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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.

A mathematical model for the transmission dynamics of foot-and-mouth disease that incorporates direct and indirect disease transmission pathways as well as vaccine failure and culling clinically infected animals is developed, analyzed and simulated. The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model steady states. Meanwhile, optimal control theory is applied to the proposed model to identify optimal vaccination and culling strategies that can lead to effective control of the disease. Using data from literature, illustrations were performed to support analytical findings.