Question

[Markov Models] Consider the following situation:

• There are three possible states: healthy, sick and dead.
• Healthy people can get sick, and sick people can recover and become healthy.
• Healthy people can die, and sick people can die. Dead people stay dead.
• Each ‘cycle’ is one day long.
• If you are healthy today, there is an 80% chance that you will be healthy tomorrow, and a 5% chance that you die. If you do not stay healthy or die, you become sick.
• If you are sick today, there is a 60% chance that you will be sick tomorrow, and a 10% chance that you will die. If you do not stay sick or die, you recover (become healthy).
• In ‘Cycle 0’, there are 1,000 healthy people, 800 sick people and 0 dead people.

a. (6 marks) Draw a Markov diagram for the situation above (hint: it’s the diagram with the circles and arrows).

b. (6 marks) Calculate the number of healthy people, sick people and dead people in Cycle 2. If necessary, round your answers to the nearest whole number. Show your work. (Hint: Cycle 2 is 2 cycles after Cycle 0. If Cycle 0 is today, then Cycle 1 is tomorrow, and Cycle 2 is the day after tomorrow.)

Healthy People in Cycle 2: ____________

Sick People in Cycle 2: ___________

Dead People in Cycle 2: __________

Work:

Answer 1

Health:-

Health is a state of physical, mental and social well-being in which disease and infirmity are absent...Achieving and maintaining health is an ongoing process, shaped by both the evolution of health care knowledge and practices as well as personal strategies and organized interventions for staying healthy.

Sick:-

If you are sick, you are ill. Sick usually means physically ill, but it can sometimes be used to mean mentally ill. If you are sick , you become disturbed or distressed; extremely upset, as by grief, disappointment, disgust, failure, etc.

Dead:-

no longer existing, or no longer having success or making progress. Some believe that employee loyalty to organizations is dead because lifetime employment is no longer possible. The online service attracted far fewer customers than predicted and is practically dead, analysts said.

• Healthy people can get sick, and sick people can recover and become healthy.
• Healthy people can die, and sick people can die. Dead people stay dead.
• Each ‘cycle’ is one day long.
• If you are healthy today, there is an 80% chance that you will be healthy tomorrow, and a 5% chance that you die. If you do not stay healthy or die, you become sick.
• If you are sick today, there is a 60% chance that you will be sick tomorrow, and a 10% chance that you will die. If you do not stay sick or die, you recover (become healthy).
• In ‘Cycle 0’, there are 1,000 healthy people, 800 sick people and 0 dead people.

Well Sick Dead

Stroke Post- Stroke 1 Post- Stroke 2 Well Post-Stoke Dead

Markov states STROKE DEAD WELL DISABLED POST MI1 POST MI POST MI2 POST MI3 DEAD TEMPORARY STATE TUNNEL STATES 10

Disease Modelling of chronic diseases such as diabetes or asthma plays an important role in medical decision making. State transition models are the most frequently used method. The objective is to illustrate the elements and the most important underlying procedures for designing a decision analytic Markov model with only three-states.

METHOD: Being "healthy" can be interpreted as a norm state, being "sick" as a temporary state and "dead" as an absorbing state. Transitions with accompanying transition probabilities that allow a cohort of model objects "to flow" between the cumulative exhaustive and mutually exclusive states complete the model structure. Half-cycle correction helps in overcoming the fitting problem of the discrete time valuation of Markov models. A model with the three states healthy, sick and dead is the easiest way to define a reasonable model that covers almost all aspects of a Markov disease model. The absorbing state dead helps in terminating a model. The temporary state sick acts as an event counter and the state healthy serves as a reservoir of modelling objects. The definition of the number and length of cycles completes the definition of a simple state transition model. Additional supplementary material with a functional sample model is provided.