulation of great gerbil burrows, KazakhstanIntroductionBackground and modelBiology of the gerbils in the Prebalkhash regionModel description

ResultsHotspot sizeGerbil density and loss of immunityHow many hotspots?

DiscussionAcknowledgmentReferences