DCS/CSCI 2350: Social & Economic Networks How does a disease - PDF document

3/26/18 DCS/CSCI 2350: Social & Economic Networks How does a disease propagate in a network? Chapter 21 of EK Mohammad T . Irfan Flu outbreak (2018) u January 11, 2018 1

3/26/18 Zika outbreak (2015—2016) u March 2016 Zika outbreak (2015—2016) u November 21, 2016 2

3/26/18 Example (February 2015) u Measles outbreak (CA, December’14—Feb’15) Image: Fox 40 Example (December 2014) u Ebola epidemic 3

3/26/18 Example (January 2014) Important factors of epidemics u Pathogen u How contagious is it? u How long is the infectious period? u How severe is it? u Contact network u “Contact” depends on pathogen: flu vs. STD u Examples u Human diseases– travel pattern u Animal diseases (e.g., 2001 F&M disease in the UK) u Plant diseases– spatial footprint 4

3/26/18 Diffusion vs. epidemics u Similar mechanism of spread u No decision making in epidemics u Epidemics: probabilistic model u A person having flu will infect another person in his contact network with some probability Modeling epidemics u Branching model u Network is a tree u SIR model u One cannot be infected multiple times u General network structure (directed graph) u SIS model u One can be infected multiple times 5

3/26/18 Branching model (p, k) u Contact network is a tree with k branches from each internal node u An infected node infects others in contact with a probability p u If probability p is high This node is infected first 6

3/26/18 u If probability p is low Will it become an epidemic? u Basic reproductive number, R 0 u R 0 = Expected # of new cases of the disease caused by a single person u R 0 = p k u Dichotomy u R 0 < 1 => disease will die out for sure u R 0 > 1 => disease will persist with positive prob. u Knife-edge u R 0 = 1: critical value 7

3/26/18 Insights from the branching model u R 0 = p k u How to prevent an epidemic? u Reduce the value of p – sanitary practice u Reduce the value of k – quarantine SIR Model u General directed graph as contact network u 3 possible stages for each node u Susceptible (S): Not yet infected, but susceptible u Infectious (I): Infected and may infect others within t I period (or steps) u Removed (R): Cured (will never be susceptible or infectious) u Each step: u An infectious node infects its neighbors with probability p 8

3/26/18 • S: No shade • I: Shaded+ dark border • R: Shaded+ thin border • t I = 1 • p = 0.5 Basic reproductive number u Dichotomy does not hold for SIR model on general graph u R 0 = expected number of new infections caused by a node u R 0 can be > 1, but the disease may still die out (next: an example) 9

3/26/18 Example: R 0 > 1 doesn't cause epidemic in SIR Model parameters: p = 2/3, t I = 1 R 0 = 4/3 (why?) Probability that a layer will be uninfected = ? Percolation: static view of SIR u Coin flips are done in advance u Paths originating from the initially infected nodes denote future infections 10

3/26/18 Other models: SIS u SIS model u S: Susceptible u I: Infectious u A node can become infected multiple times u Dichotomy result exists (not covered here) NetLogo experiment on SIR u Models Library à Networks à Virus on a network u Edit the "go" button and uncheck "Forever" u Edit the max to 100% for the following: u virus-spread-chance (p) u recovery-chance [proxy for infectious period t I ] 11

3/26/18 NetLogo (continued) u Then set the slider to 50% for: u virus-spread-chance (p) u recovery-chance [proxy for infectious period t I ] u Set the slider to 100% for: u gain-resistance-chance u Experiment by varying the virus-spread- chance (p) and average-node-degree (k) 12