Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

Area of Science:

• Mathematical modeling
• Complex systems dynamics
• Information science

Background:

• Rumor spreading significantly impacts society in the digital age.
• Existing models often simplify the complexities of real-world rumor dynamics.
• Understanding rumor propagation is crucial for social stability and information integrity.

Purpose of the Study:

• To propose a novel stochastic rumor-spreading model.
• To analyze the model's mathematical properties, including solution existence and stability.
• To investigate the influence of time delays and white noise on rumor dynamics.

Main Methods:

• Development of a stochastic differential equation model with Holling II functional response.
• Mathematical analysis to prove the existence of a unique global positive solution.
• Analysis of asymptotic behavior around equilibrium points of the deterministic system.
• Numerical simulations to validate theoretical findings.

Main Results:

• The existence and uniqueness of a global positive solution for the proposed model were established.
• The asymptotic behavior of the system near rumor-free and rumor-local equilibria was characterized.
• Numerical simulations confirmed the theoretical analysis and demonstrated the model's validity.
• Key factors like transmission rate, noise intensity, and time delay were shown to significantly affect rumor spreading patterns.

Conclusions:

• The developed stochastic model provides a more realistic framework for studying rumor propagation.
• Time delays and white noise introduce complex dynamics that critically influence rumor spread.
• The findings offer insights into controlling and mitigating the negative impacts of rumors in information societies.