Lectyre6

The SIR model

S: The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.

I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.

R for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called "recovered" or "resistant".

The SIS model

Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections do not give immunity upon recovery from infection, and individuals become susceptible again.

Decision Based Models

• Payoffs: Utility of making a particular choice

• Signals

  • Public information
  • Private Information

Scenario: Graph where everyone starts witn b.

Small set S of early adopters of A

• Hard-wire S — they keep using A no matter what payoffs tell them to do 

Stopping cascade

1 Two facts: - 1) If G\S contains a cluster of density >= (1-q) then S cannot cause a cascade

• 2) If S fails to create a cascade, then ° there is a cluster of density >= (1-q) in G\S