Assembling evidence for identifying reservoirs of infection
Authors: Mafalda Viana, Rebecca Mancy, Roman Biek, Sarah Cleaveland, Paul C. Cross, James O. Lloyd-Smith, Daniel T. Haydon
Journal: Trends in Ecology & Evolution (2014)

•We review the problem of identifying reservoirs of infection for multihost pathogens and provide an overview of current approaches and future directions.•We provide a conceptual framework for classifying patterns of incidence and prevalence.•We review current methods that allow us to characterise the components of reservoir-target systems.•Ecological theory offers promising new ways to prioritise populations when designing interventions.•We propose using interventions as quasi-experiments embedded in adaptive management frameworks.•Integration of data and analysis provides powerful new opportunities for studying multihost systems. Many pathogens persist in multihost systems, making the identification of infection reservoirs crucial for devising effective interventions. Here, we present a conceptual framework for classifying patterns of incidence and prevalence, and review recent scientific advances that allow us to study and manage reservoirs simultaneously. We argue that interventions can have a crucial role in enriching our mechanistic understanding of how reservoirs function and should be embedded as quasi-experimental studies in adaptive management frameworks. Single approaches to the study of reservoirs are unlikely to generate conclusive insights whereas the formal integration of data and methodologies, involving interventions, pathogen genetics, and contemporary surveillance techniques, promises to open up new opportunities to advance understanding of complex multihost systems. Many pathogens persist in multihost systems, making the identification of infection reservoirs crucial for devising effective interventions. Here, we present a conceptual framework for classifying patterns of incidence and prevalence, and review recent scientific advances that allow us to study and manage reservoirs simultaneously. We argue that interventions can have a crucial role in enriching our mechanistic understanding of how reservoirs function and should be embedded as quasi-experimental studies in adaptive management frameworks. Single approaches to the study of reservoirs are unlikely to generate conclusive insights whereas the formal integration of data and methodologies, involving interventions, pathogen genetics, and contemporary surveillance techniques, promises to open up new opportunities to advance understanding of complex multihost systems. Most disease-causing organisms, including many important human, livestock, and wildlife pathogens, are capable of infecting multiple hosts [1Cleaveland S. et al.Diseases of humans and their domestic mammals: pathogen characteristics, host range and the risk of emergence.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2001; 356: 991-999Crossref PubMed Scopus (759) Google Scholar, 2Taylor L.H. et al.Risk factors for human disease emergence.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2001; 356: 983-989Crossref PubMed Scopus (1852) Google Scholar, 3Woolhouse M.E. et al.Population biology of multihost pathogens.Science. 2001; 292: 1109-1112Crossref PubMed Scopus (572) Google Scholar]. Therefore, determining how hosts enable persistence [4Streicker D.G. et al.Differential sources of host species heterogeneity influence the transmission and control of multihost parasites.Ecol. Lett. 2013; 16: 975-984Crossref PubMed Scopus (87) Google Scholar] and which hosts are crucial for the persistence of these multihost pathogens [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar] is essential for the design of effective control measures. Failure to establish this understanding can hamper policy formulation and lead to ineffective or counter-productive control measures with costly implications for socially, economically, or ecologically important populations. Reservoirs of infection can be ecologically complicated structures comprising one or more interacting populations or species (Box 1 [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar]). Although a range of developments has led to better theoretical conceptualisation of reservoirs [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar, 6Ashford R.W. What it takes to be a reservoir host.Belg. J. Zool. 1997; 127: 85-90Google Scholar, 7Ashford R.W. When is a reservoir not a reservoir?.Emerg. Infect. Dis. 2003; 9: 1495-1496Crossref PubMed Scopus (69) Google Scholar, 8Nishiura H. et al.How to find natural reservoir hosts from endemic prevalence in a multi-host population: a case study of influenza in waterfowl.Epidemics. 2009; 1: 118-128Crossref PubMed Scopus (35) Google Scholar, 9Dobson A.P. Population dynamics of pathogens with multiple host species.Am. Nat. 2004; 164: S64-S78Crossref PubMed Scopus (416) Google Scholar], their empirical characterisation remains a challenge. In this article, we review methods currently used to characterise each of the components that comprise a reservoir according to the framework in Box 1. Specifically, we first present a conceptual approach for classifying patterns of incidence and prevalence (see Glossary) that result from the connectivity between source and target populations (black arrows in Figure I in Box 1). We then review methods that allow us to identify maintenance or nonmaintenance populations (squares or circles in Figure I, Box 1), how they are connected (arrows in Figure I, Box 1), and the role that each of these populations has in maintaining the pathogen (i.e., reservoir capacity).Box 1Disease reservoirs frameworkOur study of epidemiology is usually motivated by the need to control disease in a particular host population or a subset of a population. Following Haydon et al. [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar], we refer to this as the 'target population'. Populations that are direct sources of infection for the target are termed 'source populations'. A 'reservoir of infection' is defined with respect to a target population as 'one or more epidemiologically connected populations or environments in which a pathogen can be permanently maintained and from which infection is transmitted to the target population' [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar]. Some reservoirs can be simple and comprise a single nontarget host population (Figure IA). However, they can comprise a more structured set of connected host subpopulations termed 'maintenance community' (Figure IB–D). Individually, some of these populations can maintain the pathogen ('maintenance populations'), whereas others cannot ('nonmaintenance populations').Thus, infection reservoirs can be constituted in a variety of ways. Reservoirs can be wildlife species [e.g., possums (Eichosurus vulpecula) as a reservoir of bovine TB in cattle in New Zealand; or wildebeest (Connochaetes taurinus) as a reservoir of malignant catarrh fever for cattle in Tanzania]; domesticated species (e.g., dogs as a reservoir of rabies for humans in many developing countries; cattle as a reservoir of Escherichia coli 0157 for humans in the UK), or subsets of the same species (e.g., adults as a reservoir of respiratory syncytial virus for children, men as an element of the reservoir of human papillomavirus for women).Other definitions of reservoirs have been proposed [7Ashford R.W. When is a reservoir not a reservoir?.Emerg. Infect. Dis. 2003; 9: 1495-1496Crossref PubMed Scopus (69) Google Scholar, 55Drexler J.F. et al.Bats host major mammalian paramyxoviruses.Nat. Commun. 2012; 3 (796)Crossref PubMed Scopus (507) Google Scholar]. Although Ashford's [7Ashford R.W. When is a reservoir not a reservoir?.Emerg. Infect. Dis. 2003; 9: 1495-1496Crossref PubMed Scopus (69) Google Scholar] definition is appealing for its generality, and Drexler et al.'s [55Drexler J.F. et al.Bats host major mammalian paramyxoviruses.Nat. Commun. 2012; 3 (796)Crossref PubMed Scopus (507) Google Scholar] for its evolutionary perspective, we use Haydon et al.'s [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar] due to not only its acceptance within the epidemiological literature, but also its direct application for designing interventions. Our study of epidemiology is usually motivated by the need to control disease in a particular host population or a subset of a population. Following Haydon et al. [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar], we refer to this as the 'target population'. Populations that are direct sources of infection for the target are termed 'source populations'. A 'reservoir of infection' is defined with respect to a target population as 'one or more epidemiologically connected populations or environments in which a pathogen can be permanently maintained and from which infection is transmitted to the target population' [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar]. Some reservoirs can be simple and comprise a single nontarget host population (Figure IA). However, they can comprise a more structured set of connected host subpopulations termed 'maintenance community' (Figure IB–D). Individually, some of these populations can maintain the pathogen ('maintenance populations'), whereas others cannot ('nonmaintenance populations'). Thus, infection reservoirs can be constituted in a variety of ways. Reservoirs can be wildlife species [e.g., possums (Eichosurus vulpecula) as a reservoir of bovine TB in cattle in New Zealand; or wildebeest (Connochaetes taurinus) as a reservoir of malignant catarrh fever for cattle in Tanzania]; domesticated species (e.g., dogs as a reservoir of rabies for humans in many developing countries; cattle as a reservoir of Escherichia coli 0157 for humans in the UK), or subsets of the same species (e.g., adults as a reservoir of respiratory syncytial virus for children, men as an element of the reservoir of human papillomavirus for women). Other definitions of reservoirs have been proposed [7Ashford R.W. When is a reservoir not a reservoir?.Emerg. Infect. Dis. 2003; 9: 1495-1496Crossref PubMed Scopus (69) Google Scholar, 55Drexler J.F. et al.Bats host major mammalian paramyxoviruses.Nat. Commun. 2012; 3 (796)Crossref PubMed Scopus (507) Google Scholar]. Although Ashford's [7Ashford R.W. When is a reservoir not a reservoir?.Emerg. Infect. Dis. 2003; 9: 1495-1496Crossref PubMed Scopus (69) Google Scholar] definition is appealing for its generality, and Drexler et al.'s [55Drexler J.F. et al.Bats host major mammalian paramyxoviruses.Nat. Commun. 2012; 3 (796)Crossref PubMed Scopus (507) Google Scholar] for its evolutionary perspective, we use Haydon et al.'s [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar] due to not only its acceptance within the epidemiological literature, but also its direct application for designing interventions. Long-term ecological data on multihost systems are sparse and challenging to collect [10Begon M. et al.Transmission dynamics of a zoonotic pathogen within and between wildlife host species.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 1999; 266: 1939-1945Crossref Scopus (159) Google Scholar, 11Carslake D. et al.Inference of cowpox virus transmission rates between wild rodent host classes using space–time interaction.Proc. Biol. Sci. 2006; 273: 775-782Crossref PubMed Scopus (15) Google Scholar, 12Kilpatrick A.M. et al.Host heterogeneity dominates West Nile virus transmission.Proc. Biol. Sci. 2006; 273: 2327-2333Crossref PubMed Scopus (413) Google Scholar]; this, combined with the inherent difficulty of identifying reservoirs of infection, means that each data set or approach in isolation is unlikely to result in a sufficient evidence base to inform control strategies. Here, we further discuss how to enrich this evidence base. Almost inevitably, the need to intervene will precede adequate understanding of the dynamics of reservoir-target systems. Our central thesis is that interventions that are meticulously planned to optimise both the immediate short-term benefits to the target population and the longer-term understanding of how reservoirs function, applied together with a formal integration of data and methods [13O'Cathain A. et al.Three techniques for integrating data in mixed methods studies.BMJ. 2010; 341: c4587Crossref PubMed Scopus (861) Google Scholar], can provide powerful new opportunities for studying complex multihost systems (e.g., [14Lembo T. et al.Exploring reservoir dynamics: a case study of rabies in the Serengeti ecosystem.J. Appl. Ecol. 2008; 45: 1246-1257Crossref PubMed Scopus (150) Google Scholar]). Data on patterns of incidence and prevalence provide indirect information on the connectivity between source and target populations (i.e., black arrows in Figure I, Box 1). Building upon the 'community-epidemiology continuum' framework developed by Fenton and Pedersen [15Fenton A. Pedersen A.B. Community epidemiology framework for classifying disease threats.Emerg. Infect. Dis. 2005; 11: 1815-1821Crossref PubMed Scopus (133) Google Scholar], specific patterns can be assigned to 'zones' (Figure 1 and Table 1) defined in relation to the relative magnitudes of the force of infection from one or more source(s) (x-axis in Figure 1; thickness of arrows in Figure I, Box 1), and R0,T, the basic reproduction number of the pathogen within the target.Table 1Description of the dynamics and genetic signature of each disease zone captured in Figure 1 (main text)ZoneProcessObservationExampleDynamicsGeneticsALow frequency of spillover infection with no onward transmission in the target population. Low incidence with isolated, epidemiologically independent casesLow incidence with long gaps between outbreaks that exceed the average combined incubation and infection periodsGenetic independence between casesLyme disease in humansHuman rabiesBFrequent, dead-end spillover leads to cases at a rate that could appear to indicate target-to-target transmission (but it is not)Sometimes low incidence with frequent outbreaks (e.g., West Nile virus in humans). However, low frequency with high incidence can also occur (e.g., Rift Valley fever in humans)Genetic independence between cases allows distinction from zones with similar incidence rates arising from target-to-target transmission (zones C/D)West Nile virus in humans and horsesRift Valley fever in humansWildebeest-associated malignant catarrhal fever in cattleVampire bat rabies in humans and/or livestockCLimited target-to-target transmission causes isolated stuttering chains of transient nature and, thus, self-limiting outbreaksLow-to-medium incidence with frequent small outbreaksGenetics reveals that stuttering chains are unlinked based on cases having shared ancestry only in the distant past. Critical to distinguish from zones B/DMonkeypoxCattle brucellosis in YellowstoneEarly severe acute respiratory syndromeH5N1 avian influenzaFood-borne Escherichia coliDSimilar dynamics to zone C but chains initiated at high enough frequency to create a pseudo-endemic pattern (i.e., cases are always present in the target population)Medium-to-high incidence with frequent small outbreaks. Reveals pseudo-endemicityGenetics reveal that chains are separate and temporally superimposed (rather than linked), showing frequent transmission from source. Critical to distinguish from zone CWildlife CDV in the SerengetiPossibly TB in African lionsWildlife rinderpest (but see 78Roeder P. et al.Rinderpest: the veterinary perspective on eradication.Philos. Trans. R. Soc. Lond. B: Biol. Sci. 2013; 368: 20120139Crossref PubMed Scopus (109) Google Scholar)ERare introductions that result in large and usually sustained outbreaks due to R0,T >1. Size of target population is important because higher R0,T leads to a faster depletion of susceptibles, increasing the CCS required for persistenceHigh incidence with endemic circulation influenced by, for example, seasonal dynamicsInvasion can be traced to a single or a small number of spillover eventsHIVInfluenza in humansMycoplasma ovipneumonia in bighorn sheepBat rabies in skunksFFrequent introductions and large outbreaks associated with a high number of spillover events. Difficult to identify dynamically. Contribution from source unclear due to high R0,T in target populationHigh incidenceGenetics reveal multiple co-circulating lineages in the target population, with new lineages appearing through spillover events. Multiple spillovers from the source mean that it is more difficult to eliminateSouthern African Territories strains of cattle foot-and-mouth disease in sub-Saharan AfricaBovine TB in UKJackal-dog rabies in southern Africa Open table in a new tab If the target population is a 'dead-end' host from which transmission does not occur, then R0,T = 0. For a sufficiently low force of infection, the interval between cases in the target host is longer than the infectious period of single cases (Figure 1, zone A) and cases are not directly linked. As the force of infection from alternative sources increases, we observe cases in the target population with increasing frequency. At higher values, cases can overlap in time and space but remain epidemiologically unlinked and, as long as variability in the pathogen is high enough, genetically distinct (Figure 1, zone B). Target populations in which limited transmission can occur but R0,T <1 will, when the force of infection from the source is low, exhibit the classic 'stuttering chain' dynamics (Figure 1, zone C) in which outbreak sizes follow an overdispersed distribution [16Blumberg S. Lloyd-Smith J.O. Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains.PLoS Comput. Biol. 2013; 9: e1002993Crossref PubMed Scopus (116) Google Scholar]. As R0,T →1, these outbreaks can become large. However, as the interval between introductions becomes shorter than the average duration of outbreaks, we observe a pseudo-endemic pattern in which the target population can appear to be a maintenance population even when it is not (Figure 1, zone D). Systems in which R0,T is close to 1 present particular threats because small changes in their epidemiology within the target population, through either pathogen evolution or changes in the target population structure, can cause R0,T to exceed 1 and lead to an endemic situation and/or epidemic behaviour [17Antia R. et al.The role of evolution in the emergence of infectious diseases.Nature. 2003; 426: 658-661Crossref PubMed Scopus (394) Google Scholar]. If R0,T >1 then any spill-over events can give rise to substantial epidemics. Stochastic extinction will still occur frequently if R0,T is only slightly greater than 1 (Figure 1, zone E); however, if the outbreak 'takes off' or R0,T >>1, then there are three broad possible outcomes: (i) the target population sustains a major epidemic after which the pathogen becomes extinct in the target population [e.g., distemper virus in wolves (Canis lupus) and harbour seals (Phoca vitulina)]; (ii) the target population sustains a major epidemic after which the pathogen proceeds towards an endemic state in the target population (e.g., HIV; the target population is then a square in Figure I, Box 1); (iii) control measures within the target population reduce R0,T to below 1, so a major epidemic is averted and the pathogen becomes extinct in the target population (e.g., severe acute respiratory syndrome). If R0,T >1 and the force of infection from the reservoir is large (Figure 1, zone F), fadeout is unlikely (e.g., Southern African Territories strains of foot-and-mouth disease in cattle in sub-Saharan Africa). Dynamics ranging from pseudo-endemicity to true endemicity lie on an ascending diagonal from right to left (Figure 1, arrow), along which increasing R0,T compensates for a declining force of infection from the reservoir. These different situations are likely to be hard to distinguish using patterns of incidence and prevalence alone. However, higher resolution spatiotemporal data and pathogen genetic sequence data, together with sophisticated analytical techniques such as state-space modelling, can provide some of the necessary tools to examine these patterns (See 'Connectivity within the reservoir'). Given the challenges of isolating pathogens from wildlife populations, patterns of incidence and prevalence are typically obtained from longitudinal seroprevalence surveys or age-seroprevalence curves. These have been used to investigate infection dynamics of various multihost systems, such as canine distemper virus (CDV) in carnivore communities of the Serengeti [18Cleaveland S. et al.Serological and demographic evidence for domestic dogs as a source of canine distemper virus infection for Serengeti wildlife.Vet. Microbiol. 2000; 72: 217-227Crossref PubMed Scopus (181) Google Scholar, 19Packer C. et al.Viruses of the Serengeti: patterns of infection and mortality in African lions.J. Anim. Ecol. 1999; 68: 1161-1178Crossref Scopus (154) Google Scholar], Kenya [20Prager K.C. et al.Rabies virus and canine distemper virus in wild and domestic carnivores in northern Kenya: are domestic dogs the reservoir?.Ecohealth. 2012; 9: 483-498Crossref PubMed Scopus (46) Google Scholar], and Yellowstone [21Almberg E.S. et al.A serological survey of infectious disease in Yellowstone National Park's canid community.PLoS ONE. 2009; 4: e7042Crossref PubMed Scopus (72) Google Scholar], Trypanosoma cruzi in wildlife hosts in the USA [22Brown E.L. et al.Seroprevalence of Trypanosoma cruzi among eleven potential reservoir species from six states across the southern United States.Vector Borne Zoonotic Dis. 2010; 10: 757-763Crossref PubMed Scopus (75) Google Scholar] and hepatitis E in wild boars (Sus scrofa) in Europe [23Carpentier A. et al.High hepatitis E virus seroprevalence in forestry workers and in wild boars in France.J. Clin. Microbiol. 2012; 50: 2888-2893Crossref PubMed Scopus (83) Google Scholar]. However, their interpretation remains fraught with uncertainties mainly owing to cross-reactivity, declining antibody titres, cut-off thresholds used to distinguish positive and negative reactions, and difficulties with the detectability of antibodies because these depend on the relation between immunity and infection resistance (e.g., a detectable antibody does not always imply protection and the time of exposure remains unknown for pathogens that create life-long immunity in the host) [24Gilbert A. et al.Deciphering serology to understand the ecology of infectious diseases in wildlife.Ecohealth. 2013; 3: 298-313Crossref Scopus (140) Google Scholar]. New statistical approaches, such as latent class methods and site-occupancy modelling, have been suggested recently to improve estimates of prevalence from imperfect tests by allowing uncertainty in the detection of infection state [25Lachish S. et al.Infection dynamics of endemic malaria in a wild bird population: parasite species-dependent drivers of spatial and temporal variation in transmission rates.J. Anim. Ecol. 2011; 80: 1207-1216Crossref PubMed Scopus (84) Google Scholar]. Although still in early stages of development, advanced modelling techniques, such as Bayesian process models, can enable inferences of timing of exposure from age-seroprevalence data, accounting for non-stationary epidemiological dynamics [26Heisey D.M. et al.Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross-sectional data.Ecol. Monogr. 2010; 80: 221-240Crossref Scopus (74) Google Scholar], and/or detect cross-species transmission [27Blackwood J. et al.Resolving the roles of immunity, pathogenesis and immigration for rabies persistence in vampire bats.Proc. Natl. Acad. Sci. U.S.A. 2013; https://doi.org/10.1073/pnas.1308817110Crossref Scopus (124) Google Scholar], to identify which host species is the most likely source of infection. Methods to identify plausible reservoirs typically focus on thresholds that define individual populations as maintenance or nonmaintenance (squares or circles in Figure I, Box 1). Therefore, we discuss critical community size (CCS) as an intuitive measure of persistence that can be traced back to the reservoir framework proposed by Haydon et al. [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar]. CCS can be loosely defined as the host population size below which a pathogen cannot persist [28Bartlett M.S. Measles periodicity and community size.J. R. Stat. Soc. Ser. A. 1957; 120: 48-70Crossref Google Scholar, 29Bartlett M.S. Deterministic and stochastic models for recurrent epidemics.in: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press1956: 81-109http://projecteuclid.org/euclid.bsmsp/1200502549Google Scholar]. Thus, a maintenance population can be defined as a host population in which a pathogen persists because the population size is greater than CCS, whereas a nonmaintenance population is one smaller than CCS [5Haydon D.T. et al.Identifying reservoirs of infection: a conceptual and practical challenge.Emerg. Infect. Dis. 2002; 8: 1468-1473Crossref PubMed Scopus (598) Google Scholar]. However, there are several challenges to the study of CCS in practice. The first challenge is to define the population in which persistence is to be measured. Given that persistence is sensitive to the complex relation between demographic and epidemiological factors, it is difficult to estimate in the presence of population structure [30Ferrari M.J. et al.The dynamics of measles in sub-Saharan Africa.Nature. 2008; 451: 679-684Crossref PubMed Scopus (258) Google Scholar, 31Swinton J. et al.Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations.J. Anim. Ecol. 1998; 67: 54-68Crossref Scopus (178) Google Scholar]; therefore, CCS is most commonly discussed in the context of single well-mixed populations, although these are rare in natural systems. The second challenge is in defining persistence, particularly because any estimate of CCS is likely to be sensitive to the choice of persistence metric [32Conlan A.J.K. et al.Resolving the impact of waiting time distributions on the persistence of measles.J. R. Soc. Interface. 2010; 7: 623-640Crossref PubMed Scopus (41) Google Scholar]. In his original work, Bartlett defined CCS as the size of a population in which extinction was as likely as not following a major outbreak [29Bartlett M.S. Deterministic and stochastic models for recurrent epidemics.in: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press1956: 81-109http://projecteuclid.org/euclid.bsmsp/1200502549Google Scholar]. However, persistence might also be measured from an initial condition corresponding to the endemic equilibrium [33Lloyd A.L. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics.Theor. Popul. Biol. 2001; 60: 59-71Crossref PubMed Scopus (279) Google Scholar, 34Nåsell I. On the time to extinction in recurrent epidemics.J. R. Stat. Soc. Ser. B. 1999; 61: 309-330Crossref Scopus (143) Google Scholar]. Lloyd-Smith et al. [35Lloyd-Smith J.O. et al.Should we expect population thresholds for wildlife disease?.Trends Ecol. Evol. 2005; 20: 511-519Abstract Full Text Full Text PDF PubMed Scopus (370) Google Scholar] point out that the relation between persistence and population size is not well described as a step function, but instead increases in a gradual manner. CCS can also be thought of in relation to the probability of extinction within a given time or the time until a given proportion (usually 50%) of introductions (or simulations) have gone extinct [36Farrington C.P. Grant A.D. The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease.J. Appl. Probab. 1999; 36: 621-950Crossref Scopus (1) Google Scholar]. Once appropriate definitions are adopted, the final challenge is estimating CCS. The main approaches used are: (i) empirical observation, which consist of plotting incidence data against population size [28Bartlett M.S. Measles periodicity and community size.J. R. Stat. Soc. Ser. A. 1957; 120: 48-70Crossref Google Scholar, 37Bartlett M.S. The critical community size for measles in the United States.J. R. Stat. Soc. Ser. A. 1960; 123: 37-44Crossref Google Scholar, 38Choisy M. Rohani P. Changing spatial epidemiology of pertussis in continental USA.Proc. Biol. Sci. 2012; 279: 4574-4581Crossref PubMed Scopus (30) Google Scholar, 39Gunning C.E. Wearing H.J. Probabilistic measures of persistence and extinction in measles (meta)populations.Ecol. Lett. 2013; 16: 985-994Crossref PubMed Scopus (13) Google Scholar]; (ii) analytic expressions [34Nåsell I. On the time to extinction in recurrent epidemics.J. R. Stat. Soc. Ser. B. 1999; 61: 309-330Crossref Scopus (143) Google S