Optimal control and cost-effectiveness analysis of a caputo fractional-order model for foot-and-mouth disease with environmental transmission

This study develops a Caputo fractional-order mathematical model to investigate the transmission dynamics of Foot-and-Mouth Disease (FMD) with explicit inclusion of environmental transmission pathways. The model integrates time-dependent control measures, including vaccination, movement restrictions, biosecurity, surveillance, culling, and treatment. A fractional optimal control framework is employed to derive cost-effective intervention strategies that minimize disease burden while accounting for memory effects inherent in FMD dynamics. Furthermore, a cost-effectiveness analysis is conducted to evaluate and rank competing control strategies based on incremental cost-effectiveness ratios (ICERs). Analytical results concerning the positivity, boundedness, and stability of solutions are established, and numerical simulations illustrate the effectiveness of the proposed interventions. The findings indicate that surveillance-only strategies offer the most cost-effective approach in resource-limited settings, while integrated control provides the greatest reduction in infections at a higher cost. This work provides policymakers with actionable insights for designing economically viable FMD control programs.