Mathematical modeling and analysis of monkeypox 2022 outbreak with the environment effects using a Cpauto fractional derivative

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Monkeypox is a serious global challenge to human health after the COVID-19 pandemic. Although this infection is not new, still many variations have been noticed in its epidemiology. Numerous approaches have been applied to analyze the dynamics of this infection. In this study, we present a mathematical model to study various epidemiological aspects of monkeypox. Transmission from human to animal, human to human, and through the environment (surface) are considered while formulating the proposed model. The model is constructed based on a classical system of seven nonlinear differential equations. Further, the classical epidemic model is reconstructed using the standard Caputo derivative to examine the dynamical aspects of monkeypox disease in the presence of memory effects. Initially, the necessary mathematical properties of the fractional model are carried out. The model exhibits three equilibrium points: monkeypox-free equilibrium, infected animal-free endemic equilibrium, and coexistence equilibrium. Additionally, we give a thorough theoretical analysis that considers solution positivity and stability results of equilibriums of the Caputo monkeypox model. Furthermore, the parameters of the proposed model are estimated using the nonlinear least square method from the reported cases of monkeypox in the United States in a recent outbreak in 2022. Finally, the numerical solution of the model is carried out using the well-known Adams-Bashforth-Moulton scheme and simulation is performed to explore the role of memory index and various preventing measures on the disease incidence.