Questions 10 a, b, c and d 10. Suppose that an individual can either be susceptible to a disease or infected with thedisease. The probability of an infection for a susceptible person is 0.05 per day, andthe 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. Whatfraction is susceptible after 1 day?(d) Suppose that initially the population is 90% susceptible and 10% infected. Whatfraction is susceptible after 2 days?11. There are three kinds of vegetation in an ecosystem: grass, shrubs, and trees. Everyyear, 25% of grassland plots are converted to shrubs, 20% of shrub plots are convertedto 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?

Markov model for the system: S I / \ / \ / \ / \ I(0.12) S(0.05) \ /…

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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?

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