2 Complete the following challenge from the textbook, Business Dynamics: Systems Thinking and Modeling for a Complex World. pownload SiR model from the exam page on canvas. Extending the SIR Model, pages 316-317 [ you need to work on the parts discussed in the following paragraphs, NOT the whole CHALLENGE]: The SIR model, useful as it is, invokes a number of restrictive assumptions. ... Most importantly, the model assumes there is no incubation period. Individuals infected with a disease in the SIR model immediately become infectious. In reality, most diseases have a latency, or incubation period, and people become infectious before exhibiting any symptoms of illness. People exposed to chicken pox become highly infectious several days prior to the emergence of symptoms, some 14 to 21 days after initial exposure. Modify the SIR model by disaggregating the stock of infectious individuals into two categories: Asymptomatic Infectives and Symptomatic Infectives. The infection rate moves people from the susceptible category into the asymptomatic infective population, that is, people who are infected with the disease but do not yet exhibit any symptoms. After the incubation period, people begin to exhibit symptoms (typically while remaining infectious) and move into the symptomatic infective category. Assume that the rate at which people become sick is a first-order process with a constant average incubation period. Susceptible people can contact the disease by coming into contact with either symptomatic or asymptomatic infectives. The contact rate and infectivity for asymptomatic and symptomatic individuals often differ. Once people fall ill (become symptomatic) they often reduce their contact rate with the outside world, either to avoid infecting others or simply because they are too sick to follow their normal routine. Asymptomatic individuals, in contrast, usually do not know they are infected, do not exhibit any symptoms, and continue to contact others at their normal rate. Similarly, the infectivity of a disease prior to the emergence of symp-toms is often different from the infectivity after symptoms appear. In measles, for example, people are most infectious from 5 days prior to 5 days after the appearance of the characteristic rash. Modify the formulation for the infection rate to capture the differing contact rates and infectivity of the symptomatic and asymptomatic infective populations. Run the model for a hypothetical disease with an incubation period similar to chicken pox. Because the incubation period for chicken pox is 14 to 21 days, as-sume an average of 18 days. Assume the average duration of illness is 4 days. Set the contact rate for asymptomatic infectives to four per person per day, but because those exhibiting symptoms remain in bed in self-imposed quarantine, set the con-tact rate for the symptomatic population to only one per person per day. Assume infectivity is 0.25 for both asymptomatic and symptomatic populations. Also assume an initial population of 10,000, all of whom are initially susceptible except for one asymptomatic infective person. Run the model and describe the results. How does the inclusion of an incubation period affect the dynamics? By the time 1 % of the population exhibits symp-toms, what fraction of the susceptible population remains uninfected? How many susceptible remain by the time 10% of the population has become sick? Explore the response of the epidemic to different incubation times and infectivity