Department of Mathematics

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A study on the Monkeypox virus disease using the Mathematical Modelling
(Department of Mathematics, NITS, 2025) Gupta, Abhishekh
In this study, we proposed a novel mathematical model to analyze the transmission dynamics of the Monkeypox virus. The model is formulated as a system of non-linear ordinary differential equations, incorporating key epidemiological classes for both hu man and rodent populations: susceptible, exposed, infected, and recovered humans (SEIR), and susceptible and infected rodents (SI). We conducted a thorough anal ysis of the model’s equilibrium points, identifying the Monkeypox-Free Equilibrium point (MFE), the Rodent-Free Endemic Equilibrium point (RDEE), and the Endemic Equilibrium point (EE). We rigorously established the local asymptotic stability of the model at the MFE and RDEE. Furthermore, the global asymptotic stability of the endemic equilibrium was demonstrated through the construction and analysis of a suitable Lyapunov function. A sensitivity analysis was performed on the parameters comprising the basic reproduction number to determine their relative influence on dis ease transmission. Finally, the theoretical findings were complemented and illustrated through specific numerical simulations.