Mathematical Modeling and backward bifurcation in monkeypox disease under real observed data

We propose a mathematical model to analyze the monkeypox disease in the context of the known cases of the USA epidemic. We formulate the model and obtain their essential properties. The equilibrium points are found and their stability is demonstrated. We prove that the model is locally asymptotical stable (LAS) at disease free equilibrium (DFE) under $$. The presence of an endemic equilibrium is demonstrated, and the phenomena of backward bifurcation is discovered in the monkeypox disease model. In the monkeypox infectious disease model, the parameters that lead to backward bifurcation are $$, $$, and $$. When $$, we determine the model's global asymptotical stability (GAS). To parameterize the model using real data, we obtain the real value of the model parameters and compute $$. Additionally, we do a sensitivity analysis on the parameters in $$. We conclude by presenting specific numerical findings.