# infectious disease homework help

Assignment SIR model (60 points)

Upload assignment as .doc, .docx, .xls, .xlsx or .pdf file

You must show all intermediate steps of your work to receive full credit.

Question 1 (15 points).

Using the three difference equations listed of the SIR model, create a 3 column population model in excel which shows the population from time step 1 to time step 30. Let your starting populations be: St = 99, It = 1, Rt = 0. Let a = 0.001, and let γ = 0.05.

A. Create a line graph showing the populations of St, It, and Rt through time.

B. Holding all other variables constant, try increasing and decreasing the infection coefficient a. How does changing the value of a affect the behavior of the model?

C. Holding all other variables constant, vary the infection coefficient γ (by increasing and decreasing the value). How does changing the value of γ affect the behavior of the model? Why?

Question 2 (15 points).

The infection coefficient a must be constant, but there is also an upper bound on its size in a biologically meaningful model. Using your population model in Excel, set all parameters to their original value (as specified at the beginning of question 1), and then let a = 1.

A. What happens to the population if a = 1? What is the biological significance of a = 1?

B. Now keeping a = 1, let the starting population of infected individuals I0 = 5. What is the value of St at the second time step? Does this make sense? Why or why not?

C. If we let a = .1, what is the largest starting population of It that makes sense?

Question 3 (15 points).

Imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. Let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals.

A. Rewrite the difference questions for St+1 and It+1 (from question 1), to incorporate the effects of quarantine. (Hint: quarantine should affect the term representing the proportion of susceptible individuals who are infected each time step)

B. Quarantine can be viewed as a way of modifying the transmission coefficient (a) by reducing the number of individuals which can be infected. This modified transmission coefficient can be referred to as a’. Write and equation for a’ that incorporates both a and q.

Question 4 (10 points).

Imagine an island with a starting population of 100 individuals. 1 of those is infected with a deadly disease. Once infected, this disease will kill an individual in 4 days. Calculate the removal rate (γ), then using the removal rate, calculate what value of a will result in an epidemic.

Question 5 (5 points)

Check out the internet for values of Ro for the flu, HIV and Ebola (mention your source). What can you tell from those numbers?

## Needs help with similar assignment?

We are available 24x7 to deliver the best services and assignment ready within 3-4 hours? Order a custom-written, plagiarism-free paper

Get Answer Over WhatsApp Order Paper Now