SIR epidemics and vaccination on random graphs with clustering

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Susceptible-Infectious-Recovered (SIR) epidemic models are crucial for understanding disease spread.
• Previous models often assumed homogeneous infectivity and simple network structures.
• Social networks exhibit clustering and group structures that influence epidemic dynamics.

Purpose of the Study:

• To analyze SIR epidemics on random graphs with clustering and non-homogeneous infectivity.
• To extend existing epidemic models by relaxing assumptions on individual and neighbor infectivity.
• To investigate the impact of random vaccination on epidemic outcomes.

Main Methods:

• Utilizing a generalized configuration model to represent clustered social networks.
• Employing branching process approximations to model disease spread.
• Deriving expressions for the basic reproduction number, outbreak probability, and final epidemic size.

Main Results:

• Developed a model for SIR epidemics on clustered random graphs with heterogeneous infectivity.
• Provided analytical expressions for key epidemiological parameters.
• Demonstrated that the basic reproduction number equals the perfect vaccine-associated reproduction number in this model.

Conclusions:

• Clustering and non-homogeneous infectivity significantly impact epidemic dynamics.
• Branching process approximations offer a robust method for analyzing complex epidemic models.
• The study provides insights into disease control strategies, including vaccination, in structured populations.