Impact of Fractional Derivatives on Monkeypox Outbreak Control: Theory, Modeling, and Applications

Monkeypox, an emerging zoonotic disease, has gained increasing global attention due to its rising incidence and potential for sustained human-to-human transmission, underscoring the need for advanced mathematical tools to support effective control strategies. This study develops a fractional-order mathematical model of monkeypox transmission that incorporates the Caputo, Caputo–Fabrizio, and Atangana–Baleanu derivatives to capture memory and nonlocal effects in both human and rodent populations. From a theoretical perspective, the use of fractional operators provides a more general framework for describing epidemic dynamics, allowing the model to account for historical influences on disease progression. The numerical implementation of the model is carried out using the fractional Adams–Bashforth predictor–corrector method, ensuring accurate approximation of the system’s dynamics under different fractional settings. Simulation results demonstrate that decreasing the fractional order (for example, from 0.9 to 0.5) leads to an increase in the basic reproduction number, thereby intensifying disease transmission. In addition, higher contact rates among humans and rodents significantly amplify outbreak magnitude and persistence. Conversely, increased treatment rates substantially reduce infection levels and promote faster recovery within the population. From an applied public health perspective, these findings highlight the importance of reducing contact rates and strengthening treatment capacity as effective intervention strategies for mitigating monkeypox transmission. Overall, the study demonstrates the usefulness of fractional-order modeling in capturing complex epidemic behavior and provides valuable insights for designing more efficient control measures.