Monkeypox dynamical system with stability and computational analysis of the transmission

This work offers a deterministic approach for the movement of monkeypox (Mpox) virus environmental transmission in the context of immunization and quarantine. It emphasizes the critical role of awareness and treatments in potentially slowing the spread of the disease. It highlights how global awareness and the use of medications, supported by a mathematical model (MM), can effectively reduce the incidence of newly acquired diseases and help control pandemic disease. This work improves our understanding of the structure and behavior of mpox, which affects control and prevention strategies. For this, population are {classified} into two parts, namely, human and rodent population. In this study, a novel mathematical model (MM) of the Mpox is developed and examined. For this, boundedness and positivity, both equilibrium states (DFE, EE), stability analysis (local and global) of the model are studied and analyzed {with the DFE and EE points, respectively}. Furthermore, bifurcation and sensitivity analysis of the model are investigated {using} the central manifold theory and {the} forward index method, respectively. Furthermore, numerical simulations of the model are performed by the \(RK\)-4 method, to validate the analytical findings.