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The monkeypox virus (MPXV) is what causes monkeypox (MPX) disease, which is comparable to both smallpox and cowpox. Using classical, fractional-order and complex order differential equations, we offer a deterministic mathematical model of the monkeypox virus in this study to research its possible breakouts in United States. The complex order derivative makes the fractional order derivative and the integer order derivative more common when the imaginary part of the complex order equals zero and when the real part in complex order derivatives is zero in this case, the new behaviour appears that doesn't appear in integer and fractional order derivatives. Eight nonlinear complex order differential equations make up this model consisting of humans and rodents population sizes. The population of humans Nh is divided into five different classes. The population of rodent Nr is divided into three classes, and the derivatives are described in the Atangana-Baleanu-Caputo sense and Mittag-Leffler kernels are employed. Numerical methods to simulate complex order systems such as The standard and nonstandard two-step Lagrange interpolation methods are utilised to fit the model. The basic reproduction number of the model is given. The stability of the suggested model's disease-free equilibrium point is shown. Finally, we study the duration and monkeypox outbreak's transmission pattern in the United States from June 13 to Sep 16, 2022, numerical simulations to illustrate our findings are presented. The results show that keeping diseased people apart from the general population decreases the spread of disease.