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This study models epidemic spreading and vaccination using susceptible-infected-susceptible (SIS) dynamics. Results reveal complex phase transitions, showing how vaccine efficiency impacts disease-free, epidemic, and mixed states.

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Epidemic models often simplify vaccination as instantaneous or non-competing.
  • Understanding the interplay between ongoing disease spread and contact-based vaccination is crucial for public health strategies.

Purpose of the Study:

  • To investigate the complex dynamics arising from the simultaneous occurrence of epidemic spreading and contact-based vaccination.
  • To analytically and numerically characterize the phase transitions and emergent states in a coupled susceptible-infected-susceptible (SIS) model.

Main Methods:

  • Analytical investigation using mean-field theory to derive the model's phase diagram.
  • Numerical simulations on homogeneous random networks to validate analytical predictions.

Main Results:

  • A rich phase diagram emerges, detailing disease-free, epidemic, and mixed states (coexistence of susceptible, infected, and vaccinated individuals).
  • Continuous phase transitions occur when vaccine protection is low, transitioning between states.
  • A tricritical point leads to a bistable regime with discontinuous phase transitions as vaccine efficiency increases.

Conclusions:

  • The model accurately captures the intricate relationship between epidemic spread and vaccination dynamics.
  • Vaccine efficiency critically determines the system's final state, influencing transitions from endemic to disease-free or bistable regimes.
  • Mean-field theory and simulations provide robust predictions for these complex interactions on networks.