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Dynamical Analysis of an Improved Bidirectional Immunization SIR Model in Complex Network.

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This study shows that increasing immunization rates among susceptible individuals effectively reduces infectious disease spread in complex networks. Bidirectional immunization strategies are key for epidemic control.

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Infectious diseases spread rapidly in complex networks.
  • Effective immunization strategies are crucial for disease control.
  • Understanding transmission dynamics in heterogeneous networks is challenging.

Purpose of the Study:

  • To investigate the impact of bidirectional immunization on infectious disease spread.
  • To analyze epidemic dynamics in complex networks using a bilinear SIR model.
  • To develop and validate a continuous-time Markov chain (CTMC) model for infectious disease transmission.

Main Methods:

  • Developed a bilinear SIR model incorporating vaccination and clinical interventions.
  • Derived basic reproduction numbers and outbreak thresholds for homogeneous and heterogeneous networks.
  • Employed continuous-time Markov chain (CTMC) analysis, including transition probabilities and steady-state distributions.
  • Validated the CTMC model against mean-field (MF) simulations.

Main Results:

  • The CTMC model accurately captures stochastic fluctuations in disease transmission.
  • CTMC and MF simulations showed strong concordance, validating the CTMC approach.
  • Increased immunization rates among susceptible individuals significantly decrease steady-state infection density.
  • Bidirectional immunization strategies demonstrate effectiveness in reducing disease spread.

Conclusions:

  • The CTMC model provides a robust framework for analyzing infectious disease dynamics in complex networks.
  • Vaccination targeting susceptible individuals is a critical factor in lowering infection density.
  • Findings offer valuable theoretical insights for designing effective epidemic prevention and control strategies.