Monkeypox virus is primarily transferred to humans via wild animals including rodents and more often the transmission ensues between humans to humans. This disease has been neglected in the past and little effort has been made by research to study the dynamics of the disease. This paper aims to use a fractional stochastic modeling approach to investigate the Monkeypox model dynamics. In this work, a fractionalized mathematical model is constructed with an emphasis on the unstigmatized and stigmatized in the community. First, we carried out a deterministic model using fractional-order operator with Atangana–Baleanu–Caputo derivative. The basic properties and the dynamical behavior of the deterministic model are investigated. Next, the existence and uniqueness of the solutions of the model based on the fractional stochastic approach are examined. Numerical simulations of deterministic and stochastic fractional model are conducted to support the analytical results which depict that fractional order derivative has a serious effect on the dynamics of the monkeypox. This work presented more detailed the characteristic of the monkeypox dynamics than deterministic fractional operators. The infection rate in humans has an impact on the spread of the disease in the human compartment.
- Existence and uniqueness