1. Suppose there is a population of 1000 people and 500 of them have already adopted a new behavior. In the next time period, how many will begin the behavior if there is a constant hazard of .5? What about if the hazard is .5 * current adoption base? Show your work.
2. Draw a CDF (cumulative distribution over time) graph for internal influence and another for external influence. (No numbers, just the general shape). Label which of the graphs reflects a constant hazard.
3. (Two points) Open the NetLogo model “epiDEM Basic,” which simulates a S-I-R diffusion model.
https://www.netlogoweb.org/launch#https://www.netl…
Set it to 400 people, 20% infection-chance, 30% recovery-chance, and average recovery time of 100. Let it run for about 100 simulated hours (this will only take a few seconds of real time). Now examine the “Cumulative Infected and Recovered” and the “Infection and Recovery Rates” data. Note that NetLogo draws these graphs too flat to read, so you will probably want to click the three horizontal lines and either “download CSV” or “view full screen.” Include a copy of the graph. (Note the “download PNG” button just gives you the smushed graph so you might want to screenshot). What does the shape of the “% infected” line on the “cumulative infected and recovered” graph suggest about internal influence vs external influence?
4. What is the R0? Read the “model info” tab to learn what “R0” means and then explain it in your own words. (If you use a source besides the “model info” tab please cite it). Given the parameters in question #3, after 20 hours R0 is probably around 5.5. Play around with the “infection-chance,” “recovery-chance,” and “average-recovery-time” sliders. Include a screenshot if you can find a combination of parameters that gets R0 below 5 after 50 hours.
5. Consider Granovetter’s threshold model of collective behavior and whether each of the following assumptions about a population of 500 would be consistent with frequent riots.
* a uniform distribution of rioting thresholds from 0 to 100
* a normal distribution of rioting thresholds with a mean of 10 and a standard deviation of 2.
* a normal distribution of rioting thresholds with a mean of 12 and a standard deviation of 4.
* a Poisson distribution with a mean of 10
Explain the model and use it to justify your answer.
(if your stats knowledge is too rusty to visualize what these distributions look like, see pdf attached)
6. According to Rossman and Fisher’s simulation, under what conditions does it matter if an innovation starts with the most central person in a network?
7. In Centola’s model would a “simple contagion” spread faster in a pure ring lattice or a Watts-Strogatz with 2% rewiring? Why? How about a “complex contagion”? Why?