In a community of Npop =10000 people, Ni=100 random people are infected initially on Day 1 (30% are asymptomatic)

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. Answer the following questions:


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


2) Do the following sensitivity analysis: Use the parameters in (1), 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.