In a community of Npop =10000 people, Ni=100 random people are infected initially on Day 1 (30% are asymptomatic).All people are following the same standard practice of social distancing. Each person is in close contact with Ncl=2 people and in casual contact with Nca=3 people on a daily basis. (In forming the close contact groups, imagining lining up all people in a circle, people adjacent to each other are considered close contacts.) Close contacts are the same people all the time and casual contacts are random and vary on a daily basis. Infected people pass the virus to other people until they are quarantined. Pas=30% of the newly infected people are asymptomatic. Asymptomatic people can pass the virus for Nasd=10 days on the average before being quarantined. Symptomatic people can pass the virus for Nsd=5 days on the average before being quarantined. The probabilities of infecting a close and casual contact on a daily basis are Pcl=10% and Pca=1% respectively. Make other assumptions as needed. Write computer program to answer the following questions:

1)What is the daily infection number for the next 60 days? What is the percentage of asymptomatic cases? What is the percentage of cases that are infected by asymptomatic carriers? What is the daily number of people being quarantined (assuming the quarantine duration is 20 days for every person)? In answering these questions, run your model 100 times, plot the average, and one standard deviation above and below the average as a function of day number. (On Day 1, you can assume asymptomatic and symptomatic people can pass the virus for [1, 10] and [1, 5] days, respectively, with a uniform distribution before they are quarantined). Plot other parameters you find interesting or useful.

2)Adjust the parameters so that the average daily infection number remains more or less stable for 20 days (between day 31-50)

3)Do the following sensitivity analysis: Use the parameters in 2), but change one of Nca, Nasd, Nsd, Pcl, Pca in turn to have an upward and downward trend for total case numbers on the average. Do the same plots in 1) for each change in parameters.

4)Discuss at the least the following:

oFor the parameters in 2), justify the stable daily infection numbers in theory or with reason.

oDo simulations appear to be correct for the given assumptions? What make you arrive this conclusion?

oDo the parameters appear to reflect the actual situation at Miami, in the U.S. or other countries?

oAnything interesting/surprising in your results?