1 (100 points): assume that the recovery time for an individual from an infectious disease can be modeled as a normal distribution. (a) calculate the time, d, in days for an individual to recover from being initially infected, with a 95% confidence level, assuming that the likelihood of recovering at any time is modeled as a normal distribution with a mean of 5 days and a standard deviation of 0.5 days. (b) use the sir model that you constructed previously. assume that a city of 10 million people is confronted with a potential infectious epidemic. a ship arrives at the international airport carrying 100 individuals who are infected, but are unaware that they are infected. while contagious, infected individuals come into transmission contact with another individual once every 2 days. the recovery process is modeled using the poisson process from part (a). assume that recovered individuals that survive develop immunity to the disease. plot the fraction of susceptible individuals, infected individuals, and recovered individuals as a function of time throughout the epidemic. (c) what fraction of the total population will have ultimately come down with the infectious disease once the epidemic is over? how many days after the ship docking did this number finally reach steady state (i.e., the epidemic is completely over). (d) what is the basis for this structured model (i.e., scale, time, etc.)? what is/are the major assumptions associated with the structure?
