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Modeling and analysis of monkeypox disease using fractional derivatives
Samuel Okyere1, Joseph Ackora-Prah1
1Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
This study uses fractional calculus to model monkeypox transmission in Ghana. Mathematical analysis and simulations show fractional derivatives impact disease dynamics, potentially aiding in rapid infection eradication.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Monkeypox outbreaks are increasing globally.
- Understanding transmission dynamics is crucial for control.
Purpose of the Study:
- To investigate monkeypox transmission kinetics in Ghana using fractional-order derivatives.
- To analyze the stability and solutions of the proposed mathematical model.
Main Methods:
- Application of Atangana-Baleanu fractional derivatives (Caputo sense).
- Analysis of equilibrium points and basic reproduction number (R0).
- Proof of solution existence, uniqueness, and Hyers-Ullam stability.
Main Results:
- The basic reproduction number (R0) was calculated as 0.1940.
- Numerical simulations demonstrated the influence of the fractional operator on model compartments.
- Fractional-order derivatives significantly affect disease dynamics.
Conclusions:
- Fractional calculus provides valuable insights into monkeypox transmission.
- The model suggests potential for rapid infection control under specific parameters (e.g., π = 0.2 leading to eradication in 5 days).
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