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Analysis of stochastic dynamics in a multistable logistic-type epidemiological model
Irina Bashkirtseva1, Lev Ryashko1
1Ural Federal University, Ekaterinburg, Russia.
The European Physical Journal. Special Topics
|June 22, 2022
Summary
This study introduces a discrete susceptible-infected model to predict epidemic spread. It analyzes survival dynamics, synchronization, and noise-induced extinction, offering insights into disease propagation.
Area of Science:
- Epidemiology and Mathematical Modeling
- Dynamical Systems Theory
Background:
- Epidemic spread analysis is crucial for public health.
- Understanding disease dynamics requires robust mathematical models.
- Previous models often simplify complex population interactions.
Purpose of the Study:
- To propose and analyze a discrete logistic-type susceptible-infected model.
- To investigate bifurcation analysis of survival regimes, including chaotic dynamics.
- To explore synchronization phenomena and the impact of random disturbances on epidemic spread.
Main Methods:
- Discrete dynamical systems analysis.
- Bifurcation analysis to identify survival regimes.
- Numerical simulations and analytical methods (confidence domains) for studying noise effects.
- Analysis of in-phase and anti-phase synchronization.
Main Results:
- Identification of parametric zones for multistability and basins of coexisting attractors.
- Characterization of regular and chaotic survival regimes.
- Demonstration of in-phase and anti-phase synchronization between susceptible and infected populations.
- Analysis of noise-induced extinction mechanisms.
Conclusions:
- The proposed model captures complex epidemic dynamics, including chaos and multistability.
- Synchronization phenomena play a significant role in population oscillations.
- Random disturbances can lead to epidemic extinction through various mechanisms.
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