Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

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.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Ala’Aldeen D (2001) Risk of deliberately induced Anthrax outbreak. Lancet 358:1386–1388

    Article  Google Scholar 

  • Beyer W, Turnbull PCB (2009) Anthrax in animals. Mol Aspects Med 30:481–489

    Article  Google Scholar 

  • Bouzianas DG (2009) Medical countermeasures to protect humans from Anthrax bioterrorism. Trends Microbiol 17(11):522–528

    Article  Google Scholar 

  • CDC (2014) Report on the potential exposure to Anthrax. Technical Report 7/11, centers for disease control and prevention

  • 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 Association

  • D’Aamelio E (2015) Historical evolution of human Anthrax from occupational disease to potentially global threat as bioweapon. Environ Int 85:133–146

    Article  Google Scholar 

  • 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 54:32–40

    Google Scholar 

  • Fasanella A (2005) Molecular diversity of Bacillus anthracis in Italy. J Clin Microbiol 43:3398–3401

    Article  Google Scholar 

  • Fasanella A, Galante D, Garofolo G, Jones MH (2010) Anthrax undervalued zoonosis. Vet Microbiol 140:318–331

    Article  Google Scholar 

  • Fouet A (2002) Diversity among French Bacillus anthracis isolates. J Clin Microbiol 40:4732–4734

    Article  Google Scholar 

  • Friedman A, Yakubu A-A (2013) Anthrax epizootic and migration: persistence or extinction. Math Biosci 241(1):137–144

    Article  MathSciNet  MATH  Google Scholar 

  • Furniss PR, Hahn BD (1981) A mathematical model of an Anthrax epizootic in the Kruger National Park. Appl Math Model 5(3):130–136

    Article  Google Scholar 

  • Grabenstein JD (2008) Countering Anthrax: vaccines and immunoglobulins. Clin Infect Dis 46:129–136

    Article  Google Scholar 

  • Hahn BD, Furniss PR (1983) A deterministic model of an Anthrax epizootic: threshold results. Ecol Model 20(2–3):233–241

    Article  Google Scholar 

  • Hart CA, Beeching NJ (2002) A spotlight on Anthrax. Clin Dermatol 20:365–375

    Article  Google Scholar 

  • Hugh-Jones M (1999) 1996–1997 Global Anthrax report. J Appl Microbiol 87:189–91

    Article  Google Scholar 

  • Hugh-Jones M, de Vos EV (2002) Anthrax and wildlife. Rev Sci Tech 2:359–389

    Article  Google Scholar 

  • 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 95:1224–1229

    Article  Google Scholar 

  • Jamie WE (2002) Anthrax: diagnosis, treatment, prevention. Prim Care Update OB/GYNS 9:117–121

    Article  Google Scholar 

  • Jernigan DB (2002) Investigation of bioterrorism-related Anthrax, United States, 2001: epidemiologic findings. Emerg Infect Dis 8:1019–1028

    Article  Google Scholar 

  • Meselson M, Guillemin J, Hugh-Jones M (1994) The Sverdlovsk outbreak of 1979. Science 266:1202–1208

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

  • Pantha B, Day J, Lenhart S (2016) Optimal control applied in an Anthrax epizootic model. J Biol Syst 24(4):495–517

    Article  MathSciNet  MATH  Google Scholar 

  • Pasteur L, Chamberland C, Roux E (1881) Le vaccin du charbon. CR Acad Sci Paris 92:666–668

    Google Scholar 

  • Pontryagin LS (1962) The mathematical theory of optimal processes. Wiley, New York

    Google Scholar 

  • Riedel S (2005) Anthrax: a continuing concern in the era of bioterrorism. BUMC Proc 18:234–243

    Google Scholar 

  • Saad-Roy CM, van den Driessche P, Yakubu A-A (2017) A mathematical model of Anthrax transmission in animal populations. Bull Math Biol 79:303–324

    Article  MathSciNet  MATH  Google Scholar 

  • Schwartz M (2009) Dr Jekyll and Mr Hyde: A short history of Anthrax. Mol Aspects Med 30:347–355

    Article  Google Scholar 

  • Sterne M (1939) The use of Anthrax vaccines prepared from avirulent (uncapsulated) variants of Bacillus anthracis onderstepoort. J Vet Sci Animal Ind 13:307–312

    Google Scholar 

  • Twenhafel NA (2010) Pathology of inhalational Anthrax animal model. Vet Pathol 47(5):819

    Article  Google Scholar 

  • Webb G (2005) Being prepared: modeling the response to an Anthrax attack. Ann Intern Med 142:667–668

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kennesaw State University, 275 Kennesaw State University Rd., MD#1102, Kennesaw, GA, 30144, USA

    Ana-Maria Croicu

Authors
  1. Ana-Maria Croicu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ana-Maria Croicu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Croicu, AM. An Optimal Control Model to Reduce and Eradicate Anthrax Disease in Herbivorous Animals. Bull Math Biol 81, 235–255 (2019). https://doi.org/10.1007/s11538-018-0525-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-018-0525-0

Keywords

Search

Navigation