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International Conference on Applied Mathematics, Modeling and Computational Science

AMMCS 2017: Recent Advances in Mathematical and Statistical Methods pp 385–395Cite as

A Simple Model of Between-Hive Transmission of Nosemosis

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 259))

Abstract

We present a simple metapopulation extension of a mathematical model of Nosemosis for the between-hive transmission of the disease in an apiary. The transmission of the disease between neighbouring colonies is modeled by impulsive transfer of pathogens. The model is studied in computer simulations. Our results illustrate how the disease, starting from a single colony, can spread and lead to drastic reduction in the bee population in the apiary, even in the subcritical case.

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References

  1. Becerra-Guzmán, F., Guzmán-Novoa, E., Correa-Benítez, A., Zozaya-Rubio, A.: Length of life, age at first foraging and foraging life of Africanized and European honey bee (Apis mellifera) workers, during conditions of resource abundance. J. Apicult. Res. 44(4), 151–156 (2005)

    Article  Google Scholar 

  2. Betti, M.I., Wahl, L.M., Zamir, M., Rueppell, O.: Effects of infection on honey bee population dynamics: a model. PloS One 9(10), e110237 (2014)

    Article  Google Scholar 

  3. Betti, M.I., Wahl, L.M., Zamir, M.: Reproduction number and asymptotic stability for the dynamics of a honey bee colony with continuous age structure. Bull. Math. Biol. 79(7), 1586–1611 (2017)

    Article  MathSciNet  Google Scholar 

  4. Fries, I.: Comb replacement and Nosema disease (Nosema apis Z.) in honey bee colonies. Apidologie 19, 343–354 (1988)

    Article  Google Scholar 

  5. Free, J.B.: The drifting of honey-bees. J. Agric. Sci. 51, 294–306 (1958)

    Article  Google Scholar 

  6. Goblirsch, M., Huang, Z.Y., Spivak, M., Amdam, G.V.: Physiological and behavioral changes in honey bees (Apis mellifera) induced by Nosema ceranae infection. PloS One 8(3), e58165 (2013)

    Article  Google Scholar 

  7. Higes, M., Martn-Hernndez, R., Garrido-Bailn, E., Garca-Palencia, P., Meana, A.: Detection of infective Nosema ceranae (Microsporidia) spores in corbicular pollen of forager honeybees. J. Invertebr. Pathol. 97, 76–78 (2008)

    Article  Google Scholar 

  8. Jatulan, E.O., Rabajant, J.F., Banaay, C.G.B., Fajardo Jr., A.C., Jose, E.C.: A mathematical model of intra-colony spread of American foulbrood in European honeybees (Apis mellifera L.). Plos One 10(12), e0143805 (2015)

    Article  Google Scholar 

  9. Kang, Y., Blanco, K., Davis, T., Wang, Y., DeGrandi-Hoffman, G.: Disease dynamics of honeybees with Varroa destructor as parasite and virus vector. Math. Biosc. 275, 71–92 (2016)

    Article  MathSciNet  Google Scholar 

  10. Khoury, D.S., Myerscough, M.R., Barron, A.B., Marshall, J.A.R.: A quantitative model of honey bee colony population dynamics. PloS One 6(4), e18491 (2011)

    Article  Google Scholar 

  11. Kribs-Zaleta, C.M., Mitchell, C.: Modeling colony collapse disorder in honeybees as a contagion. Math. Biosc. Eng. 11(6), 1275–1294 (2014)

    Article  MathSciNet  Google Scholar 

  12. Lacey, B.: A two year study of Nosema ceranae in Ontario. Ont. Bee J. 33(2), 14–16 (2014)

    Google Scholar 

  13. Petric, A., Guzman-Novoa, E., Eberl, H.J.: A mathematical model for the interplay of Nosema infection and forager losses in honey bee colonies. J. Biol. Dyn. 11(S2), 348–378 (2017)

    Article  MathSciNet  Google Scholar 

  14. Ratti, V., Kevan, P.G., Eberl, H.J.: A mathematical model of the honeybeevarroa destructor-acute bee paralysis virus system with seasonal effects. Bull. Math. Biol. 77(8), 1493–1520 (2015)

    Article  MathSciNet  Google Scholar 

  15. Ratti, V., Kevan, P.G., Eberl, H.J.: A discrete-continuous modeling framework to study the role of swarming in a honeybee-Varroa destrutor-virus system. In: Belair, J. (ed.) Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pp. 299–308. Springer, Berlin (2016)

    Chapter  Google Scholar 

  16. Ratti, V., Kevan, P.G., Eberl, H.J.: A mathematical model of forager loss in honeybee colonies infested with Varroa destructor and the acute bee paralysis virus. Bull. Math. Biol. 79(6), 12181253 (2017)

    Article  MathSciNet  Google Scholar 

  17. Statistical Overview of the Canadian Honey and Bee Industry and the Economic Contribution of Honey Bee Pollination 2013–2014. http://www.agr.gc.ca/resources/prod/doc/pdf/1453219857143-eng.pdf

  18. Sakagami, S.F., Fukuda, H.: Life tables for worker honeybees. Res. Pop. Ecol. 10(2), 127–139 (1968)

    Article  Google Scholar 

  19. Soetaert, K., Petzoldt, T., Setzer, R.W.: Solving differential equations in R: package deSolve. J. Stat. Softw. 33(9), 1–25 (2010)

    Article  Google Scholar 

  20. Sumpter, D.J.T., Martin, S.J.: The dynamics of virus epidemics in varroa-infested honey bee colonies. J. Animal Ecol. 73(1), 51–63 (2004)

    Article  Google Scholar 

  21. Weston, S., Calaway, R.: Getting Started with doParallel and foreach. https://cran.r-project.org/web/packages/doParallel/vignettes/gettingstartedParallel.pdf (2017)

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Authors and Affiliations

  1. Mohawk College and McMaster University, 1280 Main Street West, Hamilton, ON, L8S 0A3, Canada

    Nasim Muhammad

  2. University of Guelph, 50 Stone Rd E, Guelph, ON, N1G 2W1, Canada

    Hermann J. Eberl

Authors
  1. Nasim Muhammad
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  2. Hermann J. Eberl
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Corresponding author

Correspondence to Hermann J. Eberl .

Editor information

Editors and Affiliations

  1. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  2. Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada

    Herb Kunze

  3. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roman Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roderick Melnik

  5. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

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Muhammad, N., Eberl, H.J. (2018). A Simple Model of Between-Hive Transmission of Nosemosis. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_35

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