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# Probability in Propagation - PowerPoint PPT Presentation

Probability in Propagation. Transmission Rates. Models discussed so far assume a 100% transmission rate to susceptible individuals (e.g. Firefighter problem) Almost no diseases are this contagious Whooping cough: 90% transmission rate HIV: 2% transmission rate. Example.

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### Probability in Propagation

• Models discussed so far assume a 100% transmission rate to susceptible individuals (e.g. Firefighter problem)

• Almost no diseases are this contagious

• Whooping cough: 90% transmission rate

• HIV: 2% transmission rate

• Assume node A is infected.

• Let the transmission rate be p. In this example, p=0.8.

• What is the chance that B is infected?

• If B was infected by A, what is the chance that C is infected by B?

• What is the overall chance that C is infected?

• Both A and B are infected.

• What is the chance that C is infected in a 1-threshold model?

• What about a 2-threshold model?

Now let p=0.6. Let’s work out the possible scenarios from the previous slide.

• A and B start out infected. Let p=0.6 as in the previous slide.

• What is the chance that C is infected in a 1-threshold model?

• Let the probability that D is infected be 0.7. What is the probability that E gets infected?

• Repeat for a 2-threshold model.

• A and B start infected. They can infect C and/or D

• If one node, say C, is uninfected, in the next time step it could be infected by A or B again, but it could also be infected by D.

• If we change to an SIS or SIR or SIRS model, all these calculations change.

• The way the disease propagates at each time step changes

• Too much to calculate by hand, especially in big nets!

• Take a network. Set some nodes as I and others as S.

• When there is a probability, make a decision (infect or not). Repeat for as long as the simulation runs. Get results.

• Repeat the simulation, making decisions that may go the other way (e.g. a 60% transmission rate may lead to infection in one simulation and no infection in another)

• Do the simulation a lot of times, and look at the average result.

• SI model

• 1-threshold

• transmission rate = 0.7

• Assume a susceptible node can be infected at each time step

• Use a random number generator to get a number between 0 and 100

• http://www.random.org/

• If number <70, infect, otherwise do not.

• A and B are infected, 50% chance D is infected

• Does C become infected?

• Random number to see if infection comes from A

• If not from A, random number to see if infection comes from B

• 50% chance D is infected

• Random number to decideif D is actually infected

• Does E become infected?

• If C is infected, random numberto see if C infects

• If D is infected, random number to see if D infects

• Initial infection

• D (100% chance of infection)

• H (80% chance of infection)