Related Experiment Video
Updated: Jun 10, 2026
09:49
Experimental Model to Evaluate Resolution of Pneumonia
Published on: February 17, 2023
A memory-driven pneumonia dynamics model validated against Ethiopian mortality data: a fractional-order differential
Mideksa Tola Jiru1, Sathish Kumar Kumaravel2
1Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, 600 062, India. mideksatol@gmail.com.
Scientific Reports
|June 8, 2026
Summary
This study introduces a fractional-order pneumonia model that incorporates memory effects, offering a more accurate representation of disease dynamics than traditional models. The findings highlight the crucial role of memory in epidemic modeling and suggest key intervention targets.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Pneumonia remains a major global health threat, particularly for vulnerable populations.
- Existing mathematical models inadequately capture pneumonia's complex dynamics due to factors like immune history and treatment delays.
- Classical integer-order models fail to account for the 'memory' inherent in disease transmission.
Purpose of the Study:
- To develop and analyze a novel Caputo fractional-order SEIHR model for pneumonia.
- To incorporate epidemiological memory and hereditary effects into the disease modeling framework.
- To provide the first complete stability analysis for a fractional-order pneumonia model.
Main Methods:
- Utilized Caputo fractional calculus to introduce memory effects into an SEIHR model.
- Performed comprehensive well-posedness analysis, including solution positivity and boundedness.
- Employed the next-generation matrix method to calculate the basic reproduction number ([Formula: see text]).
- Applied fractional linearization theory and Lyapunov functional construction for stability analysis.
Main Results:
- Established the biological validity and mathematical rigor of the fractional-order model.
- Proved the local and global asymptotic stability of both disease-free and endemic equilibria.
- Demonstrated that the fractional-order parameter (α) precisely regulates memory strength, influencing disease duration and convergence.
- Sensitivity analysis identified transmission rate (β) and infection force (Λ) as critical intervention targets.
- Bifurcation analysis revealed a threshold ([Formula: see text]=1) for disease elimination versus endemicity.
- The model showed excellent fit to WHO pneumonia mortality data in Ethiopia (R²=0.995).
Conclusions:
- Epidemiological memory is an indispensable component of accurate pneumonia modeling.
- Fractional-order models offer superior biological realism compared to integer-order models for diseases with memory effects.
- The study provides a robust mathematical framework for understanding and potentially controlling pneumonia transmission.
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