An Edge-Based Model of SEIR Epidemics on Static Random Networks

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Infectious disease spread is often modeled using compartmental models.
• Networks provide a framework to represent population structures influencing disease transmission.
• SEIR (Susceptible-Exposed-Infectious-Recovered) models account for a latent period.

Purpose of the Study:

• To formulate and validate an edge-based SEIR model on networks.
• To investigate the impact of network properties and disease parameters on epidemic dynamics.
• To analyze the stochasticity of SEIR dynamics using simulation methods.

Main Methods:

• Formulation of an edge-based SEIR model using probability generating functions.
• Computation of the basic reproduction number via the next generation matrix method.
• Analytical derivation of the final epidemic size.
• Stochastic simulations using Gillespie's algorithm with varying degree distributions.
• Validation of model predictions against stochastic simulations.

Main Results:

• The SEIR model accurately predicts epidemic dynamics, aligning well with stochastic simulations.
• Infection and recovery rates significantly influence disease transmission dynamics.
• The exposed rate delays disease spread; a high exposed rate approximates SIR dynamics.
• Networks with higher average degrees lead to earlier and higher epidemic peaks.

Conclusions:

• The validated SEIR model offers a robust method for understanding disease spread in networks.
• Network structure and disease parameters are critical factors in epidemic control.
• Findings have implications for designing effective public health interventions and mitigation strategies.