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Updated: Jan 16, 2026
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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
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Modelling the dynamically consistent numerical methods for COVID-19 disease with cost effectiveness strategies.
Shuo Li1, Muhammad Amjad Abbas2, Ihsan Ullah Khan2
1School of Mathematics and Data Sciences, Changji University, Changji, 831100, Xinjiang, China.
Scientific Reports
|September 30, 2025
Summary
This study compares numerical methods for modeling COVID-19 spread. The non-standard finite difference (NSFD) scheme accurately tracks the disease, outperforming Euler and RK-4 methods for epidemic modeling.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Science
Background:
- COVID-19, caused by SARS-CoV-2, spreads rapidly via contact.
- Accurate mathematical models are crucial for understanding and controlling epidemic dynamics.
- Existing numerical schemes may not fully capture the complexities of continuous epidemic models.
Purpose of the Study:
- To evaluate and compare the performance of different numerical schemes for a deterministic COVID-19 SEIHR epidemic model.
- To assess the effectiveness of the non-standard finite difference (NSFD) scheme against traditional methods like Euler and Runge-Kutta of order 4 (RK-4).
- To analyze the stability of disease-free and endemic equilibria using the NSFD scheme.
Main Methods:
- Development and application of a deterministic SEIHR epidemic model for COVID-19.
- Computation of the basic reproduction number (R0) using the next-generation matrix.
- Implementation and comparison of Euler, RK-4, and non-standard finite difference (NSFD) numerical schemes.
- Analysis of local and global stability for model equilibria.
Main Results:
- Euler and RK-4 schemes produced numerical solutions that deviated from the continuous model's behavior.
- The NSFD scheme demonstrated superior accuracy, providing results analogous to the continuous model.
- The NSFD scheme effectively captured the dynamics of the SEIHR model and provided precise mathematical outcomes.
Conclusions:
- The non-standard finite difference (NSFD) scheme is a robust and accurate tool for modeling COVID-19 transmission dynamics.
- NSFD schemes offer a reliable approach for simulating epidemic models, ensuring mathematical precision.
- This study validates the utility of NSFD methods in understanding and managing infectious disease outbreaks like COVID-19.
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