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Mathematical modeling of tuberculosis using Caputo fractional derivative: a comparative analysis with real data
Sanjay Bhatter1, Sangeeta Kumawat1, Sunil Dutt Purohit2
1Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, India.
Scientific Reports
|April 12, 2025
Summary
This study introduces a fractional-order epidemiological model for tuberculosis (TB) in China. The fractional model offers a 28.5% improvement in accuracy for TB transmission dynamics compared to traditional models.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Tuberculosis (TB) remains a significant global health challenge.
- Accurate epidemiological modeling is crucial for effective public health interventions.
- Traditional integer-order models may not fully capture complex disease dynamics.
Purpose of the Study:
- To develop and analyze a novel epidemiological model for tuberculosis transmission in China using the Caputo fractional-order derivative.
- To assess the mathematical properties and stability of the proposed fractional model.
- To evaluate the model's accuracy and efficiency in fitting real-world TB data.
Main Methods:
- Application of the Caputo fractional-order derivative to an epidemiological model.
- Analysis of model properties: non-negativity, boundedness, existence, and uniqueness of solutions.
- Sensitivity analysis using the basic reproduction number and visualization with 3D plots.
- Parameter estimation, including the optimal fractional order (approx. 0.93).
- Numerical simulations using the Adams-Bashforth-Moulton method.
- Comparison with integer-order models using the Root Mean Square Error (RMSE) metric.
Main Results:
- The fractional-order tuberculosis model was rigorously analyzed for its mathematical properties.
- Sensitivity analysis revealed key parameters influencing TB transmission dynamics.
- The optimal fractional order was determined to be approximately 0.93, providing the best fit to empirical data.
- Numerical simulations demonstrated a 28.5% improvement in efficiency (accuracy) using the fractional model compared to its integer-order counterpart.
- The fractional-order model showed superior accuracy in describing tuberculosis transmission dynamics.
Conclusions:
- Fractional-order epidemiological models offer a more refined and accurate approach to understanding infectious disease dynamics.
- The proposed Caputo fractional-order model provides enhanced insights into tuberculosis transmission in China.
- These findings highlight the potential of fractional calculus in improving public health strategies and decision-making for infectious diseases.
Keywords:
Caputo fractional operatorNumerical simulationsParameter estimationSensitivity analysisTuberculosisMore Related Videos
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