Early epidemic spread, percolation and Covid-19

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Human-to-human infectious diseases spread via population interactions.
• Early outbreak stages are modeled using graphs representing individual interactions.
• Existing models often assume uniform interaction types and transmission probabilities.

Purpose of the Study:

• To extend existing epidemic models to account for diverse interaction types with varying transmission probabilities.
• To derive an explicit formula for the basic reproduction number (R0) in heterogeneous interaction networks.
• To assess epidemic potential and the probability of an outbreak becoming an epidemic in real-world population structures.

Main Methods:

• Graph theory and percolation theory frameworks are employed.
• Development of a novel mathematical model for disease transmission in complex networks.
• Application of the model to population data from different countries, adjusting for tree and degree distributions.

Main Results:

• An explicit formula for the basic reproduction number (R0) is derived, dependent on transmission probabilities and graph degree distributions.
• The study extends previous findings from single-interaction models to multi-interaction scenarios.
• Calculations for COVID-19-like scenarios show a very low probability of an outbreak not becoming an epidemic without interventions.

Conclusions:

• The developed framework accurately models infectious disease spread in populations with heterogeneous interactions.
• The basic reproduction number (R0) is a key metric influenced by interaction diversity and network structure.
• Urgent implementation of public health interventions is critical to prevent widespread epidemics, as natural containment is unlikely.