Advertisement

Bulletin of Mathematical Biology

, Volume 81, Issue 1, pp 235–255 | Cite as

An Optimal Control Model to Reduce and Eradicate Anthrax Disease in Herbivorous Animals

  • Ana-Maria Croicu
Original Article
  • 71 Downloads

Abstract

Anthrax is a fatal infectious disease which can affect animals and humans alike. Anthrax outbreaks occur periodically in animals, and they are of particular concern in herbivores, due to substantial economic consequences associated with animal death. The purpose of this study is to develop optimal control interventions that focus on vaccinating susceptible animals and/or removing infected carcasses. Our mathematical goal is to minimize the infectious animal population while reducing the cost of interventions. Optimal control interventions are derived theoretically, and numerical results with conclusions are presented.

Keywords

Anthrax Differential equations Optimal control State equations Adjoint equations 

References

  1. Ala’Aldeen D (2001) Risk of deliberately induced Anthrax outbreak. Lancet 358:1386–1388CrossRefGoogle Scholar
  2. Beyer W, Turnbull PCB (2009) Anthrax in animals. Mol Aspects Med 30:481–489CrossRefGoogle Scholar
  3. Bouzianas DG (2009) Medical countermeasures to protect humans from Anthrax bioterrorism. Trends Microbiol 17(11):522–528CrossRefGoogle Scholar
  4. CDC (2014) Report on the potential exposure to Anthrax. Technical Report 7/11, centers for disease control and preventionGoogle Scholar
  5. Conger TH (2001) Anthrax epizootic texas, summer of 2001. In: Proceedings of the one hundred and fifth annual meeting, volume 207. United States Animal Health AssociationGoogle Scholar
  6. D’Aamelio E (2015) Historical evolution of human Anthrax from occupational disease to potentially global threat as bioweapon. Environ Int 85:133–146CrossRefGoogle Scholar
  7. Dragon DC, Elkin BT (2001) An overview of early Anthrax outbreaks in Northern Canada: field reports of the health animal branch, Agriculture, Canada, 1962–1971. Artic 54:32–40Google Scholar
  8. Fasanella A (2005) Molecular diversity of Bacillus anthracis in Italy. J Clin Microbiol 43:3398–3401CrossRefGoogle Scholar
  9. Fasanella A, Galante D, Garofolo G, Jones MH (2010) Anthrax undervalued zoonosis. Vet Microbiol 140:318–331CrossRefGoogle Scholar
  10. Fouet A (2002) Diversity among French Bacillus anthracis isolates. J Clin Microbiol 40:4732–4734CrossRefGoogle Scholar
  11. Friedman A, Yakubu A-A (2013) Anthrax epizootic and migration: persistence or extinction. Math Biosci 241(1):137–144MathSciNetCrossRefzbMATHGoogle Scholar
  12. Furniss PR, Hahn BD (1981) A mathematical model of an Anthrax epizootic in the Kruger National Park. Appl Math Model 5(3):130–136CrossRefGoogle Scholar
  13. Grabenstein JD (2008) Countering Anthrax: vaccines and immunoglobulins. Clin Infect Dis 46:129–136CrossRefGoogle Scholar
  14. Hahn BD, Furniss PR (1983) A deterministic model of an Anthrax epizootic: threshold results. Ecol Model 20(2–3):233–241CrossRefGoogle Scholar
  15. Hart CA, Beeching NJ (2002) A spotlight on Anthrax. Clin Dermatol 20:365–375CrossRefGoogle Scholar
  16. Hugh-Jones M (1999) 1996–1997 Global Anthrax report. J Appl Microbiol 87:189–91CrossRefGoogle Scholar
  17. Hugh-Jones M, de Vos EV (2002) Anthrax and wildlife. Rev Sci Tech 2:359–389CrossRefGoogle Scholar
  18. Jackson PJ, Hugh-Jones ME, Adair DM (1998) PCR analysis of tissue samples from the 1979 Sverdlovsk Anthrax victims: the presence of multiple Bacillus anthracis strains in different victims. Proc. Natl. Acad. Sci. USA 95:1224–1229CrossRefGoogle Scholar
  19. Jamie WE (2002) Anthrax: diagnosis, treatment, prevention. Prim Care Update OB/GYNS 9:117–121CrossRefGoogle Scholar
  20. Jernigan DB (2002) Investigation of bioterrorism-related Anthrax, United States, 2001: epidemiologic findings. Emerg Infect Dis 8:1019–1028CrossRefGoogle Scholar
  21. Meselson M, Guillemin J, Hugh-Jones M (1994) The Sverdlovsk outbreak of 1979. Science 266:1202–1208CrossRefGoogle Scholar
  22. Mushayabasa S, Marijani T, Masocha M (2015) Dynamical analysis and control strategies in modeling Anthrax. Comput Appl Math 36:1333–1348.  https://doi.org/10.1007/s40314-015-0297-1 MathSciNetCrossRefzbMATHGoogle Scholar
  23. NIAID (2006) Biodefense research agenda for CDC category A agents. Technical report, US Department of Health and Human Services, National Institute of Allergy and Infectious Diseases (NIAID), pp 15–23 (2006). https://www.niaid.nih.gov/sites/default/files/cata_2006.pdf
  24. Pantha B, Day J, Lenhart S (2016) Optimal control applied in an Anthrax epizootic model. J Biol Syst 24(4):495–517MathSciNetCrossRefzbMATHGoogle Scholar
  25. Pasteur L, Chamberland C, Roux E (1881) Le vaccin du charbon. CR Acad Sci Paris 92:666–668Google Scholar
  26. Pontryagin LS (1962) The mathematical theory of optimal processes. Wiley, New YorkGoogle Scholar
  27. Riedel S (2005) Anthrax: a continuing concern in the era of bioterrorism. BUMC Proc 18:234–243Google Scholar
  28. Saad-Roy CM, van den Driessche P, Yakubu A-A (2017) A mathematical model of Anthrax transmission in animal populations. Bull Math Biol 79:303–324MathSciNetCrossRefzbMATHGoogle Scholar
  29. Schwartz M (2009) Dr Jekyll and Mr Hyde: A short history of Anthrax. Mol Aspects Med 30:347–355CrossRefGoogle Scholar
  30. Sterne M (1939) The use of Anthrax vaccines prepared from avirulent (uncapsulated) variants of Bacillus anthracis onderstepoort. J Vet Sci Animal Ind 13:307–312Google Scholar
  31. Twenhafel NA (2010) Pathology of inhalational Anthrax animal model. Vet Pathol 47(5):819CrossRefGoogle Scholar
  32. Webb G (2005) Being prepared: modeling the response to an Anthrax attack. Ann Intern Med 142:667–668CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsKennesaw State UniversityKennesawUSA

Personalised recommendations