Analytical study of a modified monkeypox virus model using Caputo–Fabrizio fractional derivatives

Monkeypox virus causes a zoonotic disease known as monkeypox, which poses a significant public health risk. To address this, we developed a novel mathematical model incorporating a hospital class functioning as a control measure. Our comprehensive non-linear compartmental model includes nine distinct compartments for both human and rodent populations, delineating Susceptible, Exposed, Infected, Isolated, Quarantined, Hospitalized, and Recovered humans, as well as Susceptible, Exposed, and Infected rodents. The Caputo–Fabrizio fractional derivative was employed to analyze the model. All interactions potentially leading to disease transmission within the population are accounted for. We examined the stability of the model in a disease-free state, demonstrating that the model is stable when \({R}_{0}<1\) $R_0<1$ and unstable otherwise. Multiple simulations were conducted with various input values to explore the complex dynamics of monkeypox infection under different conditions. Our study investigates the system’s dynamic behavior to develop effective disease management strategies. The dynamic behavior of the system is illustrated through numerical simulations with various input parameters, providing a critical framework for evaluating monkeypox control measures. The findings of this study are expected to contribute significantly to the understanding and management of monkeypox outbreaks.