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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Bovines Migration Effect on the Global Behavior of the Babesiosis-Bovine Epidemic Model

Journal of Environmental Accounting and Management 13(3) (2025) 289--309 | DOI:10.5890/JEAM.2025.09.005

Abdelheq Mezouaghi, Rassim Darazirar, Salih Djilali, Tahar Abbes Mounir

Faculty of Exact Sciences and informatics, Hassiba Benbouali University, Chlef 02000, Algeria

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Abstract

This study explores the impact of infected bovine immigrations on the outbreak of Babesiosis disease. A mathematical model is formulated to investigate this effect, specifically considering two cases: one with infected bovine immigration and another without it. In the first case, the immigration is assumed to occur only in bovines, excluding the tick population. The key finding of this case reveals that the epidemic remains persistent and the system admits a unique endemic equilibrium that is globally asymptotically stable. In the second case, the model assumes immigration of bovines exclusively in the susceptible and recovered populations. In this scenario, the dynamics of the model are governed by the basic reproduction number, denoted as $\mathcal{R} _{0} $. When $\mathcal{R} _{0} <1$, the disease is predicted to die out, as indicated by the global asymptotic stability of the disease-free equilibrium. Conversely, when $\mathcal{R} _{0}>1$, the disease persists, and the unique endemic equilibrium is globally asymptotically stable. To further validate these findings, numerical simulations are conducted, providing additional support for the obtained results.

References

  1. [1]  Friedman, A. and Yakubu, A.A. (2014), A bovine babesiosis model with dispersion, Bulletin of Mathematical Biology, 76(1), 98-135.
  2. [2]  Spickler, A.R. (2008), D v m, bovine babesiosis. Available at http://www.cfsph.iastate. edu/DiseaseInfo/factsheets.php, viewed at October/ 02/ 2018.
  3. [3]  McFadzean, H., Johnson, N., Phipps, L.P., Swinson, V., and Boden, L.A. (2023), Surveillance and risk analysis for bovine babesiosis in england and wales to inform disease distribution, Animals, 13(13), p.2118.
  4. [4]  Ferreira, G.C.M., Canozzi, M.E.A., Peripolli, V., de Paula Moura, G., Sánchez, J., and Martins, C.E.N. (2022), Prevalence of bovine Babesia spp., Anaplasma marginale, and their co-infections in Latin America: Systematic review-meta-analysis, Ticks and Tick-borne Diseases, 13(4), p.101967.
  5. [5]  Aranda, D.F., Trejos, D.Y., Valverde, J.C., and Villanueva, R.J. (2012), A mathematical model for Babesiosis disease in bovine and tick populations, Mathematical Methods in the Applied Sciences, 35(3), 249-256.
  6. [6]  Aranda, D.F., Trejos, D.Y., and Valverde, J.C. (2017), A discrete epidemic model for bovine Babesiosis disease and tick populations, Open Physics, 15(1), 360-369.
  7. [7]  Solorio-Rivera, J.L. and Rodríguez-Vivas, R.I. (1997), Epidemiology of bovine babesiosis. I. Epidemiological components, Revista Biomédica,8, 37-47.
  8. [8]  Solorio-Rivera, J.L. and Rodríguez-Vivas, R.I. (1997), Epidemiology of the babesiosis bovis. II. Epidemiologic indicators and elements for the design of strategies of control, Revista Biomédica, 8, pp.95-105.
  9. [9]  Balibrea, F., Martinez, A., and Valverde, J.C. (2010), Local bifurcations of continuous dynamical systems under higher order conditions, Applied Mathematics Letters, 23(3), 230-234.
  10. [10]  Pourbashash, H. (2018), Global analysis of the Babesiosis disease in bovine and tick populations model and numerical simulation with multistage modified sinc method, Iranian Journal of Science and Technology, Transactions A: Science, 42, 39-46.
  11. [11] Slimane, I., Nieto, J.J., and Ahmad, S. (2023), A fractional-order bovine babesiosis epidemic transmission model with nonsingular mittag-leffler law, Fractals, 31(02), p.2340033.
  12. [12]  Saad-Roy, C.M., Shuai, Z., and Van den Driessche, P. (2015), Models of bovine babesiosis including juvenile cattle, Bulletin of Mathematical Biology, 77(3), 514-547.
  13. [13]  dos Santos, J.P.C., Cardoso, L.C., Monteiro, E., and Lemes, N.H. (2015), A fractional‐order epidemic model for bovine babesiosis disease and tick populations, In Abstract and Applied Analysis, 2015(1), p.729894, Hindawi publishing corporation.
  14. [14]  Zafar, Z., Rehan, K., and Mushtaq, M. (2017), Fractional-order scheme for bovine babesiosis disease and tick populations, advances in Difference Equations, 86.
  15. [15] Record in the exportations of Live Cattle to Algeria this week (2019), https://euroganaderosgroup.com/en/2019/04/01/record-in-the-exportations-of-live-cattle-to-algeria-this-week/
  16. [16] Abdelheq, M., Belhamiti, O., Bouzid, L., Trejos, D.Y., and Valverde, J.C. (2019), A predictive spatio-temporal model for bovine Babesiosis epidemic transmission, Journal of Theoretical Biology, 480, 192-204.
  17. [17]  Bouzid, L. and Belhamiti, O. (2017), Effect of seasonal changes on predictive model of bovine babesiosis transmission, International Journal of Modeling, Simulation, and Scientific Computing, 8(03), p.1750030.
  18. [18]  Rovid, A., Bovine Babesiosis, The center for food security and public health (2018), https://www.cfsph.iastate.edu/Factsheets/pdfs/bovine\_babesiosis.pdf.
  19. [19]  Committee on foreign and emerging diseases of the United States animal health association, Foreign animal diseases, Boca publications group, Inc., Canada, (2008).
  20. [20]  Demeke, A., Endris, E., Birhanu, A.S. (2018), Review on bovine Babesiosis, Acta Parasitologica, 9(1), 15-26.
  21. [21]  Mahoney, D.F. (1962), Bovine babesiosis: diagnosis of infection by a complement fixation test, Australian Veterinary Journal, 38(2), 48-52.
  22. [22]  Djilali, S. (2024), Dynamics of a spatiotemporal SIS epidemic model with distinct mobility range, Applicable Analysis, 1-23.
  23. [23]  Djilali, S., Chen, Y., and Bentout, S. (2025), Dynamics of a delayed nonlocal reaction–diffusion heroin epidemic model in a heterogenous environment, Mathematical Methods in the Applied Sciences, 48(1), 273-307. https://doi.org/10.1002/mma.10327.
  24. [24] Djilali, S. (2024), Generalities on a delayed spatiotemporal host–pathogen infection model with distinct dispersal rates, Mathematical Modelling of Natural Phenomena, 19, 11.
  25. [25]  Djilali, S. (2023), Threshold asymptotic dynamics for a spatial age-dependent cell-to-cell transmission model with nonlocal disperse, Discrete \& Continuous Dynamical Systems-Series B, 28(7).

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