# mj1.atMichael Jaros' Techblog

25Mar/120

## Infection modeling: The SIR model

In the branching process model, a very simplified network structure is assumed. For real-world networks, a more general model should be applied. In order to allow for arbitrary graphs with cycles, we have to distinguish three states for each node:

• Susceptible nodes have not been infected yet and are therefore available for infection. They do not infect other nodes.
• Infectious nodes have been infected and infect other nodes with a certain probability.
• Removed (recovered) nodes have gone through an infectious period and cannot take part in further infection (neither actively nor passively).

Using these three states S, I, and R, and the length of the infectious period $t_I$ as an aditional parameter, a SIR model12 can describe infections in any network structure: Susceptible nodes are infected with a certain probability and infected nodes are removed from the model after the infectious period.

A SIR model assumes that a disease can be caught at most once by each node and is therefore adequate for the modelling of the tweetflow discovery phase. SIS (susceptible - infectious - susceptible) models allow re-infections and apply to many real-world diseases.

1. Hethcote (1989): Three basic epidemiological models []
2. Easley and Kleinberg (2010): Networks, Crowds, and Markets, p.572 []