Build numerical model for the spread of an infectious disease built upon the SIR model for transmission. The model should be based on a daily time step. (a) Assume that a city of 10 million people is confronted with a potential infectious epidemic. A plane arrives at the international airport carrying 25 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. After 4 days, infected individuals are no longer contagious. Assume that recovered individuals that survive develop immunity to the disease. (a) Plot the fraction of susceptible individuals, infected individuals, and recovered individuals as a function of time throughout the epidemic. (b) 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 plane landing did this number finally reach steady state (i.e., the epidemic is completely over). (c) In order to plan for the construction of hospitals and other medical facilities to respond to such an epidemic, how many individuals are contagious at the peak of the epidemic? How large is this fraction of the total population? On what day of the epidemic did this take place? It is viable to provide hospital beds for this number of individuals at one time? (d) Assume that there are approximately 10,000 hospital beds in the city. (This is about the number of hospital beds in New York City's 11 public hospitals.) What fraction of the total population need to be immunized in order to prevent the number of contagious individuals from exceeding this maximum at point of time during the epidemic? (e) Assuming the cost of an inoculation is $7.00 per vaccination, what is the total cost of vaccinating enough individuals to avoid any spread of the epidemic?