Skip to main content
SpringerLink
Log in

Persistence of plague outbreaks among great gerbils in Kazakhstan: effects of host population dynamics

  • Original Article
  • Published:
Population Ecology

Abstract

Outbreaks of plague (Yersinia pestis) among great gerbils (Rhombomys opimus) generally require a high host abundance to be initiated. The duration of an outbreak is expected to depend on the subsequent development of this abundance; however, prediction is nontrivial due to the complexity of the gerbil–plague system. The aim of this study was to investigate how the duration of outbreaks depends on different types of host population dynamics generated from: a cyclic model; an autoregressive model giving irregular fluctuations; and a simple model with uncorrelated fluctuations. For each model, outbreak duration was studied under various levels of mean and variability of host abundance. Its focus on the effect of different gerbil dynamics sets this study apart from the few published studies on diseases in dynamic host populations. Plague outbreaks were simulated in a cellular automaton model based on statistical analysis of archived records of plague and host abundance. Temporal autocorrelation was found to make outbreak duration less sensitive to changes in mean abundance than uncorrelated fluctuations. Cyclicity had little effect on the mean duration of outbreaks, but resulted in a multimodal distribution. For all three types of gerbil dynamics, increased variability in gerbil abundance reduced the duration of outbreaks when the mean abundance was high (paralleling results on the risk of species extinction in fluctuating environments), but increased their duration when the mean abundance was lower. Spatial heterogeneity was briefly tested and produced longer outbreaks than the homogenous case. The results are relevant to predicting plague activity in populations of great gerbils.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Alvarez LHR (2001) Does increased stochasticity speed up extinction? J Math Biol 43:534–544

    Article  CAS  PubMed  Google Scholar 

  • Anderson RM, May RM (1991) Infectious diseases of humans. Oxford University Press, Oxford

    Google Scholar 

  • Bartlett MS (1957) Measles periodicity and community size. J Royal Stat Soc Ser A Gen 120:48–70

    Article  Google Scholar 

  • Bartlett MS (1960) The critical community size for measles in the United-States. J Royal Stat Soc Ser A Gen 123:37–44

    Article  Google Scholar 

  • Begon M, Klassovskiy N, Ageyev V, Suleimenov B, Atshabar B, Bennett M (2006) Epizootiologic parameters for plague in Kazakhstan. Emerg Infect Dis 12:268–273

    Article  PubMed Central  PubMed  Google Scholar 

  • Clancy D, O’Neill PD, Pollett PK (2001) Approximations for the long-term behavior of an open-population epidemic model. Methodol Comput Appl Probab 3:75–95

    Article  Google Scholar 

  • Collins M, Knutti R, Arblaster J, Dufresne J-L, Fichefet T, Friedlingstein P, Gao X, Gutowski WJ, Johns T, Krinner G, Shongwe M, Tebaldi C, Weaver AJ, Wehner M (2013) Long-term climate change: projections, commitments and irreversibility. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM (eds) Climate Change 2013: The physical science basis Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New York

    Google Scholar 

  • Davis S, Begon M, De Bruyn L, Ageyev VS, Klassovskiy NL, Pole SB, Viljugrein H, Stenseth NC, Leirs H (2004) Predictive thresholds for plague in Kazakhstan. Science 304:736–738

    Article  CAS  PubMed  Google Scholar 

  • Davis S, Leirs H, Viljugrein H, Stenseth NC, De Bruyn L, Klassovskiy N, Ageyev V, Begon M (2007) Empirical assessment of a threshold model for sylvatic plague. J R Soc Interface 4:649–657

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Diekmann O, Heesterbeek H, Britton T (2013) Mathematical tools for understanding infectious diseases dynamics. Princeton University Press, Princeton

    Google Scholar 

  • Dobson AP, Carper ER (1996) Infectious diseases and human population history - Throughout history the establishment of disease has been a side effect of the growth of civilization. Bioscience 46:115–126

    Article  Google Scholar 

  • Dubyanskiy VM, Pole SB, Klassovskiy NL (2003) Environmental and statistical characteristics of the dynamics of the great gerbil spring abundance in geographic populations of the Central Asian natural focus of plague. Vestnik KazNU im Al-Farabi Ser Ekol 2:127–131 (in Russian with English abstract)

    Google Scholar 

  • Easterday WR, Kausrud KL, Star B, Heier L, Haley BJ, Ageyev V, Colwell RR, Stenseth NC (2012) An additional step in the transmission of Yersinia pestis? ISME J 6:231–236

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Foley P (1994) Predicting extinction times from environmental stochasticity and carrying-capacity. Conserv Biol 8:124–137

    Article  Google Scholar 

  • Foley P, Foley J (2010) Modeling Susceptible Infective Recovered dynamics and plague persistence in California rodent-flea communities. Vector Borne Zoonotic Dis 10:59–67

    Article  PubMed  Google Scholar 

  • Frigessi A, Holden M, Marshall C, Viljugrein H, Stenseth NC, Holden L, Ageyev V, Klassovskiy NL (2005) Bayesian population dynamics of interacting species: great gerbils and fleas in Kazakhstan. Biometrics 61:230–238

    Article  PubMed  Google Scholar 

  • Fu SC, Milne G (2004) A flexible automata model for disease simulation. In: Sloot PMA, Chopard B, Hoekstra AG (eds) 6th International Conference on Cellular Automata for Research and Industry. Amsterdam, pp 642–649

  • Gage KL, Kosoy MY (2005) Natural history of plague: perspectives from more than a century of research. Annu Rev Entomol 50:505–528

    Article  CAS  PubMed  Google Scholar 

  • Grassly NC, Fraser C (2006) Seasonal infectious disease epidemiology. Proc R Soc B-Biol Sci 273:2541–2550

    Article  Google Scholar 

  • Hakoyama H, Iwasa Y (2000) Extinction risk of a density-dependent population estimated from a time series of population size. J Theor Biol 204:337–359

    Article  CAS  PubMed  Google Scholar 

  • Hanski I (1999) Metapopulation ecology. Oxford University Press, USA

    Google Scholar 

  • Heesterbeek JAP, Roberts MG (1995) Mathematical models for microparasites in wildlife. In: Grenfell BT, Dobson AP (eds) Ecology of infectious diseases in natural populations. Cambridge University Press, Cambridge, pp 90–122

    Chapter  Google Scholar 

  • Heier L, Storvik GO, Davis SA, Viljugrein H, Ageyev VS, Klassovskaya E, Stenseth NC (2011) Emergence, spread, persistence and fade-out of sylvatic plague in Kazakhstan. Proc R Soc B-Biol Sci 278:2915–2923

    Article  Google Scholar 

  • Inchausti P, Halley J (2003) On the relation between temporal variability and persistence time in animal populations. J Anim Ecol 72:899–908

    Article  Google Scholar 

  • IPCC (2013) Annex I: Atlas of global and regional climate projections. In: Van Oldenborgh GJ, Collins M, Arblaster J, Christensen JH, Marotzke J, Power SB, Rummukainen M, Zhou T (eds) Climate Change 2013: The physical science basis Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press Cambridge, United Kingdom and New York

    Google Scholar 

  • Johst K, Wissel C (1997) Extinction risk in a temporally correlated fluctuating environment. Theor Popul Biol 52:91–100

    Article  CAS  PubMed  Google Scholar 

  • Kausrud KL, Viljugrein H, Frigessi A, Begon M, Davis S, Leirs H, Dubyanskiy V, Stenseth NC (2007) Climatically driven synchrony of gerbil populations allows large-scale plague outbreaks. Proc R Soc B-Biol Sci 274:1963–1969

    Article  Google Scholar 

  • Kausrud KL, Begon M, Ben Ari T, Viljugrein H, Esper J, Büntgen U, Leirs H, Junge C, Yang B, Yang MX, Xu L, Stenseth NC (2010) Modeling the epidemiological history of plague in Central Asia: palaeoclimatic forcing on a disease system over the past millennium. BMC Biol 8:112

    Article  PubMed Central  PubMed  Google Scholar 

  • Lande R (1993) Risks of population extinction from demographic and environmental stochasticity and random catastrophes. Am Nat 142:911–927

    Article  Google Scholar 

  • Lumley T (2010) mitools: tools for multiple imputation of missing data. R package version 2.0. http://cran.r-project.org/web/packages/mitools/. Accessed 1 Mar 2014

  • Nåsell I (1999a) On the quasi-stationary distribution of the stochastic logistic epidemic. Math Biosci 156:21–40

    Article  PubMed  Google Scholar 

  • Nåsell I (1999b) On the time to extinction in recurrent epidemics. Royal-Statistical-Society Epidemics Workshop. Isle Skye, Scotland, pp 309–330

    Google Scholar 

  • Nåsell I (2005) A new look at the critical community size for childhood infections. Theor Popul Biol 67:203–216

    Article  PubMed  Google Scholar 

  • Ovaskainen O, Meerson B (2010) Stochastic models of population extinction. Trends Ecol Evol 25:643–652

    Article  PubMed  Google Scholar 

  • Pelletier JD (2002) Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales. Proc Natl Acad Sci USA 99:2546–2553

    Article  PubMed Central  PubMed  Google Scholar 

  • R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org. Accessed 1 Mar 2014

  • Reijniers J, Begon M, Ageyev VS, Leirs H (2014) Plague epizootic cycles in Central Asia. Biol Lett 10:20140302

    Article  PubMed Central  PubMed  Google Scholar 

  • Ross R (1911) The prevention of malaria, 2nd edn. Murray, London

    Google Scholar 

  • Sauvage F, Langlais M, Yoccoz NG, Pontier D (2003) Modelling hantavirus in fluctuating populations of bank voles: the role of indirect transmission on virus persistence. J Anim Ecol 72:1–13

    Article  Google Scholar 

  • Schmid BV, Jesse M, Wilschut LI, Viljugrein H, Heesterbeek JAP (2012) Local persistence and extinction of plague in a metapopulation of great gerbil burrows, Kazakhstan. Epidemics 4:211–218

    Article  CAS  PubMed  Google Scholar 

  • Schwager M, Johst K, Jeltsch F (2006) Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions. Am Nat 167:879–888

    Article  PubMed  Google Scholar 

  • Smith MJ, White A, Sherratt JA, Telfer S, Begon M, Lambin X (2008) Disease effects on reproduction can cause population cycles in seasonal environments. J Anim Ecol 77:378–389

    Article  PubMed Central  PubMed  Google Scholar 

  • Stenseth NC, Samia NI, Viljugrein H, Kausrud KL, Begon M, Davis S, Leirs H, Dubyanskiy VM, Esper J, Ageyev VS, Klassovskiy NL, Pole SB, Chan KS (2006) Plague dynamics are driven by climate variation. Proc Natl Acad Sci USA 103:13110–13115

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Swinton J, Harwood J, Grenfell BT, Gilligan CA (1998) Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations. J Anim Ecol 67:54–68

    Article  Google Scholar 

  • Telfer S, Bennett M, Bown K, Carslake D, Cavanagh R, Hazel S, Jones T, Begon M (2005) Infection with cowpox virus decreases female maturation rates in wild populations of woodland rodents. Oikos 109:317–322

    Article  Google Scholar 

  • White SH, del Rey AM, Sanchez GR (2007) Modeling epidemics using cellular automata. Appl Math Comput 186:193–202

    Article  Google Scholar 

  • Wichmann MC, Johst K, Moloney KA, Wissel C, Jeltsch F (2003) Extinction risk in periodically fluctuating environments. Ecol Model 167:221–231

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank Nils Chr. Stenseth, Boris Schmid, Kyrre L. Kausrud, and Thomas Marcussen for comments and suggestions on the manuscript. Trond Reitan is acknowledged for his assistance on model selection in BUGS and for comments on the manuscript. Three anonymous reviewers have given valuable comments and advice.

Author information

Authors and Affiliations

  1. Norwegian Veterinary Institute, PO Box 750 Sentrum, 0106, Oslo, Norway

    Hildegunn Viljugrein

  2. Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, PO Box 1066 Blindern, 0316, Oslo, Norway

    Lise Heier & Hildegunn Viljugrein

  3. Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316, Oslo, Norway

    Geir O. Storvik

Authors
  1. Lise Heier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hildegunn Viljugrein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Geir O. Storvik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lise Heier.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 703 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heier, L., Viljugrein, H. & Storvik, G.O. Persistence of plague outbreaks among great gerbils in Kazakhstan: effects of host population dynamics. Popul Ecol 57, 473–484 (2015). https://doi.org/10.1007/s10144-015-0500-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10144-015-0500-7

Keywords

Search

Navigation