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

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.

Keywords

• strangles
• basic reproduction number
• final size
• sensitivity analysis
• screening procedures