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

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Monkeypox (MPXV) poses a significant public health concern, necessitating robust analytical tools.
• Understanding disease dynamics is crucial for effective control strategies during epidemics.

Purpose of the Study:

• To develop and analyze a mathematical model for monkeypox transmission dynamics.
• To investigate the stability of equilibrium points and identify conditions for backward bifurcation.
• To parameterize the model with real-world data and perform sensitivity analysis.

Main Methods:

• Formulation of a compartmental mathematical model for monkeypox.
• Analysis of equilibrium points and their local asymptotic stability (LAS).
• Investigation of backward bifurcation phenomena and global asymptotic stability (GAS).
• Parameter estimation using epidemic data and sensitivity analysis.

Main Results:

• The model demonstrates local asymptotic stability at the disease-free equilibrium (DFE) under specific conditions.
• The presence of an endemic equilibrium was confirmed.
• Backward bifurcation was identified, influenced by parameters R0, beta, and mu.
• Global asymptotic stability (GAS) was established when R0 > 1.

Conclusions:

• The developed mathematical model provides insights into monkeypox epidemiology.
• Backward bifurcation highlights complex dynamics that can influence disease persistence.
• Parameterization and sensitivity analysis offer a foundation for real-world application and prediction.