Building a Model of An Epidemic - Science Assignment Help

Assignment Task

Question - Building a model 

In the following question we will build a model of an epidemic t days after the first infectious cases are discovered. You will create an Excel spreadsheet to assist in answering the questions which must be uploaded with your answers to the questions. We will begin with the following data and assumptions:

• N — the population of the affected. This number will be given by your student ID number.

• /, — the initial number of contagious people in the population. This will be the smallest non-zero digit of your student ID number.

• Rv — the basic reproduction ratio is 3.

• a — the recovery rate is 0.2. 

(a) Using Euler's method with Is = 1, model the epidemic. You must upload a copy of your spreadsheet alongside your answers to the questions. To aid you in determining when the virus' spread ends, reduce the number of displayed decimal places to zero. Your model should terminate with the first line which shows I = O.

(b) Produce a "Scatter with Smooth Lines" plot showing 5(t), !(t), and R (t) for the duration of the epidemic.

(c) Calculate the percentage difference between the theoretical maximum number of infectious individuals and the maximum predicted by your model. Assuming the same error holds for all aspects of your model, produce a range of values for the length of the epidemic.

(d) By decreasing h to 0.1 what is your new predicted length of the epidemic?

(e) Again using h = 1, if the government introduces measures which reduce R 0 to 1.4, what effect does this have on the population?

(f) Suppose that 00 = 3, and that the government provides 50000 doses a day of a 100?fective vaccine to susceptible citizens. Produce a model for this scenario. Your model must include a "Scatter with Smooth Lines" plot showing S(t), !(s), 0(5), and V(t) for the duration of the epidemic. [Hint: think carefully about the model must be updated to accommodate the vaccinated, and what the structure of the model is at the end.]

(g) Compare the two situations from (a) and (f). 

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