A fast algorithm for calculating an expected outbreak size on dynamic contagion networks

Calculation of expected outbreak size of a simple contagion on a known contact network is a common and important epidemiological task, and is typically carried out by computationally intensive simulation. We describe an efficient exact method to calculate the expected outbreak size of a contagion on an outbreak-invariant network that is a directed and acyclic, allowing us to model all dynamically changing networks when contagion can only travel forward in time. We describe our algorithm and its use in pseudocode, as well as showing examples of its use on disease relevant, data-derived networks.

Highlights

• Used a directed acyclic graph to calculate expected outbreak size in a network.
• Showed use of expectation calculation on livestock trading, electronic communication, and random networks.
• Expectation calculation is computationally faster than simulation methods when compared to simulation methods in test cases.