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10. Suppose that an individual can either be susceptible to a disease or infected with the disease. The probability of an infection for a susceptible person is 0.05 per day, and the probability of an infected person becoming susceptible is 0.12 per day. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 1 day? (d) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 2 days?

10. Suppose that an individual can either be susceptible to a disease or infected with the disease. The probability of an infection for a susceptible person is 0.05 per day, and the probability of an infected person becoming susceptible is 0.12 per day. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 1 day? (d) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 2 days?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Questions 10 a, b, c and d

10. Suppose that an individual can either be susceptible to a disease or infected with the disease. The probability of an infection for a susceptible person is 0.05 per day, and the probability of an infected person becoming susceptible is 0.12 per day. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 1 day? (d) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 2 days? 11. There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass. The other transition probabilities between different states are zero. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the ecosystem is evenly split: one-third each grass, shrubs, and trees. What fraction of the ecosystem is covered in shrubs after 2 years?
Transcribed Image Text:10. Suppose that an individual can either be susceptible to a disease or infected with the disease. The probability of an infection for a susceptible person is 0.05 per day, and the probability of an infected person becoming susceptible is 0.12 per day. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 1 day? (d) Suppose that initially the population is 90% susceptible and 10% infected. What fraction is susceptible after 2 days? 11. There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass. The other transition probabilities between different states are zero. (a) Draw a Markov model for this system. (b) Find a transition matrix for this system. (c) Suppose that initially the ecosystem is evenly split: one-third each grass, shrubs, and trees. What fraction of the ecosystem is covered in shrubs after 2 years?
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