Global dynamics and optimal control in a brucellosis transmission model with distributed incubation delays

Xiaodong Wang; Lei Wang; Kai Wang; Zhidong Teng; Xiaodong Wang; Lei Wang; Kai Wang; Zhidong Teng

doi:10.3934/era.2026373

Electronic Research Archive

2026, Volume 34, Issue 12: 8850-8895. doi: 10.3934/era.2026373

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Research article

Global dynamics and optimal control in a brucellosis transmission model with distributed incubation delays

College of Medical Engineering and Technology, Institute of Medical Engineering Interdisciplinary Research, Xinjiang Medical University, Urumqi 830017, China

Received: 22 July 2026 Revised: 19 September 2026 Accepted: 08 October 2026 Published: 23 October 2026

In this paper, the global dynamics and optimal control strategies in a brucellosis transmission model with distribution incubation delays were investigated. The basic reproduction number of the model was first calculated, and then the threshold criteria for the global asymptotic stability of disease-free and endemic equilibria were established. Furthermore, the several effective measures for controlling the spread of diseases are introduced, and then an optimal control model that incorporates these measures was proposed. By providing a reasonable objective function, some optimal control strategies were established. Through numerical simulation of these optimal control strategies, reasonable prevention, control, and treatment measures for brucellosis were proposed.
- brucellosis model,
- global dynamics,
- optimal control strategy,
- distribution delay,
- latency
Citation: Xiaodong Wang, Lei Wang, Kai Wang, Zhidong Teng. Global dynamics and optimal control in a brucellosis transmission model with distributed incubation delays[J]. Electronic Research Archive, 2026, 34(12): 8850-8895. doi: 10.3934/era.2026373

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Abstract

In this paper, the global dynamics and optimal control strategies in a brucellosis transmission model with distribution incubation delays were investigated. The basic reproduction number of the model was first calculated, and then the threshold criteria for the global asymptotic stability of disease-free and endemic equilibria were established. Furthermore, the several effective measures for controlling the spread of diseases are introduced, and then an optimal control model that incorporates these measures was proposed. By providing a reasonable objective function, some optimal control strategies were established. Through numerical simulation of these optimal control strategies, reasonable prevention, control, and treatment measures for brucellosis were proposed.

References

[1]	J. Ariza, M. Bosilkovski, A. Cascio, J. D. Colmenero, M. J. Corbel, M. E. Falagas, et al., Prospectives for the treatment of brucellosis in the 21st century: The Ioannina recommendations, PLoS Med., 4 (2007), e317. https://doi.org/10.1371/journal.pmed.0040317 doi: 10.1371/journal.pmed.0040317
[2]	M. Corbel, Brucellosis in Humans and Animals: FAO, OIE, WHO. 2006.
[3]	F. Roth, J. Zinsstag, D. Orkhon, G. Chimed-Ochir, G. HuttonI, O. Cosivi, Human health benefits from livestock vaccination for brucellosis: Case study, Bull. World Health Organ., 81 (2003), 867–876.
[4]	G. Pappas, N. Akritidis, M. Bosilkovski, E. Tsianos, Brucellosis, N. Engl. J. Med., 352 (2005) 2325–2336. https://doi.org/10.1056/NEJMra050570 doi: 10.1056/NEJMra050570
[5]	X. Ma, G. Sun, Global dynamics of a periodic brucellosis model with time delay and environmental factors, Appl. Math. Modell., 130 (2024), 288–309. https://doi.org/10.1016/j.apm.2024.03.002 doi: 10.1016/j.apm.2024.03.002
[6]	Q. Hou, H. Qin, Global dynamics of a multi-stage brucellosis model with distributed delays and indirect transmission, Math. Biosci. Eng., 16 (2019), 3111–3129.
[7]	Q. Hou, X. Sun, J. Zhang, Y. Liu, Y. Wang, Zhen 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 doi: 10.1016/j.mbs.2012.11.012
[8]	M. Li, G. Sun, W. Zhang, Z. Jin, Model-based evaluation of strategies to control brucellosis in China, Int. J. Environ. Res. Public Health, 14 (2017), 295. https://doi.org/10.3390/ijerph14030295 doi: 10.3390/ijerph14030295
[9]	M. Li, X. Pei, J. Zhang, L. Li, Asymptotic analysis of endemic equilibrium to a brucellosis model, Math. Biosci. Eng., 16 (2019), 5836–5850. https://doi.org/10.3934/mbe.2019291 doi: 10.3934/mbe.2019291
[10]	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 doi: 10.1016/j.chaos.2017.08.027
[11]	J. Yang, R. Xu, H. Sun, Dynamics of a seasonal brucellosis disease model with nonlocal transmission and spatial diffusion, Commun. Nonlinear Sci. Numer. Simul., 94 (2021), 105551. https://doi.org/10.1016/j.cnsns.2020.105551 doi: 10.1016/j.cnsns.2020.105551
[12]	Z. Zhang, J. Zhang, L. Li, Z. Guo, Z. Zhang, G Sun, Quantifying the effectiveness of brucellosis control strategies in northern China using a mechanistic and data-driven model, Chaos Solitons Fractals, 185 (2024), 115121. https://doi.org/10.1016/j.chaos.2024.115121 doi: 10.1016/j.chaos.2024.115121
[13]	X. Wang, K. Wang, L. Wang, Z. Teng, Dynamics of a stochastic brucellosis model with vaccination and environmental pollution transmission, Qual. Theory Dyn. Syst., 23 (2024), 299. https://doi.org/10.1007/s12346-024-01158-x doi: 10.1007/s12346-024-01158-x
[14]	G. J. Kang, L. Gunaseelan, K. M. Abbas, Epidemiological modeling of bovine brucellosis in India, in 2014 IEEE International Conference on Big Data, IEEE, (2014), 6–10. https://doi.org/10.7490/f1000research.1111710.1
[15]	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 doi: 10.1142/S021833901450020X
[16]	J. Zhang, Z. Jin, L. Li, X. Sun, Cost assessment of control measure for brucellosis in Jilin province, China, Chaos Solitons Fractals, 104 (2017), 798–805. https://doi.org/10.1016/j.chaos.2017.09.004 doi: 10.1016/j.chaos.2017.09.004
[17]	Z. Liu, H. Wang, M. Wang, Z. Li, Investigation of the molecular epizootiological characteristics and tracking of the geographical origins of brucella canis strains in China, Transbound. Emerg. Dis., 67 (2020), 834–843. https://doi.org/10.1111/tbed.13404 doi: 10.1111/tbed.13404
[18]	D. Wu, W. Zhang, Y. Ma, Y. Zheng, H. Li, G. Hu, Investigation on risk factors of brucellosis outbreak caused by occupational exposure in a dairy farm (in Chinese), Dis. Surveill., 34 (2019), 473–476. https://doi.org/10.3784/j.issn.1003-9961.2019.05.022 doi: 10.3784/j.issn.1003-9961.2019.05.022
[19]	Z. Bian, L. Zhu, Y. Feng, S. Sun, Y. Qin, J. Ding, Epidemiological trend and characteristics of brucellosis in aborted dairy herds in China from 2013 to 2017 (in Chinese), Microbiol. China, 46 (2019), 618–623. https://doi.org/10.13344/j.microbiol.china.180390 doi: 10.13344/j.microbiol.china.180390
[20]	F. F. Tuon, R. B. Gondolfo, N. Cerchiari, Human-to-human transmission of Brucella a systematic review, Trop. Med. Int. Health, 22 (2017), 539–546. https://doi.org/10.1111/tmi.12856 doi: 10.1111/tmi.12856
[21]	H. Wu, W. Chen, N. Wang, L. Zhang, H. Li, Z. Teng, A delayed stage-structure brucellosis model with interaction among seasonality, time-varying incubation and density-dependent growth, Inter. J. Biomath., 16 (2023), 2250114. https://doi.org/10.1142/s1793524522501145 doi: 10.1142/s1793524522501145
[22]	Q. Hou, F. Zhang, Global dynamics of a general brucellosis model with discrete delay, J. Appl. Anal. Comput., 6 (2016), 227–241. https://www.jaac-online.com/article/doi/10.11948/2016019
[23]	M. Wu, X. Abdurahman, Z. Teng, Optimal control strategy analysis for an human-animal brucellosis infection model with multiple delays, Heliyon, 8 (2022), e12274. https://doi.org/10.1016/j.heliyon.2022.e12274 doi: 10.1016/j.heliyon.2022.e12274
[24]	Q. Hou, L. Zhang, M. Liu, Mathematical analysis of a time-delayed model on brucellosis transmission with disease testing information, Inter. J. Biomath., 13 (2020), 2050039. https://doi.org/10.1142/s1793524520500394 doi: 10.1142/s1793524520500394
[25]	A. Ma, J. Hu, X. Li, X. Xu, Q. Zhang, Hopf bifurcation and optimal control of a delayed reaction-diffusion brucellosis disease model, Int. J. Biomath., 19 (2024), 2450060. https://doi.org/10.1142/s1793524524500608 doi: 10.1142/s1793524524500608
[26]	X. He, T. Lv, J. Liu, L. Zhou, M. Fan, Dynamical modeling and optimal control of brucellosis with mixed delays and environmental transmission, Int. J. Biomath., 14 (2025), 2550136. https://doi.org/10.1142/s1793524525501360 doi: 10.1142/s1793524525501360
[27]	J. Lai, X. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission, SIAM J. Appl. Math. 74 (2014), 898–917. https://doi.org/10.1137/130930145 doi: 10.1137/130930145
[28]	Y. Hinon, S. Murakami, T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics 1473, Springer-Verlag, Berlin Heidelberg, 1991. https://doi.org/10.1007/bfb0084432
[29]	X. Q. Zhao, The linear stability and basic reproduction number for autonomous FDEs, Disc. Cont. Dyn. Sys. S, 17 (2024), 708–719. https://doi.org/10.3934/dcdss.2023082 doi: 10.3934/dcdss.2023082
[30]	J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. https://doi.org/10.1137/1.9781611970432
[31]	S. Lenhart, J. T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC, 2007. https://doi.org/10.1201/9781420011418
[32]	J. Danane, A. Meskaf, K. Allali, Optimal control of a delayed hepatitis B viral infection model with HBV DNA-containing capsids and CTL immune response, Optim. Control Appl. Methods, 39 (2018), 1262–1272. https://doi.org/10.1002/oca.2407 doi: 10.1002/oca.2407
[33]	S. Nababan, A Filippov-type lemma for functions involving delays and its application to time-delayed optimal control problems, J. Optim. Theory Appl., 27 (1979), 357–376. https://doi.org/10.1007/BF00933030 doi: 10.1007/BF00933030
[34]	L. Gollmann, D. Kern, H. Maurer, Optimal control problems with delays in state and control variables subject to mixed control-state constraints, Optim. Control Appl. Methods, 30 (2009), 341–365. https://doi.org/10.1002/oca.843 doi: 10.1002/oca.843
[35]	E. B. M. Bashier, K. C. Patidar, Optimal control of an epidemiological model with multiple time delays, Appl. Math. Comput., 292 (2017), 47–56. https://doi.org/10.1016/j.amc.2016.07.009 doi: 10.1016/j.amc.2016.07.009
[36]	H. Muhtar, H. He, X. Tai, X. Chen, S. Tong, Z. Wang, Analysis of surveillance data and epidemic situation of human brucellosis in Xinjiang, 2013 (in Chinese), Chin. J. Vect. Biol. Control, 26 (2015), 86–88. https://doi.org/10.11853/j.issn.1003.4692.2015.01.024 doi: 10.11853/j.issn.1003.4692.2015.01.024
[37]	P. Lou, L. Wang, X. Zhang, J. Xu, K. Wang, Modelling seasonal Brucellosis epidemics in Bayingolin Mongol Autonomous Prefecture of Xinjiang, China, 2010–2014, Bio. Med Res. Inter., 2016 (2016), 5103718. https://doi.org/10.1155/2016/5103718 doi: 10.1155/2016/5103718
[38]	C. Sun, H. Ma, S. Yin, Brucellosis (in Chinese), Ningxia Peoples Press, 1985.

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