lecture8 notes

12 networks lecture 8 sir model2 to analyze the reach

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: h that the probability that an infected node will infect a susceptible neighbor before the infected node is removed can be described by the probability of transmission t . Assume that the infection process is independent across links between susceptible and infected nodes. The independence assumption is clearly violated in many cases. 12 Networks: Lecture 8 SIR Model–2 To analyze the reach of infection, we can remove links (in an independent and identical manner) with probability 1 − t , and compute the resulting component size. The analysis then is analogous to the analysis of diffusion with immune nodes (with t in place of 1 − π ). How do we determine the transmission probability t ? Model 1: An infected node is removed within 1 time step (deterministic). A node infects each of its susceptible neighbor i independently within time Ti that is exponentially distributed with parameter β. We have t = P(Ti ≤ 1) = 1 − e − β . Model 2: An infected node is removed within time T ∼ exp(γ). A node infects each of its susceptible neighbor i independently within time Ti ∼ exp( β). β We have t = P(Ti ≤ T ) = β+γ . 13 Networks: Lecture 8 SIS Model–1 In the SIS model, susceptible nodes can become infected, and then recover in such a way that they become susceptible again (rather than being removed). Models diseases such as certain variations of the common cold. Consider a degree-based random meeting model: nodes interact randomly according to their degree di . Let P (d ) be the degree distribution in the society. The probability that a meeting of node i is with a degree d node is P (d )d . �d � It is essential to keep track of nodes degrees since nodes with different degrees tend to have different infection rates. Let ρd (t ) denote the fraction of nodes of degree d infected at time t . Let θ (t ) denote the probability that a given meeting is with an infected individual. Then: ∑ P (d ) ρd...
View Full Document

This document was uploaded on 03/18/2014 for the course EECS 6.207J at MIT.

Ask a homework question - tutors are online