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Mathematical analysis and computation of a spatiotemporal SIQR model
Achraf Zinihi1, Moulay Rchid Sidi Ammi2, Ahmed Bachir3
1Department of Mathematics, AMNEA Group, FST Errachidia, Moulay Ismail University of Meknes, 52000, Errachidia, Morocco. a.zinihi@edu.umi.ac.ma.
Theory in Biosciences = Theorie in Den Biowissenschaften
|October 15, 2025
Summary
Quarantine measures significantly impact disease spread by altering transmission dynamics. This study develops a mathematical model demonstrating quarantine
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems
Background:
- Understanding disease transmission dynamics is crucial for effective public health interventions.
- Spatiotemporal models are essential for capturing the complex spread of infectious diseases.
- Quarantine is a key non-pharmaceutical intervention for controlling epidemics.
Purpose of the Study:
- To propose and analyze a reaction-diffusion SIQR (Susceptible-Infectious-Quarantined-Recovered) epidemiological model.
- To investigate the influence of quarantine strategies on disease transmission in a spatial context.
- To mathematically prove the existence, uniqueness, positivity, and boundedness of the model's solutions.
Main Methods:
- Utilized C0 semigroup theory to establish fundamental properties of the model's solutions.
- Employed stability analysis of characteristic equations to determine local and global stability of equilibria.
- Developed a finite difference method for a discrete iterative scheme to obtain numerical solutions.
Main Results:
- Demonstrated the existence, uniqueness, positivity, and boundedness of the model's solutions.
- Analyzed the local and global stability of disease-free and endemic equilibria.
- Numerical simulations confirmed the significant effectiveness of the proposed quarantine control strategy.
Conclusions:
- The reaction-diffusion SIQR model provides a robust framework for studying epidemic dynamics.
- Quarantine measures play a pivotal role in controlling disease transmission and achieving favorable outcomes.
- The spatial origin of an epidemic significantly influences its evolution and spread.
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