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In a population of 300,000 people, 120,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, 4% will die each year and the others will recover. Of the people who have never been infected, 40% will become infected each year. [1] Find the initial state matrix that describes the above situation. [2] Find the transitional probability matrix (called stochastic or Markov matrix) that reflects the given conditions. [3] How many people will be infected in 4 years? (Round your answer to the nearest whole number.)

In a population of 300,000 people, 120,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, 4% will die each year and the others will recover. Of the people who have never been infected, 40% will become infected each year. [1] Find the initial state matrix that describes the above situation. [2] Find the transitional probability matrix (called stochastic or Markov matrix) that reflects the given conditions. [3] How many people will be infected in 4 years? (Round your answer to the nearest whole number.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 55E
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In a population of 300,000 people, 120,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, 4% will die each year and the others will recover. Of the people who have never been infected, 40% will become infected each year. [1] Find the initial state matrix that describes the above situation. [2] Find the transitional probability matrix (called stochastic or Markov matrix) that reflects the given conditions. [3] How many people will be infected in 4 years? (Round your answer to the nearest whole number.)
Transcribed Image Text:In a population of 300,000 people, 120,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, 4% will die each year and the others will recover. Of the people who have never been infected, 40% will become infected each year. [1] Find the initial state matrix that describes the above situation. [2] Find the transitional probability matrix (called stochastic or Markov matrix) that reflects the given conditions. [3] How many people will be infected in 4 years? (Round your answer to the nearest whole number.)
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