Investigation of monkeypox disease transmission with vaccination effects using fractional order mathematical model under Atangana-Baleanu Caputo derivative

Monkeypox has emerged as a serious threat to public health after the global eradication of smallpox in 1980. It is still prevalent as an endemic in Central and West Africa and cases are primarily captured from rural areas adjacent to the tropical rainforest. In this paper, we investigated a mathematical model to analyze the transmission dynamics of mpox in human and non-human denizens. We have utilized the fractional Atangana-Baleanu operator in Caputo sense to study the characteristics and various epidemiological aspects of mpox. We established the positivity and boundedness of the model. To understand the dynamics of the mpox model, we have shown the existence and uniqueness of the solution using Banach’s fixed point theorem. Next, using the next-generation approach, we computed the threshold parameter of mpox transmission, known as basic reproduction number. We obtained two equilibrium points of models. Model stability behavior is examined at both equilibrium points. Next, the fractional Adams-Bashforth method is employed to illustrate numerical outcomes. Additionally, numerical solutions are simulated graphically to show how various parameters affect the dynamical behavior of mpox model.