In this paper, a fractional-order model that describes transmission and control of foot-and-mouth disease is presented and analyzed. The proposed model incorporates two foot-and-mouth disease intervention strategies: vaccination of susceptible animals and quarantine of clinically infected animals. Firstly, the global existence, positivity and boundedness of solutions for the proposed model were proved. This was followed by computation of the basic reproduction number. The basic reproduction number was then used to demonstrate the global stability of the model steady states. Theoretical results were validated by solving the proposed model in MATLAB software using the modified Adams–Bashforth–Moulton predictor corrector scheme. Among several other important results, numerical results demonstrate that coupling vaccination and animal isolation could be essential to attain effective management of foot-and-mouth disease for certain disease transmission levels. However, if disease transmission exceeds a certain threshold value, then coupling vaccination and quarantine may not be sufficient to effectively manage the disease. Furthermore, simulation results also demonstrated that the qualitative nature of the solutions of the classical integer model is the same as that of the fractional-order differential model. In addition, it was shown numerically that in the presence of quarantine alone, disease outbreaks may occur.

本文提出并分析了描述口蹄疫传播和控制的分数阶模型。提议的模型包含了两种口蹄疫干预策略：易感动物的疫苗接种和临床感染动物的隔离。首先，证明了所提模型的整体存在性，正定性和解的有界性。随后是基本再现数的计算。然后，使用基本的再现数来证明模型稳态的全局稳定性。通过使用改进的Adams–Bashforth–Moulton预测器校正器方案在MATLAB软件中求解所提出的模型，验证了理论结果。在其他重要结果中，数值结果表明，在某些疾病传播水平下，接种疫苗和动物隔离对实现口蹄疫的有效管理至关重要。但是，如果疾病传播超过某个阈值，则疫苗接种和检疫相结合可能不足以有效地控制疾病。此外，仿真结果还表明，经典整数模型的解的定性性质与分数阶微分模型的解的性质相同。此外，从数字上显示，仅存在检疫，可能会爆发疾病。那么结合疫苗接种和隔离可能不足以有效控制该疾病。此外，仿真结果还表明，经典整数模型的解的定性性质与分数阶微分模型的解的性质相同。此外，从数字上显示，仅存在检疫，可能会爆发疾病。那么结合疫苗接种和隔离可能不足以有效控制该疾病。此外，仿真结果还表明，经典整数模型的解的定性性质与分数阶微分模型的解的性质相同。此外，从数字上显示，仅存在检疫，可能会爆发疾病。