Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Threshold phenomena with respect to the initiation of depopulation in a simple model of foot-and-mouth disease

1 Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan
2 Kurihara Central Hospital 3-1-1 Miyano-Chuo Tukidate Kurihara city, Miyagi, Japan
3 Department of Health Informatics, Kyoto University School of Public Health, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan
4 Zimmer Biomet G.K., 16F Sumitomo Fudosan Sibakoen Tower, 11-1, Shibakoen 2-chome, Minato-ku, Tokyo, Japan
5 Department of Infectious Diseases, Fujita Health University School of Medicine, 1-98 Dengakugakubo, Kutsukake-cho, Toyoake, Aichi, Japan
6 Department of Global Health Policy, The Faculty of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan
7 ALESS Program, Center for Global Communication Strategies, College of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan
8 The Center for Data Science Education and Research, Shiga University, 1-1-1, Banba, Hikone-city, Shiga, Japan

Depopulation is one of the important interventions for the outbreak of animal diseases. Simulation models using actual case scenarios conclude that early depopulation is the most efficient in preventing the spread of foot-and-mouth disease (FMD). However, the long delay in its initiation was often seen in the actual cases and the theoretical analyses of FMD epidemiology with depopulation needs further elaboration. Here, we investigated the qualitative features of epidemic models when depopulation at a fixed capacity was delayed. We built a simple deterministic model for FMD based on state-transition, the SEIIR model whose unit is a single farm. The model settings and parameters were determined using the data from the 2010 epidemic in Miyazaki, Japan. By numerical calculation, we showed the existence of the threshold phenomenon with respect to delays in the initiation of depopulation and if the initiation of full-fledged depopulation surpasses the certain critical timing, the final size of the epidemic rapidly increases leading to a “catastrophic situation”. We also revealed the mechanism of the threshold phenomenon from the relationship between the depopulation capacity and the increasing rate of infection. Although it can be delayed with lower transmission coefficients, the threshold phenomenon still exists. Thus, the existence of the critical timing for depopulation appears to be a universal feature of FMD epidemiology when depopulation is used as the main treatment for disease control.
  Figure/Table
  Supplementary
  Article Metrics

References

1. W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Royal Soc. Lond. A, 115 (1927), 700–721.

2. R.M. Anderson and R.M May, Infectious diseases of humans: Dynamics and control, Oxford: Oxford University Press, 1992.

3. M. C. White and X. Zhao, Threshold dynamics in a time-delayed epidemic model with dispersal, Math. Biosci., 218 (2009), 121–129.

4. Y. Lou and X. Zhao, Threshold dynamics in a time-delayed periodic SIS epidemic model, Discrete Continuous Dyn. Syst. Ser. B, 12 (2009), 169–186.

5. K. Nah, Y. Kim and J. M. Lee, The dilution effect of the domestic animal population on the transmission of p. vivax malaria, J. Theor. Biol., 266 (2010), 299–306.

6. X. Zhou and J. Cui, Threshold dynamics for a cholera epidemic model with periodic transmission rate, Appl. Math. Model., 37 (2013), 3093–3101.

7. Z. Bai, Threshold dynamics of a time-delayed SEIRS model with pulse vaccination, Math. Biosci., 269 (2015), 178–185.

8. X. Hu, Y. Zhang and F. Sun, Threshold dynamics for a pertussis model with seasonality, Int. J. Nonlinear Sci., 17 (2014), 281–288.

9. F. Zhang and X. Zhang, The threshold of a stochastic avian-human influenza epidemic model with psychological effect, Physica A, 492 (2018), 485–495.

10. D. T. Haydon, M. E. J. Woolhouse and R. P. Kitching, An analysis of foot and mouth disease epidemics in the UK, IMA J. Math. App. Med. Biol., 14 (1997), 1–9.

11. D. J. Paton, S. Gubbins and D. P. King, Understanding the transmission of foot-and-mouth disease virus at different scales, Curr. Opin. Virol., 28 (2018), 85–91.

12. C. Bravo de Rueda, M. C. de Jong, P. L. Eblé, et al., Quantification of transmission of foot-and- mouth disease virus caused by an environment contaminated with secretions and excretions from infected calves, Vet. Res., 46 (2015), 43.

13. J. Slingluff, F. Sampedro and T. J. Goldsmith, Risk assessment for the transmission of foot and mouth disease via movement of swine and cattle carcasses from fmd-infected premises to a disposal site, 2014. Available from: http://hdl.handle.net/11299/193839.

14. Veterinary science team global animal health-international disease monitoring preliminary outbreak assessment, Vitt/1200 Update FMD in East Asia, 1–2.

15. Foot and mouth disease, Japan, OIE: Follow-up report 2 : 28/04/2010, 2010. Available from: http://www.oie.int/wahis 2/public/wahid.php/Reviewreport/Review?reportid=9185.

16. Foot and mouth disease, Korea (Rep. of), OIE: Follow-up report 1 : 30/11/2010, 2010. Available from: http://www.oie.int/wahis 2/public/wahid.php/Reviewreport/Review?reportid=10002.

17. N. Muroga, Y. Hayama, T. Yamamoto, et al., The 2010 foot-and-mouth disease epidemic in Japan, J. Vet. Med. Sci., 74 (2012), 399–404.

18. Malignant exotic animal disease control guidelines, Ministry of agriculture, forestry and fisheries [MAFF] livestock industry bureau director general administrative notification No. 50-Chiku-A-3843 1975 amended by No. 51-Chiku-A-2760 [in Japanese]. Tokyo, 31.

19. Act on domestic animal infectious diseases control (law no. 166, 1951). Official gazettes of 31 May 1951, 31 March 1952, 1 August 1953, 15 August 1953, 27 August 1955, 24 March 1956, 6 June 1956, 15 September 1962, 5 June 1971, 31 December 1971, 7 May 1975, 5 July 1978, 18 May 1985, 19 December 1989, 11 April 1997 and 16 July 1999, Tokyo: Ministry of finance printing bureau, 2019. Available from: http://www.cas.go.jp/jp/seisaku/hourei/data/adaidc.pdf.

20. Infection with foot and mouth disease virus, OIE, 2018. Available from: http://www.oie.int/fileadmin/Home/eng/Health standards/tahc/current/chapitre fmd.pdf.

21. List of FMD free members: OIE-World Organisation for Animal Health, 2018. Available from: http://www.oie.int/en/animal-health-in-the-world/official-disease-status/fmd/list-of-fmd-free-members.

22. M. J. Tildesley, N. J. Savill, D. J. Shaw, et al., Optimal reactive vaccination strategies for a foot- and-mouth outbreak in the UK, Nature, 440 (2006), 83–86.

23. H. Yoon, S. H. Wee, M. A. Stevenson, et al., I. J. Hwang, C. K. Park and M. W. Stern, Simulation analyses to evaluate alternative control strategies for the 2002 foot-and-mouth disease outbreak in the Republic of Korea, Prev. Vet. Med., 74 (2006), 212–225.

24. Y. Hayama, T. Yamamoto, S. Kobayashi, et al., Mathematical model of the 2010 foot-and-mouth disease epidemic in Japan and evaluation of control measures, Prev. Vet. Med., 112 (2013), 183–193.

25. C. Dubé, M. A. Stevenson, M. G. Garner, et al., A comparison of predictions made by three simulation models of foot-and-mouth disease, N. Z. Vet. J., 55 (2007), 280–288.

26. A. Bouma, A. R. Elbers, A. Dekker, et al., The foot-and-mouth disease epidemic in the Netherlands in 2001, Prev. Vet. Med., 57 (2003), 155–166.

27. N. M. Ferguson, C. A. Donnelly and R. M. Anderson, Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain, Nature, 413 (2001), 542–548.

28. APHIS evaluation of the foot and mouth disease status of Japan, Animal and Plant Health Inspection Service Veterinary Services, 2011.

29. H. Nishiura and R. Omori, An epidemiological analysis of the foot-and-mouth disease epidemic in Miyazaki, Japan, 2010, Transbound. Emerg. Dis., 57 (2010), 396–403.

30. F. Mardones, A. Perez, J. Sanchez, et al., Parameterization of the duration of infection stages of serotype O foot-and-mouth disease virus: An analytical review and meta-analysis with application to simulation models, Vet. Res., 41 (2010), 45.

31. S. Z. Huang, A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0, Math. Biosci., 215 (2008), 84–104.

32. S. Alexandersen, M. Quan, C. Murphy, et al., Studies of quantitative parameters of virus excretion and transmission in pigs and cattle experimentally infected with foot-and-mouth disease virus, J. Comp. Pathol., 129 (2003), 268–282.

33. C. Stenfeldt, J. M. Pacheco, B. P. Brito, et al., Transmission of foot-and-mouth disease virus during the incubation period in pigs, Front. Vet. Sci., 3 (2016), 105.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved