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Stochastic dynamical analysis for the complex infectious disease model driven by multisource noises.

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This study analyzes infectious disease dynamics under white and Lévy noise, establishing a stochastic model with vaccination. Findings reveal noise intensity impacts disease extinction, offering insights for prevention strategies.

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Area of Science:

  • Epidemiology
  • Stochastic Modeling
  • Mathematical Biology

Background:

  • Infectious diseases pose significant public health challenges.
  • Stochastic factors, like noise, can influence disease transmission dynamics.
  • Understanding these influences is crucial for effective control strategies.

Purpose of the Study:

  • To establish and analyze a stochastic infectious disease model incorporating secondary vaccination and external noise.
  • To investigate the existence, uniqueness, and stability of the disease-free equilibrium.
  • To determine conditions for disease extinction and assess the impact of noise intensity.

Main Methods:

  • Development of a stochastic differential equation model for infectious diseases.
  • Application of Lyapunov functions to prove the existence and uniqueness of global positive solutions.
  • Analysis of the asymptotic behavior of the disease-free equilibrium point.
  • Derivation of sufficient conditions for disease extinction.

Main Results:

  • The existence and uniqueness of a global positive solution for the stochastic model were proven.
  • Asymptotic behavior of the disease-free equilibrium was analyzed.
  • Sufficient conditions for the extinction of the infectious disease were established.
  • The study demonstrated that varying noise intensities differentially affect disease extinction.

Conclusions:

  • Stochastic perturbations, specifically white and Lévy noise, play a critical role in infectious disease dynamics.
  • Noise intensity is a key factor influencing the probability and speed of disease extinction.
  • The findings provide a theoretical basis for developing targeted disease prevention and control measures informed by environmental stochasticity.