A generalized linear threshold model for an improved description of the spreading dynamics

Area of Science:

• Complex systems
• Network science
• Epidemiology

Background:

• Spreading processes in real-life are often complex contagions.
• The linear threshold (LT) model is commonly used but has limitations in describing temporal dynamics.
• Existing LT models struggle with discrete time steps, synchronous updating, and integration with simple contagion models.

Purpose of the Study:

• Introduce a generalized linear threshold (GLT) model for continuous-time stochastic complex contagion.
• Address the limitations of the traditional LT model in capturing spreading time evolution.
• Enable seamless integration with simple contagion models for hybrid spreading processes.

Main Methods:

• Developed a generalized linear threshold (GLT) model.
• Utilized the Gillespie algorithm for efficient implementation of the continuous-time stochastic process.
• Analyzed the time evolution and spreading sequence order.

Main Results:

• The GLT model provides a clear mathematical definition for time and a defined updating order.
• The traditional LT model underestimates spreading speed and randomness.
• The GLT model integrates effectively with susceptible-infected (SI) and susceptible-infected-recovered (SIR) models.

Conclusions:

• The proposed GLT model offers a more accurate representation of complex contagion dynamics, particularly over time.
• GLT enhances the study of spreading processes by providing a continuous-time framework.
• This model facilitates the study of hybrid contagion processes, combining simple and complex mechanisms.