Dynamics analysis of strangles with asymptomatic infected horses and long-term subclinical carriers

Lusha Shi; Jianghong Hu; Zhen Jin; Lusha Shi; Jianghong Hu; Zhen Jin

doi:10.3934/mbe.2023817

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18386-18412. doi: 10.3934/mbe.2023817

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Research article

Dynamics analysis of strangles with asymptomatic infected horses and long-term subclinical carriers

1.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
2.
Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China
3.
Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China
4.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received: 04 July 2023 Revised: 17 August 2023 Accepted: 24 August 2023 Published: 25 September 2023

Strangles is one of the most prevalent horse diseases globally. The infected horses may be asymptomatic and can still carry the infectious pathogen after it recovers, which are named asymptomatic infected horses and long-term subclinical carriers, respectively. Based on these horses, this paper establishes a dynamical model to screen, measure, and model the spread of strangles. The basic reproduction number $ \mathcal{R}_0 $ is computed through a next generation matrix method. By constructing Lyapunov functions, we concluded that the disease-free equilibrium is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, and the endemic equilibrium exits uniquely and is globally asymptotically stable if $ \mathcal{R}_0 > 1 $. For example, while studying a strangles outbreak of a horse farm in England in 2012, we computed an $ \mathcal{R}_0 = 0.8416 $ of this outbreak by data fitting. We further conducted a parameter sensitivity analysis of $ \mathcal{R}_0 $ and the final size by numerical simulations. The results show that the asymptomatic horses mainly influence the final size of this outbreak and that long-term carriers are connected to an increased recurrence of strangles. Moreover, in terms of the three control measures implemented to control strangles(i.e., vaccination, implementing screening regularly and isolating symptomatic horses), the result shows that screening is the most effective measurement, followed by vaccination and isolation, which can provide effective guidance for horse management.
- strangles,
- basic reproduction number,
- final size,
- sensitivity analysis,
- screening procedures
Citation: Lusha Shi, Jianghong Hu, Zhen Jin. Dynamics analysis of strangles with asymptomatic infected horses and long-term subclinical carriers[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18386-18412. doi: 10.3934/mbe.2023817

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Abstract

Strangles is one of the most prevalent horse diseases globally. The infected horses may be asymptomatic and can still carry the infectious pathogen after it recovers, which are named asymptomatic infected horses and long-term subclinical carriers, respectively. Based on these horses, this paper establishes a dynamical model to screen, measure, and model the spread of strangles. The basic reproduction number $ \mathcal{R}_0 $ is computed through a next generation matrix method. By constructing Lyapunov functions, we concluded that the disease-free equilibrium is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, and the endemic equilibrium exits uniquely and is globally asymptotically stable if $ \mathcal{R}_0 > 1 $. For example, while studying a strangles outbreak of a horse farm in England in 2012, we computed an $ \mathcal{R}_0 = 0.8416 $ of this outbreak by data fitting. We further conducted a parameter sensitivity analysis of $ \mathcal{R}_0 $ and the final size by numerical simulations. The results show that the asymptomatic horses mainly influence the final size of this outbreak and that long-term carriers are connected to an increased recurrence of strangles. Moreover, in terms of the three control measures implemented to control strangles(i.e., vaccination, implementing screening regularly and isolating symptomatic horses), the result shows that screening is the most effective measurement, followed by vaccination and isolation, which can provide effective guidance for horse management.

References

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