Modeling and optimal control analysis of age-structured Brucellosis under environmental transmission with vaccination and culling

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

Brucellosis is currently recognized as one of the most serious zoonotic infectious diseases, caused by Brucella abortus, and is classified by the World Organization for Animal Health as a Category B zoonotic disease. In this study, we developed a new seven-compartment model of the transmission dynamics brucellosis in sheep, which accounts for the combined effects of vaccination, age structure, culling of infected sheep, and the impact of the contaminated environment. Our analysis demonstrates that the DFE point of the system is globally and asymptotically stable when the basic reproduction number R₀ < 1. Furthermore, we show that the disease persists when R₀ > 1, in accordance with the theory of uniform persistence. In the numerical simulation section, we fit data on the number of Brucella infections in sheep in Egypt from 1999 to 2010 and estimate the model’s parameters using the least squares method. Based on this, we propose four control strategies to establish the optimal control system. We applied Pontryagin’s maximum principle to derive the necessary conditions for optimal control and perform numerical simulations. A cost-benefit analysis was conducted from the perspective of sheep farmers. Our findings suggest that the most cost-effective strategy for reducing brucellosis infection rates in sheep is to uniformly house young sheep and vaccinate them simultaneously.

Keywords

Brucellosis / vaccination / contaminated environments / uniform persistence / optimal control

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] D. Shang, D. Xiao, J. Yin, Epidemiology and control of brucellosis in China, Vet. Microbiol., 90 (2002), 165-182. https://doi.org/10.1016/s0378-1135(02)00252-3

[2] J. González-Guzmán, R. Naulin, Analysis of a model of bovine brucellosis using singular perturbations, J. Math. Biol., 33 (1994), 211-223. https://doi.org/10.1007/BF00160180

[3] J. Nie, G. Sun, X. Sun, J. Zhang, N. Wang, Y. Wang, et al., Modeling the transmission dynamics of dairy cattle brucellosis in Jilin Province, China, J. Biol. Syst., 22 (2014), 533-554. https://doi.org/10.1142/S021833901450020X

[4] J. Zhang, G. Sun, X. Sun, Q. Hou, M. Li, B. Huang, et al., Prediction and control of brucellosis transmission of dairy cattle in Zhejiang Province, China, PLoS ONE, 9 (2014), 108592. https://doi.org/10.1371/journal.pone.0108592

[5] G. Sun, Z. Zhang, Global stability for a sheep brucellosis model with immigration, Appl. Math. Comput., 246 (2014), 336-345. https://doi.org/10.1016/j.amc.2014.08.028

[6] Q. Hou, Global analysis of a multi-group animal epidemic model with indirect infection and time delay, J. Appl. Anal. Comput., 6 (2016), 1023-1040. https://doi.org/10.11948/2016066

[7] P. O. Lolika, S. Mushayabasa, C. P. Bhunu, C. Modnak, J. Wang, Modeling and analyzing the effects of seasonality on brucellosis infection, Chaos Solitons Fractals, 104 (2017), 338-349. https://doi.org/10.1016/j.chaos.2017.08.027

[8] L. Zhou, M. Fan, Q. Hou, Z. Jin, X. Sun, Transmission dynamics and optimal control of brucellosis in Inner Mongolia of China, Math. Biosci. Eng., 15 (2018), 543-567. https://doi.org/10.3934/mbe.2018025

[9] Q. Hou, X. Sun, Modeling sheep brucellosis transmission with a multi-stage model in Changling County of Jilin Province, China, J. Appl. Math. Comput., 51 (2016), 227-244. https://doi.org/10.1007/s12190-015-0901-y

[10] Q. Hou, X. Sun, J. Zhang, Y. Liu, Y. Wang, Z. Jin, Modeling the transmission dynamics of sheep brucellosis in Inner Mongolia Autonomous Region, China, Math. Biosci., 242 (2013), 51-58. https://doi.org/10.1016/j.mbs.2012.11.012

[11] C. Yang, P. O. Lolika, S. Mushayabasa, J. Wang, Modeling the spatiotemporal variations in brucellosis transmission, Nonlinear Anal. Real World Appl., 38 (2017), 49-67. https://doi.org/10.1016/j.nonrwa.2017.04.006

[12] M. Li, G. Sun, Y. Wu, J. Zhang, Z. Jin, Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm, Appl. Math. Comput., 237 (2014), 582-594. https://doi.org/10.1016/j.amc.2014.03.094

[13] B. Ainseba, C. Benosman, P. Magal, A model for ovine Brucellosis incorporating direct and indirect transmission, J. Biol. Dyn., 4 (2010), 2-11. https://doi.org/10.1080/17513750903171688

[14] C. Li, Z. Guo, Z. Zhang, Transmission dynamics of a brucellosis model: Basic reproduction number and global analysis, Chaos Solitons Fractals, 104 (2017), 161-172. https://doi.org/10.1016/j.chaos.2017.08.013

[15] K. Meng, X. Abdurahman, Study of the brucellosis transmission with multi-stage, Commun. Math. Biol. Neurosci., 2018 (2018), 20. https://doi.org/10.28919/cmbn/3796

[16] J. Zinsstag, F. Roth, D. Orkhon, G. Chimed-Ochir, M. Nansalmaa, J. Kolar, et al., A model of animal-human brucellosis transmission in Mongolia, Prev. Vet. Med., 69 (2005), 77-95. https://doi.org/10.1016/j.prevetmed.2005.01.017

[17] M. Li, G. Sun, J. Zhang, Z. Jin, X. Sun, Y. Wang, et al., Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China, Math. Biosci. Eng., 11 (2014), 1115-1137. https://doi.org/10.3934/mbe.2014.11.1115

[18] H. R. Holt, M. Walker, W. Beauvais, P. Kaur, J. S. Bedi, P. Mangtani, et al., Modelling the control of bovine brucellosis in India, J. R. Soc. Interface, 20 (2023), 20220756. https://doi.org/10.1098/rsif.2022.0756

[19] W. Wang, X. Abdurahman, Dynamics of a stochastic multi-stage sheep brucellosis model with incomplete immunity, Int. J. Biomath., 16 (2023), 08. https://doi.org/10.1142/S1793524522501388

[20] L. Zhou, M. Fan, Q. Hou, Z. Jin, X. Sun, Transmission dynamics and optimal control of brucellosis in Inner Mongolia of China, Math. Biosci. Eng., 15 (2018), 543-567. https://doi.org/10.3934/mbe.2018025

[21] B. Nannyonga, G. G. Mwanga, L. S. Luboobi, An optimal control problem for ovine brucellosis with culling, J. Biol. Dyn., 9 (2015), 198-214. https://doi.org/10.1080/17513758.2015.1056845

[22] H. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2002.

[23] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R₀ in models for infectious diseases in heterogeneous populations , J. Math. Biol., 28 (1990), 365-382. https://doi.org/10.1007/BF00178324

[24] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. https://doi.org/10.1016/s0025-5564(02)00108-6

[25] J. P. La Salle, The Stability of Dynamical Systems, Society for Industrial and Applied Mathematics, 1976. https://doi.org/10.1137/1.9781611970432

[26] X. Zhao, Dynamical Systems in Population Biology, Spring, 2nd edition, 2017. https://doi.org/10.1007/978-3-319-56433-3

[27] R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge University Press, 2012. https://doi.org/10.1017/CBO9780511810817

[28] W. Wang, X. Zhao, An epidemic model in a patchy environment, Math. Biosci., 190 (2004), 97-112. https://doi.org/10.1016/j.mbs.2002.11.001

[29] O. Diekmann, J. A. P. Heesterbeek, M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7 (2010), 873-885. https://doi.org/10.1098/rsif.2009.0386

[30] Z. Yue, Y. Mu, K. Yu, Dynamic analysis of sheep Brucellosis model with environmental infection pathways, Math. Biosci. Eng., 20 (2023), 11688-11712. https://doi.org/10.3934/mbe.2023520

[31] G. Wareth, A. Hikal, M. Refai, F. Melzer, U. Roesler, H. Neubauer, Animal brucellosis in Egypt, J. Infect. Dev. Countries, 8 (2014), 1365-1373.

[32] A. M. S. Menshawy, A. F. Vicente, Y. M. Hegazy, V. Djokic, M. E. R. Hamdy, L. Freddi, et al., Animal brucellosis in Egypt: Review on evolution, epidemiological situation, prevalent brucella strains, genetic diversity, and assessment of implemented national control measures, Microorganisms, 13 (2025), 170. https://doi.org/10.3390/microorganisms13010170