Time-delayed dynamics modeling of brucellosis transmission in sheep: precision control strategies driven by age-sex heterogeneity and target reproduction number

Jun Yang; Boqiang Cao; Ting Kang; Qingyun Wang; Jun Yang; Boqiang Cao; Ting Kang; Qingyun Wang

doi:10.3934/era.2026103

Electronic Research Archive

2026, Volume 34, Issue 4: 2279-2302. doi: 10.3934/era.2026103

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Time-delayed dynamics modeling of brucellosis transmission in sheep: precision control strategies driven by age-sex heterogeneity and target reproduction number

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2.
Ningxia Basic Science Research Center of Mathematics, Yinchuan 750021, China
3.
Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received: 27 January 2026 Revised: 22 February 2026 Accepted: 06 March 2026 Published: 16 March 2026

Brucellosis is a zoonotic disease caused by bacteria of the genus Brucella, posing a significant threats to human health and the development of the livestock industry. Experimental studies have demonstrated significant differences in infection rates among sheep of different ages and sexes. Based on this, this paper develops a time-delayed dynamical model for brucellosis transmission with age-sex structure, coupling the sheep population with environmental contamination, and incorporates a latency time delay to characterize the temporal delay in disease transmission. First, the basic reproduction number is calculated, and the global stability of both disease-free and endemic equilibria is established. Second, for three control measures (i.e., vaccination, isolation of infected sheep, and environmental disinfection) the target reproduction numbers are computed to quantitatively evaluate the relative effectiveness of each strategy in mitigating brucellosis transmission. Numerical simulations reveal that increasing the time delay reduces the number of infected sheep and the concentration of Brucella in the environment. When the target reproduction number exceeds 1, vaccination achieves optimal control efficacy, with required coverage decreasing as the time delay increases. In addition, by adjusting the input rates of female and male lambs and the time delay, the cost-effectiveness of age-based and sex-based vaccination strategies is compared, identifying the parameter regions where each strategy is economically dominant.
- time-delayed dynamical model of brucellosis,
- target reproduction number,
- stability,
- control measures,
- cost-effectiveness
Citation: Jun Yang, Boqiang Cao, Ting Kang, Qingyun Wang. Time-delayed dynamics modeling of brucellosis transmission in sheep: precision control strategies driven by age-sex heterogeneity and target reproduction number[J]. Electronic Research Archive, 2026, 34(4): 2279-2302. doi: 10.3934/era.2026103

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Abstract

Brucellosis is a zoonotic disease caused by bacteria of the genus Brucella, posing a significant threats to human health and the development of the livestock industry. Experimental studies have demonstrated significant differences in infection rates among sheep of different ages and sexes. Based on this, this paper develops a time-delayed dynamical model for brucellosis transmission with age-sex structure, coupling the sheep population with environmental contamination, and incorporates a latency time delay to characterize the temporal delay in disease transmission. First, the basic reproduction number is calculated, and the global stability of both disease-free and endemic equilibria is established. Second, for three control measures (i.e., vaccination, isolation of infected sheep, and environmental disinfection) the target reproduction numbers are computed to quantitatively evaluate the relative effectiveness of each strategy in mitigating brucellosis transmission. Numerical simulations reveal that increasing the time delay reduces the number of infected sheep and the concentration of Brucella in the environment. When the target reproduction number exceeds 1, vaccination achieves optimal control efficacy, with required coverage decreasing as the time delay increases. In addition, by adjusting the input rates of female and male lambs and the time delay, the cost-effectiveness of age-based and sex-based vaccination strategies is compared, identifying the parameter regions where each strategy is economically dominant.

References

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