N-strain epidemic model using bond percolation.

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Random networks are fundamental models in network science.
• Bond percolation is a key process for analyzing network connectivity.
• Sequential processes can lead to complex emergent structures.

Purpose of the Study:

• To investigate emergent structures in random networks after multiple bond percolation steps.
• To define and analyze competitive and collaborative sequential branching processes.
• To model seasonal N-strain disease spreading dynamics.

Main Methods:

• Utilizing generating functions for analytically exact calculations.
• Analyzing Erdős-Renyi and scale-free random graph models.
• Examining topological properties and the size of the giant connected component (GCC).

Main Results:

• Characterization of network structures resulting from sequential percolation.
• Determination of critical percolation probabilities for different branching processes.
• Analysis of the expected size of the giant connected component (GCC) across generations.

Conclusions:

• Sequential bond percolation significantly impacts random network topology.
• Competitive and collaborative branching processes yield distinct emergent structures.
• The developed model provides a framework for understanding seasonal disease dynamics.