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

F M Allehiany; Mahmoud H DarAssi; Irfan Ahmad; Muhammad Altaf Khan; Elsayed M Tag-Eldin

doi:10.1016/j.rinp.2023.106557

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

Results Phys. 2023 Jul:50:106557. doi: 10.1016/j.rinp.2023.106557. Epub 2023 May 18.

Authors

F M Allehiany¹, Mahmoud H DarAssi², Irfan Ahmad³, Muhammad Altaf Khan⁴, Elsayed M Tag-Eldin⁵

Affiliations

¹ Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Saudi Arabia.
² Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan.
³ Department of Clinical Laboratory Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi Arabia.
⁴ Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
⁵ Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt.

Abstract

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 $R_{0} < 1$ . 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 $θ_{r}$ , $τ_{1}$ , and $ξ_{r}$ . When $R_{0} > 1$ , 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 $R_{1} = 0.5905$ . Additionally, we do a sensitivity analysis on the parameters in $R_{0}$ . We conclude by presenting specific numerical findings.

Keywords: Equilibrium points; Global stability; Mathematical model; Monkeypox disease; Numerical results; Outbreak data.