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Modelling the Dynamics of Bluetongue Disease and the Effect of Seasonality

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Abstract

We present mathematical models for the midge-borne disease bluetongue, with cattle and sheep as hosts. The models take the form of delay differential equations and incorporate the incubation time of bluetongue in cattle, sheep and midges, and also the larval developmental time of midges. Recovery in cattle and sheep is also included. Both an autonomous and a periodic model are considered, to take account of seasonality. For both models we present conditions for the disease-free state to be linearly stable, and a detailed interpretation of those conditions. The results of simulations are also presented. Important findings include the need for prompt diagnosis of latent infection and appropriate action before the animal turns infectious, and the need for measures that reduce insect bites.

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Notes

  1. http://www.defra.gov.uk/animal-diseases/a-z/bluetongue/.

  2. http://www.oie.int/en/animal-health-in-the-world/oie-listed-diseases-2014/.

References

  • Charron MVP, Seegers H, Langlais M, Ezanno P (2011) Seasonal spread and control of bluetongue in cattle. J Theor Biol 291:1–9

    Article  MathSciNet  Google Scholar 

  • Gerbier G, Baldet T, Tran A, Hendrickx G, Guis H, Mintiens K, Elbers ARW, Staubach C (2008) Modelling local dispersal of bluetongue virus serotype 8 using random walk. Prev Vet Med 87:119–130

    Article  Google Scholar 

  • Gourley SA, Thieme HR, van den Driessche P (2011) Stability and persistence in a model for bluetongue dynamics. SIAM J Appl Math 71(4):1280–1306

    Article  MathSciNet  MATH  Google Scholar 

  • Gourley SA, Liu R, Wu J (2010) Spatiotemporal distributions of migratory birds: patchy models with delay. SIAM J Appl Dyn Syst 9(2):589–610

    Article  MathSciNet  MATH  Google Scholar 

  • Gubbins S, Carpenter S, Bayliss M, Wood JLN, Mellor PS (2008) Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproductive number. J R Soc Interface 5(20):363–371

    Article  Google Scholar 

  • Gubbins S, Szmaragd C, Burgin L, Wilson A, Volkova V, Gloster J, Gunn GJ (2010) Assessing the consequences of an incursion of a vector-borne disease. I. Identifying feasible incursion scenarios for bluetongue in Scotland. Epidemics 2(3):148–154

    Article  Google Scholar 

  • Hendrickx G, Gilbert M, Staubach C, Elbers A, Mintiens K, Gerbier G, Ducheyne E (2006) A wind density model to quantify the airborne spread of Culicoides species during north-western Europe bluetongue epidemic. Prev Vet Med 87(2008):162–181

    Google Scholar 

  • Mellor PS (1990) The replication of bluetongue virus in Culicoides vectors. Curr Top Microbiol Immunol 162:143–161

    Google Scholar 

  • Sedda L, Brown HE, Purse BV, Burgin L, Gloster J, Rogers DJ (2012) A new algorithm quantifies the roles of wind and midge flight activity in the bluetongue epizootic in northwest Europe. Proc R Soc B 279:2354–2362

    Article  Google Scholar 

  • Smith HL (1995) Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems, vol 41. American Mathematical Society, Providence

    MATH  Google Scholar 

  • Szmaragd C, Gunn GJ, Gubbins S (2010a) Assessing the consequences of an incursion of a vector-borne disease. II. Spread of bluetongue in Scotland and impact of vaccination. Epidemics 2(3):139–147

  • Szmaragd C, Wilson AJ, Carpenter S, Wood JLN, Mellor PS, Gubbins S (2010b) The spread of bluetongue virus serotype 8 in Great Britain and its control by vaccination. PLoS ONE 5(2):e9353

  • Wang H (2004) Positive periodic solutions of functional differential equations. J. Differ Equ 202(2):354–366

    Article  MATH  Google Scholar 

  • Wang H, Kuang Y, Fan M, Periodic solutions of systems of delay differential equations (unpublished manuscript)

  • Ward MP, Carpenter TE (1996a) Simulation modeling of the effect of climatic factors on bluetongue virus infection in Australian cattle herds. I. Model formulation, verification and validation. Prev Vet Med 27:1–12

  • Ward MP, Carpenter TE (1996b) Simulation modeling of the effect of climatic factors on bluetongue virus infection in Australian cattle herds. II. Model experimentation. Prev Vet Med 27:13–22

  • Wilson AJ, Mellor PS (2009) Bluetongue in Europe: past, present and future. Philos Trans R Soc B 364:2669–2681

    Article  Google Scholar 

  • White DM, Wilson WC, Blair CD, Beaty BJ (2005) Studies on overwintering of bluetongue viruses in insects. J Gen Virol 86(2):453–462

    Article  Google Scholar 

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Acknowledgments

We would like to thank the support of the EPSRC and AHVLA for Hayley O’Farrell’s PhD studentship.

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Authors and Affiliations

  1. Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK

    Hayley O’Farrell & Stephen A. Gourley

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  1. Hayley O’Farrell
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  2. Stephen A. Gourley
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Correspondence to Stephen A. Gourley.

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O’Farrell, H., Gourley, S.A. Modelling the Dynamics of Bluetongue Disease and the Effect of Seasonality. Bull Math Biol 76, 1981–2009 (2014). https://doi.org/10.1007/s11538-014-9989-8

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  • DOI: https://doi.org/10.1007/s11538-014-9989-8

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