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A paradox of epidemics between the state and parameter spaces
Hengcong Liu1, Muhua Zheng1, Zonghua Liu2
1Department of Physics, East China Normal University, Shanghai, 200062, China.
Scientific Reports
|May 16, 2018
Summary
Epidemic outbreaks exhibit hysteresis loops in state space, correlating with outbreak size. A paradox emerges with infectious rate and transient time, but disappears with limited epidemic duration.
Area of Science:
- Epidemiology
- Complex Systems
- Mathematical Biology
Background:
- Recurrent epidemics demonstrate hysteresis loop phenomena in state space.
- Previous studies qualitatively explained mechanisms via parameter space, lacking direct state space quantitative analysis.
Purpose of the Study:
- To quantitatively investigate epidemic hysteresis loops directly from state space.
- To analyze the relationship between outbreak size and hysteresis loop size.
- To explore parameter-dependent behaviors and paradoxes in hysteresis loop dynamics.
Main Methods:
- Direct state space analysis of epidemic data.
- Quantitative investigation of hysteresis loop size.
- Theoretical analysis of epidemic evolutionary time, infectious rate increment, and transient time effects.
Main Results:
- A positive correlation exists between outbreak size and hysteresis loop size, indicating hysteresis is inherent to real epidemic outbreaks.
- A paradox was observed: hysteresis loop size decreases with infectious rate increment in state space but increases in parameter space.
- The paradox reverses for transient time and disappears with limited epidemic evolutionary time.
Conclusions:
- Epidemic hysteresis is a natural feature directly observable in state space.
- Parameter-dependent paradoxes in hysteresis dynamics are contingent on epidemic evolutionary time.
- Theoretical analysis provides insights into observed numerical results and paradoxes.
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