Problem 1 (40 points) You are working in the CDC modeling COVID in the United States, and the date is March 2020. The country is debating how much economic cost to assume in the short term in order to reduce the spread of COVID. Your task is to model the disease and its costs in the U.S. over the next year (March 2020 April 2021), and help guide decision-making. Note that while I have calibrated the model to approximate some of the numbers in reality, this is not a valid epidemiological model nor a complete analysis of costs of the disease, so take it only as the beginning of a more complete model. Where necessary, round answers to the nearest whole number. a) Build a model in Excel that begins on March 1, 2020, and proceeds weekly through the end of April 2021. Your model should therefore have 61 time steps. Epidemiologists are telling you that the following equation represents their best projection for weekly cases moving forward: = 1000 + 13000 + 30 2 1.6 3 where t is the week (beginning with 1). Note that new cases cannot be negative, something we will want to guard against later. You will therefore want to embed an IF statement in the formula [(e.g. =IF(NewCases<0,0,NewCases) which tells Excel to check whether what you are calculating as new cases in a given time period is negative, put a zero value if true, otherwise but the value of the calculation if false]. Show a graph of new cases per week from March 1 2020 end of April 2021, with axes properly labeled. What begins to happen in late 2020? What part of the NewCases equation is causing that to happen? b) Make a graph of cumulative COVID cases. How many cases have there been by end of April 2021? c) Assume that 15% of COVID cases require hospitalization, and assume that each person remains in the hospital for three weeks. Graph the hospital demand per week from March 2020 April 2021. At what level does hospital demand peak according to this model, and when does that occur? d) Health economists tell you that hospitalization costs for COVID patients are as follows: () = 10,000,000 + 18 + 0.1 2 where q is the number of COVID patients in hospitals each week. What is the marginal cost of a COVID patient? Is it constant, rising, or falling? Why might that make sense when thinking about how hospitals work? 2 e) Calculate the hospitalization costs for COVID patients in each week, as well as the weekly hospitalization cost per patient currently hospitalized. What is the average hospital expenditure per currently hospitalized patient from March 2020 April 2021 according to your model? (In reality, the number is around $14,000). What is the total cost of hospitalizations from COVID from March 2020 - April 2021, in billions of dollars? f) Public health experts are advocating that the country assume costs in order to avert COVID transmission. These costs include those for aggressive, widespread testing and tracing, as well as costs of partial lockdowns in terms of transfers to businesses and to individuals. They propose a model that links the transmission dynamics to the expenditure on testing, tracing and lockdowns: = 1000 + 13000 + 30 2 + () 3 () = 1.6 0.1 0.9 where H is the expenditure on tracing, testing, and transfers to ease costs of lockdown. Note that H is in billions of dollars, so if H=10 that would be $10 billion. Note also that if H = 0, the evolution of new cases will be the same as above. Assume that H = 10 for now. Make a new graph of COVID cases from March 2020 April 2021 that includes both the trajectory in (a) as well as the new one with H = 10. Add this new trajectory to the graph on cumulative cases from (b) and the one on hospital use in (c). How does the trajectory when H = 10 compare to the original trajectories? Does this make sense? g) What is the new level total hospital expenditure from March 2020 April 2021? Calculate the net benefit of the government decision to spend $10 billion on reducing COVID transmission as the difference between $10 billion and the reduction in hospital expenditure compared to H = 0. What is the net benefit of having H = 10? (Note that the model is very incomplete here because we are only including in the costs of COVID as the cost of hospitalization and not taking into account mortality, care for people with long-term COVID symptoms, etc.). h) The country is debating the optimal expenditure H to reduce COVID transmission. How much should we spend on testing and tracing, and how much should we lock down, which would impose economic costs on government and on citizens? Use the Solver to calculate the optimal level of H according to this model. Provide graphs that compare the outcomes in (a)- (c) with the optimal level of expenditure H, and describe what happens to new cases, cumulative cases, and hospital demand. i) If you were to extend the model beyond April 2021, how would that affect your conclusion about the optimal level of expenditure H?