Dynamical analysis of an anthrax disease model in animals with nonlinear transmission rate
-
Published:2023
Issue:4
Volume:3
Page:370-386
-
ISSN:2767-8946
-
Container-title:Mathematical Modelling and Control
-
language:
-
Short-container-title:MMC
Author:
Kashyap Ankur Jyoti12, Bordoloi Arnab Jyoti1, Mohan Fanitsha1, Devi Anuradha1
Affiliation:
1. Department of Mathematics, The Assam Royal Global University, Assam, India 2. Department of Mathematics, Girijananda Chowdhury University, Assam, India
Abstract
<abstract><p>Anthrax is a bacterial infection caused by <italic>Bacillus anthracis</italic>, primarily affecting animals and occasionally affecting humans. This paper presents two compartmental deterministic models of anthrax transmission having vaccination compartments. In both models, a nonlinear ratio-dependent disease transmission function is employed, and the latter model distinguishes itself by incorporating fractional order derivatives, which adds a novel aspect to the study. The basic reproduction number $ \mathcal{R}_0 $ of the epidemic is determined, below which the disease is eradicated. It is observed that among the various parameters, the contact rate, disease-induced mortality rate, and rate of animal recovery have the potential to influence this basic reproduction number. The endemic equilibrium becomes disease-free via transcritical bifurcations for different threshold parameters of animal recovery rate, disease-induced mortality rate and disease transmission rate, which is validated by utilizing Sotomayor's theorem. Numerical simulations have revealed that a higher vaccination rate contributes to eradicating the disease within the ecosystem. This can be achieved by effectively controlling the disease-induced death rate and promoting animal recovery. The extended fractional model is analyzed numerically using the Adams-Bashforth-Moulton type predictor-corrector scheme. Finally, it is observed that an increase in the fractional order parameter has the potential to reduce the time duration required to eradicate the disease from the ecosystem.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Ocean Engineering
Reference51 articles.
1. J. G. Wright, C. P. Quinn, S. Shadomy, N. Messonnier, Use of anthrax vaccine in the United States: recommendations of the Advisory Committee on Immunization Practices (ACIP), 2009, MMWR Recomm. Rep., 59 (2010), 1–30. 2. A. N. Survely, B. Kvasnicka, R. Torell, Anthrax: a guide for livestock producers, Western Beef Resource Committee, 2001. Available from: https://extension.colostate.edu/docs/pubs/ag/anthrax-guide.pdf. 3. F. Baldacchino, V. Muenworn, M. Desquesnes, F. Desoli, T. Charoenviriyaphap, G. Duvallet, Transmission of pathogens by Stomoxys flies (Diptera, Muscidae): a review, Parasite, 20 (2013), 26. https://doi.org/10.1051/parasite/2013026 4. S. S. Lewerin, M. Elvander, T. Westermark, L. N. Hartzell, A. K. Norström, S. Ehrs, et al., Anthrax outbreak in a Swedish beef cattle herd-1st case in 27 years: case report, Acta. Vet. Scand., 52 (2010), 7. https://doi.org/10.1186/1751-0147-52-7 5. K. M. Good, C. Marobela, A. M. Houser, A report of anthrax in cheetahs (Acinonyx jubatus) in Botswana, J. S. Afr. Vet. Assoc., 76 (2005), 186. https://doi.org/10.10520/EJC99644
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
|
|