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Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function
1Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan.
Chaos (Woodbury, N.Y.)
|April 1, 2019
Summary
This study models epidemic spread using a network-based SIR model with saturated treatment. Limited treatment capacity can prevent disease eradication even when the basic reproduction number (R0) is below one.
Area of Science:
- Epidemiology
- Mathematical Biology
- Network Science
Background:
- Epidemic modeling is crucial for understanding disease spread.
- Limited treatment resources during outbreaks can lead to saturation effects.
- Previous models often assume unlimited treatment capacity.
Purpose of the Study:
- To develop a network-based SIR epidemic model incorporating a saturated treatment function.
- To analyze the impact of treatment saturation on disease dynamics.
- To investigate conditions for disease eradication and persistence.
Main Methods:
- Development of a network-based Susceptible-Infected-Recovered (SIR) model.
- Inclusion of a saturated treatment function to represent limited healthcare capacity.
- Mathematical analysis of model dynamics, including threshold values (R0) and bifurcation analysis.
Main Results:
- A threshold value R0 was identified, determining the stability of the disease-free equilibrium.
- Bifurcation analysis at R0=1 revealed complex dynamics.
- Backward bifurcation indicates that R0<1 may not guarantee disease eradication due to stable endemic equilibria.
- Forward bifurcation can lead to multiple equilibria, necessitating control of initial infections.
Conclusions:
- Saturated treatment functions are essential for realistic epidemic modeling.
- The basic reproduction number (R0) alone is insufficient to predict disease eradication when treatment is limited.
- Control strategies must consider initial infection levels and potential for multiple stable states.
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