Predicting the rate of invasion of the agent of Lyme disease Borrelia burgdorferi

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1 Journal of Applied Ecology 2013, 50, doi: / Predicting the rate of invasion of the agent of Lyme disease Borrelia burgdorferi Nicholas H. Ogden 1 *, L. Robbin Lindsay 2 and Patrick A. Leighton 3 1 Zoonoses Division, Centre for Food-borne, Environmental & Zoonotic Infectious Diseases, Public Health Agency of Canada, Saint-Hyacinthe, QC, Canada; 2 Zoonoses & Special Pathogens Division, National Microbiology Laboratory, Public Health Agency of Canada, Winnipeg, MB, Canada; and 3 Faculte demedicine veterinaire, Universite de Montreal, Saint-Hyacinthe, QC, Canada Summary 1. Identifying invading tick populations provides early warning for emerging tickborne diseases that are expanding their geographic range. But how fast do tickborne pathogens invade after ticks become established? 2. Surveillance data for the tick Ixodes scapularis and the agent of Lyme disease Borrelia burgdorferi in southern Canada, an area where these species currently are invading, revealed a space-time cluster of ticks of low B. burgdorferi infection prevalence in southern Quebec signalling the location where tick populations became established beginning in The cluster disappeared in 2009, indicating a 5-year gap between tick and B. burgdorferi invasion. 3. Simulations of a model of I. scapularis populations and B. burgdorferi transmission identified numbers of immigrating ticks, rather than host density and diversity, as key determinants of the speed of pathogen invasion after ticks become established. 4. Greater numbers of immigrating infected nymphs would be expected in Central compared with Eastern Canada because nymphal and larval ticks in source populations in Midwestern USA are active in spring when migratory birds can carry ticks north. Whereas in northeastern USA, tick populations that are sources for immigrating ticks for Eastern Canada have active nymphs, but few larvae are active in spring. Consequently, we hypothesized that a 5-year gap would occur between tick and B. burgdorferi invasion in Eastern Canada, but a much shorter gap would occur in Central Canada. 5. Consistent with this hypothesis, analysis of surveillance data revealed clusters of ticks with low infection prevalence of 5 years duration in locations in Eastern Canada where I. scapularis is invading, but a nonsignificant cluster of only 3-year duration in regions of Central Canada where I. scapularis is invading. 6. Synthesis and applications. We have identified the speed at which the pathogen Borrelia burgdorferi invades following the invasion of the tick Ixodes scapularis, and that the synchrony of larval and nymphal tick activity in spring is a key factor determining the gap between tick and pathogen invasion. This has immediate application in interpreting imminence of Lyme disease risk when surveillance identifies emerging tick populations in Canada. It also has general application in predicting of the speed of invasion of emerging tickborne pathogens elsewhere in the world. Key-words: Borrelia burgdorferi, emerging infectious disease, invasion, Ixodes scapularis, surveillance Introduction Arthropod species that are vectors of disease, and the pathogens they carry, are of increasing concern for public *Correspondence author. nicholas.ogden@phac-aspc.gc.ca and animal health as invasive species in the context of climate and other environmental changes (Mainka & Howard 2010). A number of key invasion events have occurred in recent decades, including northward expansion of the range of Bluetongue virus in Europe (Purse et al. 2005), introduction and spread of West Nile virus in North America Reproduced with the permission of the Minister of Health

2 The rate of invasion of the agent of Lyme disease 511 (Kilpatrick 2011), introduction of Chikungunya virus into Italy (Angelini et al. 2008), and emergence of Lyme disease risk in Canada (Ogden et al. 2009). Detailed knowledge of the ecology of the invader and the invasion process (Ogden et al. 2008a; Epanchin-Niell & Hastings 2010) is required to predict invasion patterns, and design key public and animal health responses of surveillance, prevention and control (Ogden et al. 2008a). For emerging Lyme disease risk in Canada, we have extensive knowledge of the ecology of the Lyme disease system and a 20 year time series of passive surveillance data for the tick vector Ixodes scapularis Say, which comprises submissions of ticks by members of the public via medical and veterinary clinics (Ogden et al. 2006, 2010). Ticks dispersed from tick populations by hosts such as migratory birds are also detected by the system, which limits its specificity for identifying the location of established reproducing tick populations (Ogden et al. 2006, 2008b). However, by more detailed analysis of the numbers of ticks submitted per unit population (Koffi et al. 2012), or by detecting space-time clusters of ticks with low prevalence of infection with the bacterial agent of Lyme disease Borrelia burgdorferi Johnson (emergent I. scapularis populations being initially B. burgdorferi-free: Ogden et al. 2010), we can identify the spatio-temporal occurrence of emerging tick populations more precisely (Ogden et al. 2010; Leighton et al. 2012). Lyme disease is emerging in Canada because I. scapularis is expanding its range into and across Eastern and Central Canada (Ogden et al. 2009). In the absence of an effective vaccine, public health responses involve providing information on prevention, control, diagnosis and treatment to the public and healthcare practitioners targeted to the geographic locations where first the tick, and then B. burgdorferi have invaded the local woodland/ ecotone communities. We have developed a number of tools to assist in identifying likely or actual risk locations, including predictive risk maps (Ogden et al. 2008a). More recently, we have estimated the rate at which tick populations are invading, and identified environmental factors affecting that rate (Leighton et al. 2012). With these two tools, we now have a clear picture of where and when tick vector populations will establish. An important additional piece of information required, however, is how long it takes B. burgdorferi to invade the locations where the tick populations have become established. B. burgdorferi infection prevalence within host-seeking ticks, as well as tick abundance and/or occurrence, is a key determinant of public health risk from Lyme disease. Early identification of emerging tick populations provides an early warning for Lyme disease risk emergence, but how early is that warning, and how long will it take before nymphal tick infection prevalence values reach those (>20%) associated with the high Lyme disease incidence seen in northeastern USA? In Eastern Canada, tick populations establish free of B. burgdorferi infection because: (i) a threshold abundance of ticks in newly established populations must be reached before the basic reproduction number for B. burgdorferi can rise above unity (Norman et al. 1999); (ii), in Eastern Canada B. burgdorferi invasion may be inherently less rapid than tick invasion because of the life cycle and seasonal activity of the ticks (Fig. 1). Ticks invade northwards by being carried on migratory birds (and possibly some mammals) moving north in springtime when nymphal ticks are active but very few larval ticks are active (Ogden et al. 2008a,b). Any infected nymphal ticks engorging on migratory birds will moult into adults, which will feed mostly on reservoir-incompetent whitetailed deer Odocoileus virginianus Zimmermann (Telford et al. 1988), so this route of B. burgdorferi invasion is severely limited or a dead end. Some migratory bird Fig. 1. A diagram of the Ixodes scapularis life cycle (solid lines) and Borrelia burgdorferi transmission cycle (broken lines). Stages that are carried into Canada by hosts in spring are indicated by bird symbols. The inset shows stylized annual seasonal activity patterns of immature I. scapularis in northeastern (NE upper panel) and Midwestern (MW lower panel) USA.

3 512 N. H. Ogden, R. Lindsay & P. A. Leighton species are competent reservoirs (Brinkerhoff et al. 2010), but infective northward migrating passerines in spring are uncommon, and northward migratory birds in northeastern North America carry few larval I. scapularis (Ogden et al. 2008b). However, any larvae that acquire infection from an infected bird would become infective immigrant nymphs, which usually feed on competent reservoir hosts (e.g. rodents) and be able to introduce B. burgdorferi. Consistent with this understanding of the invasion process, B. burgdorferi is absent or occurs at low prevalence in ticks and hosts in locations where the ticks have recently become established (Bouchard et al. 2011). The infection-free ticks produced locally are detectable in passive surveillance as space-time clusters of submitted ticks with low infection prevalence because the locally produced ticks dilute the infection prevalence in ticks arriving from the USA that are also collected in passive surveillance (Ogden et al. 2010). Here, we analysed infection prevalence in ticks collected in passive surveillance in southern Canada to identify the invasion of tick populations by detecting spatial clusters of ticks with low infection prevalence (Ogden et al. 2010). We then assessed the time it takes for these clusters to disappear as B. burgdorferi invades where the ticks have become established. We then used an existing simulation model of B. burgdorferi transmission to explore possible processes in the ecology of the system that may affect the speed at which B. burgdorferi invades following tick invasion. Specifically, we investigated the relative importance of the numbers of immigrating infected and uninfected ticks, compared to the ecological conditions (host density and biodiversity) at the point of invasion. Materials and methods ANALYSIS OF PASSIVE SURVEILLANCE DATA Since 1990, I. scapularis ticks have been collected in a passive surveillance system in Canada, which involves voluntary participation of veterinary and medical clinics (Ogden et al. 2006) that submit ticks to provincial and territorial laboratories. Ticks are then sent to the National Microbiology Laboratory (NML) of the Public Health Agency of Canada for confirmation of species and testing for B. burgdorferi infection. Ticks collected from people or animals with a recent travel history are not included in analyses. From 1996 to 2004, ticks were analysed for B. burgdorferi infection by a number of different polymerase chain reaction (PCR) methods, although these did not vary in their sensitivity and specificity (Ogden et al. 2006). The most recently used of these methods (from 2003 to the present), comprises a two-test PCR procedure, as previously described (Ogden et al. 2008b). In a previous study (Ogden et al. 2010), we analysed the infection prevalence of ticks collected in passive surveillance in southern Quebec from 1991 to early 2008 and identified a space-time cluster of ticks collected from 2004 to 2008 that had low infection prevalence. Here, we perform similar analysis for all of Eastern and Central Canada, using surveillance data up to In contrast to previous analyses, state of tick engorgement and host of origin were not significantly associated with infection and are not included in analyses. First, the data were screened for the occurrence of different broad geographic patterns of infection prevalence in immigrating ticks from the USA: infection prevalence in Northeastern I. scapularis populations in the USA is generally higher than that in Midwestern populations (Diuk-Wasser et al. 2012). Different parts of Canada will receive ticks carried by migratory birds from different parts of the USA. The Atlantic provinces are likely to receive ticks carried up the Atlantic flyway from northeastern USA, while ticks carried into western Ontario (from 80 W according to genotyping of B. burgdorferi in ticks: Ogden et al. 2011) and locations further west are most likely receive ticks carried up the Mississippi flyways from Midwestern I. scapularis populations. Ticks carried into eastern Ontario and Quebec may come from the westernmost northeastern tick populations of northeastern USA that occur in Pennsylvania, western New Jersey and western New York state (Ogden et al. 2008a,b) where the prevalence of infection in I. scapularis may be relatively low (see supplemental information of Gatewood et al for details of regional variations in infection prevalence in ticks in northern states of the USA). To test for differences in prevalence among these regions, a logistic regression model was created in STATA version 11 (Statacorp LP, College Station, TX USA) with tick infection status as the outcome and location (Atlantic provinces, Quebec and Ontario east of 80 W, vs. ticks collected west of 80 W) as the explanatory variable. The outcomes were used to decide whether or not separate cluster analyses by location were required. Space-time clustering of infected ticks was performed in SATSCAN version 8.0 using a Bernoulli model (Kulldorff 1997) with temporal precision of 1 year for using a circular search window. Cases and controls were PCR-positive and PCR-negative ticks, respectively. Maximal spatial cluster size was 50% of submitted ticks, and latitude and longitude for each submitted tick were those of the municipality of origin identified on the submission obtained from Natural Resources Canada (Geographical Names of Canada graphical-name/search/name.php). The distribution and statistical significance of the clusters were explored by 999 Monte Carlo replications, and the likelihood function was maximized over all window locations and sizes. The level of statistical significance was P < MODELLINGTHERATEOFI. SCAPULARIS AND B. BURGDORFERI INVASION An existing model of B. burgdorferi transmission was used (Ogden & Tsao 2009), which models transmission between a seasonally dynamic reservoir host population (the white-footed mouse Peromyscus leucopus Rafinesque, which is the predominant reservoir host for B. burgdorferi in northern USA and Canada for example Bouchard et al. 2011), an alternative host to capture the rest of the vertebrate host community (B. burgdorferi and I. scapularis being host generalists: Kurtenbach et al. 2006) and a seasonally dynamic I. scapularis tick population. The model yields estimates of tick abundance and infection prevalence that would be seen in the field depending on the input parameters. Peromyscus leucopus and alternative host populations are constructed as susceptible-infected (SI) models of B. burgdorferi transmission, that is, we are modelling transmission of B. burgdorferi genotypes that are transmitted lifelong by P. leucopus and other hosts (Ogden et al. 2007). The model contains key elements of realism via parameterization from field and laboratory studies

4 The rate of invasion of the agent of Lyme disease 513 on I. scapularis, reservoir hosts and B. burgdorferi infection in, and transmission from, reservoir hosts: (i) contact rates between ticks and P. leucopus that are equivalent to those seen in the field in northeastern North America; (ii) seasonality in tick abundance due to climate-dependent and climate-independent influences on interstadial tick development and tick activity; (iii) seasonality in P. leucopus abundance driven by seasonal population processes (mortality and birth rates) and regulation as observed at the northern edge of the range of this rodent or in experimental studies; (iv) a realistic, climate-dependent time-lag between larval ticks acquiring infection and the emergence of nymphal ticks capable of transmitting infection with field-observed tick mortality rates; (v) density-dependent rates of mortality of on-host ticks; and (vi) dependence of tick survival and abundance on the abundance of reservoir hosts and reservoir-incompetent deer that also act as hosts for immature and adult I. scapularis in the model (Ogden et al. 2007). Values for deer, P. leucopus and the alternative host abundance can be parameterized to reflect conditions in individual locations. Similarly, transmission coefficients from the alternative host can be parameterized according to the community of hosts (other than deer and P. leucopus) that occur at any particular location as described in Ogden & Tsao (2009). For our study, the model was slightly modified to include (i) invasion of uninfected adult ticks reflecting engorged nymphal ticks carried north by migratory birds or other species in spring (assuming that all adult ticks feed on reservoir-incompetent deer so any incoming infected engorged nymphs cannot import the infection they carry); and (ii) invasion of infected nymphs reflecting imported larvae that are carried north on infectious hosts in spring, or that acquire infection from infectious birds that arrive in spring in a location in Canada. Thus, equations for the rate of change in the number of questing adult ticks and infected questing nymphs were modified as follows: Rate of change in the number of infected questing nymphal ticks: dqn i dt ¼ EL ir t s þ ELia t s þ IN ðk qnr þ k qnd þ k qna ÞQN i h i l qn QN i where QN i is the number of infected questing nymphs at time t, EL ir and EL ia are the numbers of engorged larvae that moult into infected questing nymphs at time t having acquired infection from P. leucopus and alternative hosts (respectively), the term (k qnr + k qnd + k qna )*QN i * h i represents the rate of removal of infected questing nymphs by successful host finding, and l qn * QN i represents the rate of mortality of infected questing nymphs. IN is a new term representing the numbers of immigrating infected nymphs that were introduced annually on the 1st June on the assumption that engorged infective larvae carried by, or arising from, incoming infective birds would moult into nymphs that become active the following spring. Rate of change in the number of questing adult ticks: dqa ¼ EN r t v dt þ ENa t v þ ENd t v þ IA k qa QA h a l qa QA Where EN r t v þ ENa t v þ ENd t v are the numbers of engorged larvae that moult into adults at time t have fed on rodents, alternative hosts and deer (respectively), the term k qa * QA * h a represents the rate of removal of questing adult ticks by successful host finding, and l qa * QA represents the rate of mortality of questing adults. IA is a new term representing the numbers of immigrating adult ticks that were introduced annually on 15th October on the assumption that engorged nymphs from incoming birds in spring would moult into adult ticks and become active at the start of the adult questing season the following autumn. A diagram of the modelled system is presented in Fig. 1. In the model simulations, we aimed to simulate the time scale of changes in infection prevalence that have been seen (or could be seen) in adult ticks collected in passive tick surveillance during the period when, and in locations where, tick populations are establishing, followed by establishment of B. burgdorferi transmission cycles. To do this, we calculated the infection prevalence in questing adult ticks in the model each year for a simulated 10 years with a time interval of 1 day. The infection prevalence was calculated from: P ¼ ½ðQA IAÞNt NŠþ½IN 0:13Š QA þ IA The first term in the numerator provides the number of infected adult ticks produced by the new resident tick population, and the second term provides the number of immigrating infected adult ticks assuming that the infection prevalence of immigrating adult ticks is 13% (Ogden et al. 2006). QA is the number of questing adults in that state on 15th October for a particular year of simulation, and IA is the annual number of immigrating adults set for the simulations. N i is the total number of infected engorged nymphs, and N the total number of infected and uninfected engorged nymphs, produced in the system over 1 year up to 15th October, which provides the infection prevalence in questing adult ticks that had been produced within the new resident tick population. The denominator provides the total number of questing adults in that state on 15th October for that particular year of simulation. Sensitivity analysis Using the starting values for the model as described in Ogden & Tsao 2009 (with the exception that there were no pre-seeded ticks at the start of simulations) and default values of 100 immigrating adult ticks and 1 immigrating infected nymph per year, a number of simulations were run to assess the effect of changing key ecological parameters on the delay between tick population establishment and B. burgdorferi establishment. These parameters were: (i) the numbers of immigrating infected nymphs (which were varied from 1 to 100), (ii) the numbers of immigrating adult ticks (which were varied from 100 to 5000), (iii) the numbers of deer (which were varied from 2 to 25), (iv) the numbers of P. leucopus rodent hosts (seasonal maxima for which were varied from 102 to 612 by adjusting year-round constant mortality rates), (v) the numbers of alternative hosts (which were varied from 2 to 120), and (vi) the basic daily rate adult ticks found their hosts (which was varied from 0.06 to 0.3), which acts as a proxy for abiotic and plant community effects on the rates that host-seeking ticks contact their hosts. Simulation of invasion in southern Quebec We simulated invasion in southern Quebec where a cluster of low-prevalence ticks submitted in passive surveillance was correlated with locations where I. scapularis populations were known to be establishing (Ogden et al. 2010), and for where we also

5 514 N. H. Ogden, R. Lindsay & P. A. Leighton have information on-host community composition. To do so, we created a host community for a 1 km 2 woodland in southern Quebec: P. leucopus abundance (at peak) was set at 444, deer abundance was set at 9 (using local density estimates: and the alternative host community (comprising shrews, squirrels, voles and birds) was set at 300. The density of hosts was obtained from a number of sources. In Bouchard et al. (2011), the ratio of mammalian alternative hosts to Peromyscus spp. mice was 0.6, the numbers of mice in mid-summer in our simulations was 240, so the total alternative mammalian hosts were set at 140. The mean densities of breeding birds in southern Quebec has been assessed at 449 per km 2, and in woodland habitats, approximately one-third of these are ground-feeding species (Kennedy, Dilworth-Christie & Erskine 1999), so the total alternative hosts was set at 300. Again, apart from these values, starting values and parameters were those for Ogden & Tsao (2009). Simulations were run for a range of values for immigrating infected nymphs and adult ticks. Results ANALYSIS OF PASSIVE SURVEILLANCE DATA The prevalence of infection in ticks collected in eastern Ontario and Quebec (1069/10836, 9.8%) was significantly lower than that of ticks collected in the maritime provinces and Manitoba and western Ontario [424/3713, 11.4% and 161/1334, 12.1%, respectively: Odds Ratio (OR) = 0.86, 95% confidence interval (CI) = , P < 0.01). After removal of data from space-time clusters of low infection prevalence ticks, ticks collected in the maritime provinces had higher prevalence (275/1955, 14.1%) than those collected elsewhere in Canada (1076/ 8778, 12.2%) although this was marginally significant (OR = 0.87, 95% CI = , P = 0.056). Three space-time clusters of ticks with low infection prevalence were found. One cluster occurred in southern Quebec in the same location ( N, W with a km radius) and starting in the same year (2004) as that found in Ogden et al. (2010) (Fig. 2) except the cluster ceased to exist as a distinct region of lowprevalence ticks in 2009 [110/1885 (5.8%) were positive vs. 206 (10.9%) expected, Relative risk (RR) = 0.449, Log likelihood ratio = 39.42, P = 0.001]. The period between the first identification of evidence of tick population establishment in this region in 2004 (indicated by low infection prevalence in ticks submitted in passive surveillance as a consequence of infection-free ticks produced within the cluster diluting infection prevalence in ticks carried in from the USA) and increasing infection prevalence in 2009 (suggesting the establishment of efficient B. burgdorferi transmission cycles) was, therefore, 5 years (Fig. 3). Infection prevalence in ticks collected outside the spatial limits of the cluster was relatively constant varying slightly around a mean 12.8% (Fig. 3). Cluster analysis for the Maritime provinces of Nova Scotia and New Brunswick revealed a cluster centred on MB ON N, W with a km radius, from 2004 to 2010 [149/1758 (8.5%) were positive vs. 201 (11.4%) expected, RR = 0.6, Log likelihood ratio = 14.54, P < 0.01). A cluster occurred also in south-eastern Ontario centre on N, W with a km radius, from 2007 to 2010 [75/1852 (4.0%) were positive vs. 183 (9.9%) expected, RR = 0.37, Log likelihood ratio = 51.34, P < 0.001] (Fig. 2). Temporal changes in prevalence of infection in ticks within identified clusters are compared with the prevalence of infection in ticks from Western Ontario and Manitoba in Fig QC 1 NB 500 km Fig. 2. The locations of I. scapularis ticks (red dots) collected in passive surveillance in Canada, (MB, Manitoba, ON, Ontario; QC, Quebec; NB, New Brunswick; PEI, Prince Edward Island; NS, Nova Scotia; NFL, Newfoundland & Labrador). Also shown are three circular clusters of ticks with low B. burgdorferi infection prevalence in southern Quebec (1), southeastern Ontario (2) and Nova Scotia and New Brunswick (3). Prevalence Within Cluster Outside Cluster Model predicted Year Fig. 3. The prevalence of B. burgdorferi infection in adult ticks collected within and outside the spatial bounds of a space-time cluster of ticks with low infection prevalence in southern Quebec. Also shown is the model-simulated prevalence of infection in adult ticks in a site within the cluster. PEI NFL 3 NS

6 The rate of invasion of the agent of Lyme disease 515 Prevalence Year MODELLING THE RATE OF I. SCAPULARIS AND B. BURGDORFERI INVASION Sensitivity analysis The temporal gap between tick establishment (indicated by declining infection prevalence) and establishment of efficient B. burgdorferi transmission cycles (as indicated by increasing infection prevalence) varied particularly, and inversely, with the numbers of immigrating infected nymphs and the numbers of immigrating adult ticks (Fig. 5a,b) and increased with very low deer densities (Fig. 5d). Increasing host-finding rates for adult ticks slightly shortened the gap (Fig. 5e), while changing abundance of P. leucopus rodents and alternative hosts had an effect on the final infection prevalence but had little effect on the gap (Fig. 5c,f). Simulation of invasion in southern Quebec Using the starting values of one immigrating infectious nymph and 100 immigrating adult ticks, the model simulated the 5-year decline in prevalence observed in the surveillance data, that is, initial prevalence values ( ) are those for immigrating ticks alone, from locally produced infection-free ticks dilute the infection prevalence in immigrating ticks causing the decline, while from 2009 onwards, increasing prevalence indicated the production of infected ticks locally as B. burgdorferi transmission cycles become established (Fig. 3). This result was maintained only across a very limited range of parameter values: one immigrating infected engorged larva that survives the moult to become a questing infective nymph, and engorged nymphal ticks that survive to become questing adults (Fig. 6). Discussion Western Ontario and Manitoba Eastern Ontario Quebec Maritimes Fig. 4. The prevalence of B. burgdorferi infection in adult ticks collected in passive surveillance within space-time clusters identified in eastern Ontario, Quebec and the Maritime Provinces, compared with the prevalence of infection in ticks collected in western Ontario and Manitoba where no significant cluster was detected. For clarity, confidence interval bars are not shown. In this study, we used spatio-temporal analysis of a longterm data set on infection prevalence in the tick population to provide the first quantitative estimate of the time gap between tick invasion and the subsequent increase in Lyme disease risk associated with invasion of B. burgdorferi. We then used a mechanistic model of B. burgdorferi transmission to explore ecological factors that determine the speed B. burgdorferi invades after tick populations become established. This allowed us to produce a framework for predicting how fast significant Lyme disease risk will emerge in locations into which the tick vectors are spreading. Analysis of recent passive surveillance data allowed us to confirm and further characterize a space-time cluster of ticks of low infection prevalence associated with the emergence of newly established I. scapularis populations in southern Quebec. Field studies here have identified that emergent tick populations are initially B. burgdorferi-free (Ogden et al. 2008a, 2010), which is consistent with modelling studies that identify that a threshold abundance of vector ticks must be reached for B. burgdorferi transmission to be maintained (e.g. Norman et al. 1999; Ogden et al. 2007). These ticks initially dilute the prevalence of infection in ticks arriving from the USA causing locationspecific declines in the infection prevalence in ticks collected in passive surveillance that detect where the tick populations are becoming established (Ogden et al. 2010). However, here we have continued our longitudinal analysis of passive surveillance data and identified that the cluster disappeared after 5 years, suggesting that under the environmental conditions in this location, the gap between I. scapularis becoming established (indicated by declining infection prevalence) and B. burgdorferi becoming established (indicated by increasing infection prevalence) was 5 years. When our simulation model was parameterized with host abundances expected for the region, the timing of changes in infection prevalence simulated for ticks collected in passive surveillance was that observed in southern Quebec: that is, a gap of 5 years between the first sign of tick establishment and the first sign of establishment of efficient B. burgdorferi transmission cycles. The range of values for numbers of immigrating infectious nymphal and adult ticks that produced this gap was very limited: one immigrating infected engorged larva that survives the moult to become a questing infective nymph, and between 5 and 250 engorged nymphal ticks that survive to become questing adults per km 2. A ratio of immigrating engorged nymphs to one engorged larvae would be particularly consistent with the ratio expected of ticks carried north by migratory birds in spring when nymphal ticks are active and when larval ticks are found at low abundance on hosts due to the typical spring seasonality of nymphal and late summer activity for larval I. scapularis in northeastern North America (reviewed in Ogden et al. 2007). A total number of immigrating engorged nymphal ticks that survive to become questing adults may provide an estimate of the numbers of immigrating ticks per km 2 in southeastern Canada. The simulated decline in prevalence was lower than that observed, but this result

7 516 N. H. Ogden, R. Lindsay & P. A. Leighton (a) (b) (c) (d) (e) (f) Fig. 5. Analysis of the sensitivity of the time gap between ticks and B. burgdorferi becoming established, in model simulations, to changes in: (a) the number of immigrating infected engorged larval ticks (that survive to be infective questing nymphs, (b), the number of immigrating engorged nymphal ticks (that survive to be questing adult ticks), (c) the numbers of alternative hosts (to deer or P. leucopus mice), (d) the numbers of deer, (e) the rate (HFRA) at which questing adult ticks find deer, and (f) the peak annual number of P. leucopus mice. Note that high infection prevalence in ticks in (a) and (d) at the start of the simulations occurred when there were very low numbers of adult ticks produced by the new resident tick population or immigrating compared with the numbers of infected immigrating nymphs at this point of the simulation. In simulations depicted in (b) when numbers of immigrating adult ticks were set very high, the prevalence of infection in the immigrating ticks dominated that in ticks produced by the new local population, thus limiting the final calculated infection prevalence. was not surprising. Our simulation is for one establishing tick population whereas in the zone of tick population emergence in southern Quebec, tick establishment is likely occurring in <50% of the land surface (Ogden et al. 2010). Therefore, within the observed cluster in our surveillance data, the numerator for the observed prevalence would be the sum of locally produced infected ticks (which are few) plus immigrating infected ticks in the emerging tick populations and in all areas in between these tick populations. The prevalence of infected adult ticks at the end of the simulation was similar to that observed in locations where B. burgdorferi transmission has become established in Canada (Lindsay et al. 1997). Space-time clusters of ticks with low infection prevalence were identified in other areas of Eastern Canada: eastern Ontario and the Maritimes (Nova Scotia and

8 The rate of invasion of the agent of Lyme disease 517 Number of immigrating adults Number of immigrating infected nymphs Gap between tick & B. burgdorferi establishment Fig. 6. The duration of the gap between I. scapularis and B. burgdorferi establishment in model simulations for a range of values for the numbers of immigrating infected engorged larval ticks (that survive to be infective questing nymphs), and the numbers of immigrating engorged nymphal ticks (that survive to be questing adult ticks). Values for numbers of immigrating ticks that provided a 5-year gap are indicated by the red line. New Brunswick), where tick populations are establishing ( The cluster in the Maritime provinces spanned 7 years, which is likely to reflect a less temporally synchronous, and more spatially patchy, emergence of tick populations than in southern Quebec (L.R. Lindsay unpublished data). These findings support our assumptions on the tick and B. burgdorferi immigration mechanisms and the parameterization of our model. There was no significant spacetime cluster among ticks collected in western Ontario and Manitoba (although there was a nonsignificant short 3-year decline in prevalence from ) even though I. scapularis and B. burgdorferi have become established in a number of locations in the region ( mb.ca/health/lyme/surveillance.html). This supports our simulation results of only a very short gap, which may not be detectable in passive surveillance, between I. scapularis and B. burgdorferi establishment in locations where there are high numbers of immigrating infected engorged larvae as would be expected where immigrating ticks come from locations where larval and nymphal ticks are seasonally synchronous such as the Midwest USA (Brinkerhoff et al. 2011). In our simulations when the number of infected questing nymphs that immigrated as engorged larvae reached 100 (equalling the numbers of adult ticks that immigrated), there was no observable gap between I. scapularis and B. burgdorferi establishment (Fig. 4a). In nature, questing larval ticks outnumber questing nymphal ticks by an order of magnitude when the activity of these instars is seasonally synchronous in spring (Gatewood et al. 2009), so for every questing adult tick that immigrated in our model into Manitoba and western Ontario, it would be expected that there would be 10 questing nymphal ticks. For there to be no detectable gap between I. scapularis and B. burgdorferi establishment, the infection prevalence would have to be in the order of 10%. This level of prevalence was not be seen in engorged larval ticks collected from northward migrating birds in Eastern Canada (Ogden et al. 2008a,b) but may be more likely in engorged larval ticks immigrating into western Ontario and Manitoba from populations in Midwestern USA (Brinkerhoff et al. 2011). Sensitivity analyses indicated that the main factors determining the interval between I. scapularis and B. burgdorferi establishment are the actual and relative rates of immigration of infected engorged larvae and engorged nymphs. We created a virtual community of tick hosts that is realistic for the situation in southeastern Canada, but in sensitivity analysis variations in reservoir host abundance and community had a relatively limited impact on the gap between I. scapularis and B. burgdorferi establishment. This means that while the abundance of deer, P. leucopus mice and other mammalian and avian species that form the community of hosts for ticks and pathogens determines the final equilibrium prevalence of B. burgdorferi infection in host-seeking ticks, any dilution effect may have a limited effect on the gap between tick and B. burgdorferi invasion. Clearly, the model could be parameterized to have more profound effects on tick survival and B. burgdorferi transmission (Ogden et al. 2007; Ogden & Tsao 2009), so while our assumptions in setting model parameters may be appropriate in most cases, there may be some specific locations where establishment of B. burgdorferi is more rapid or slow. Here, we have identified the speed at which B. burgdorferi invades following I. scapularis establishment in Canada by analysis of surveillance data, and explored the factors that may determine the duration of the interval between these events using a simulation model. Our results suggest that under current conditions of tick invasion in Eastern Canada, early identification of I. scapularis populations (Koffi et al. 2012) gives a window of c. 5 years before significant Lyme disease risk emerges. Using this time window, there may be imminent increased risk of Lyme disease in southeastern Ontario: the start of the space-time cluster identified in this region was 2007, suggesting that in 2012 infection prevalence in questing ticks will rise increasing the risk of Lyme disease to the public. In contrast, our study suggests that in regions receiving immigrating ticks that originate in locations where larval and nymphal activity is seasonally synchronous (such as western Ontario and Manitoba), B. burgdorferi transmission cycles would become established, and risk to the public from Lyme disease would rise, much more rapidly with the early identification of newly established tick populations providing little or no early warning of significant risk to the public. Similar effects of seasonal tick synchrony on tickborne pathogen invasion would be expected in other parts of the world where ticks and tickborne pathogens are expanding their range, and where seasonal activity of larval and nymphal ticks in source populations may vary depending on their location (e.g. I. ricinus in Europe: Randolph et al. 1999, 2002; Estrada-Pe~na et al. 2004). Invasion from locations where ticks and B. burgdorferi are established into immediate

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