Monkeypox Transmission through Human Interaction: A Compartmental Model Study

Background

In this study, with a mathematical model, we provide an epidemic model for Mpox virus infection. This paper aims to develop a mathematical epidemic model that captures some of the key characteristics of Mpox.

Materials and Methods

The endemic equilibrium, disease-free equilibrium, and basic Reproduction Number (R ₀) of the model are investigated. Moreover, we focused on how the virus that causes Mpox behaves dynamically. To investigate the existence and uniqueness of the proposed system's solution for the Mpox viral infection, the Derrick and Grossman theorems are utilized. In addition, the solution pathways are studied numerically, emphasizing the influence of the parameters on the Mpox virus dynamics. The Mpox model is described by its fundamental mathematical properties, such as equilibrium, stability, and reproduction number. Using the Lyapunov technique, the Global Asymptotically Stable (GAS) human endemic equilibrium is only displayed when the human basic reproduction number is less than unity. It is demonstrated to be Locally Asymptotically Stable (LAS) when the basic reproduction number for humans is greater than unity by using the definite function of the endemic equilibrium point where the infection resides in the human-to-human population of the model.

Results

Based on numerical simulations, it appears that people's immunological state varies based on how they recover from an Mpox virus infection.

Conclusion

Our study emphasizes that treatment, vaccination, and public awareness are the only preventive strategies concerning Mpox. Moreover, our findings indicate that while the disease can be managed and controlled, attaining long-lasting immunity remains unfeasible due to the lack of conclusive treatments and vaccines for Mpox infection. For the special case, where there is only human-to-human transmission of Mpox, the disease-free equilibrium of the model is shown to be Locally Asymptotically Stable (LAS) whenever the associated reproduction number is less than unity.