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Spatio-temporal numerical modeling of reaction-diffusion measles epidemic system
Nauman Ahmed1, Zhouchao Wei2, Dumitru Baleanu3
1Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.
Chaos (Woodbury, N.Y.)
|November 3, 2019
Summary
This study presents a novel numerical method for the susceptible-exposed-infected-recovered (SEIR) measles model. The chaos-free finite difference scheme ensures accurate and stable disease transmission predictions.
Area of Science:
- Epidemiology
- Mathematical Biology
- Numerical Analysis
Background:
- Measles remains a significant public health concern globally.
- Accurate modeling of infectious disease dynamics is crucial for effective intervention strategies.
- Existing numerical methods may face challenges with stability and solution positivity.
Purpose of the Study:
- To develop and analyze a numerical solution for the susceptible-exposed-infected-recovered (SEIR) measles model.
- To evaluate the numerical stability and identify the bifurcation value of the transmission parameter.
- To ensure the proposed numerical scheme is chaos-free and preserves solution positivity.
Main Methods:
- Implementation of a finite difference scheme for the SEIR model.
- Analysis of numerical stability properties of the proposed method.
- Determination of the bifurcation value for disease transmission.
Main Results:
- The proposed finite difference scheme provides a stable numerical solution for the SEIR measles model.
- The method is demonstrated to be chaos-free, preventing unphysical oscillations.
- The positivity of the solution, representing population compartments, is preserved.
Conclusions:
- The developed numerical method offers a reliable tool for studying measles transmission dynamics.
- The findings contribute to the advancement of computational epidemiology.
- This approach enhances the accuracy and trustworthiness of epidemic modeling.
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