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Consider an epidemiological model that computes the number of people infected with a contagious illness in a closed population over time. Specifically, the SIR model involves coupled equations relating the number of susceptible people St, the number of infected people It, and the number of people who have recovered R. You estimate that if individuals have recovered in a given period, there is a 100 percent chance that they will remain recovered. If individuals are infected in a given period, there is a 50 percent chance that they will remain infected and a 50 percent chance that they will recover in the next period. If individuals are susceptible in a given period, there is a

Consider an epidemiological model that computes the number of people infected with a contagious illness in a closed population over time. Specifically, the SIR model involves coupled equations relating the number of susceptible people St, the number of infected people It, and the number of people who have recovered R. You estimate that if individuals have recovered in a given period, there is a 100 percent chance that they will remain recovered. If individuals are infected in a given period, there is a 50 percent chance that they will remain infected and a 50 percent chance that they will recover in the next period. If individuals are susceptible in a given period, there is a

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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Question 2 Consider an epidemiological model that computes the number of people infected with a contagious illness in a closed population over time. Specifically, the SIR model involves coupled equations relating the number of susceptible people St, the number of infected people I4, and the number of people who have recovered R. You estimate that if individuals have recovered in a given period, there is a 100 percent chance that they will remain recovered. If individuals are infected in a given period, there is a 50 percent chance that they will remain infected and a 50 percent chance that they will recover in the next period. If individuals are susceptible in a given period, there is a 20 percent chance they will remain susceptible, but there is a 80 percent chance of being infected in the next period. (a) Write out the corresponding Markov system. (b) What is the long-run distribution of SIR individuals? (c) Write out the general solution of the underlying system of difference equations. Now assume that the initial distribution of susceptible So, infected Io, and recovered Ro is 3/8, 5/8, and 0/8, respectively. (d) Is there an absorbing state in this dynamic system? Explain. (e) What is the distribution of SIR people after 4 time periods?
Transcribed Image Text:Question 2 Consider an epidemiological model that computes the number of people infected with a contagious illness in a closed population over time. Specifically, the SIR model involves coupled equations relating the number of susceptible people St, the number of infected people I4, and the number of people who have recovered R. You estimate that if individuals have recovered in a given period, there is a 100 percent chance that they will remain recovered. If individuals are infected in a given period, there is a 50 percent chance that they will remain infected and a 50 percent chance that they will recover in the next period. If individuals are susceptible in a given period, there is a 20 percent chance they will remain susceptible, but there is a 80 percent chance of being infected in the next period. (a) Write out the corresponding Markov system. (b) What is the long-run distribution of SIR individuals? (c) Write out the general solution of the underlying system of difference equations. Now assume that the initial distribution of susceptible So, infected Io, and recovered Ro is 3/8, 5/8, and 0/8, respectively. (d) Is there an absorbing state in this dynamic system? Explain. (e) What is the distribution of SIR people after 4 time periods?
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