BSC 417

1
Lecture 9

• BSC 417

2
Outline

• Last homework, question 2
• Homework some background first
• Chapter 3, Q6-8 (on the board)
• Sensitivity analysis infectious disease model
• Case analysis infectious disease model

3
Question 2

• Concept of a conveyor
• Special kind of reservoir
• Transit time
• Characteristic of conveyors
• Flow through
• Outflow for those exiting the reservoir
• Leakage
• Before transit time is complete, some leave
• Leakage fraction
• Fraction of individuals that leak out (controlled
  by death rate)
• Conveyors are useful in modeling transformations
  as processes

4
(No Transcript)
5
More on Q2

• Losing resistance
• (1/ResistanceTime)Resistant Fish

6
Other points to digest on last times homework

• Be sure your purpose statement includes
• An adequate description/definition of the system
• What is its scope?
• The behaviors we want to understand
• Be specific
• The questions we want to address
• Only include questions that this model is capable
  of addressing
• If you want to look at other questions, revisit
  model

7
Background to homework

• What is meant by structural validity of a model?
• How do we model predictive validity?

8
Structural validity

• Comparing the model with its description
• Check out the units
• Does it make logical sense?
• Do the relationships look like what they are
  supposed to be?
• Are all the arrows correct?
• How could the model be enhanced to better reflect
  the real system?
• What other variables would you include?

9
Predictive validity

• Setting test cases for assumptions
• Does the model behave according to the theory?
• Can be used to change model OR theory!

10
(No Transcript)
11
(No Transcript)
12
Sensitivity analysis

• Identifying variables that are
• High leverage variables
• Low leverage variables

13
High leverage variables

• Variables that have a high impact on the systems
  behavior
• When values of these variables are changed, the
  system behavior changes a great deal
• The system is sensitive to changes in this
  variable

14
Why are high leverage variables important?

• This is where we want to focus our mitigation
  strategies
• These are the keys to the model

15
John Snows natural experiment

• Cholera outbreak in London

16
Variables interventions

• Contact with infected people
• Living near Broad Street
• Drinking water source
• Possible interventions
• Reducing contact between people (quarantine)
• Evacuating people from their homes
• Cutting off drinking water source

17
Low leverage variables

• Variables that have a minimal impact on the
  system
• Values can be changed without upsetting system
  behavior
• Less critical
• Things that we can allow to change without
  adversely affecting system behavior

18
Low leverage

• Initial number of sick fish?
• Others?

19
Short-term carbon cycle
20
Steps in the sensitivity analysis

• 1. Identify exogenous variables
• Use a bulls eye diagram
• Excluded exogenous endogenous
• Useful for showing boundaries of the model,
  positing other variables you might include,
  describing a model that has grown too complex for
  a flow diagram
• Variables that you set
• Converters with no variables pointing in and some
  starting values for reservoirs
• 2. Make a series of model runs
• Vary exogenous factors slightly over an
  hypothesized reasonable range

21
Sensitivity steps, continued

• 3. Compare system behavior in each run
• Note changes in shape and level
• Relate to common measures
• E.g., percentage change in a stock
• Spreadsheet analysis
• 4. Identify high and low leverage variables
• And explain (ie, understand) why it is that they
  behave that way

22
Examples
23
Case analysis

• Using real world scenarios as inputs to a model
• Each case is different
• Run multiple models for comparability purposes

24
Next time

• Meet in GP 152
• Bring your books and disks for installing
  software
• No homework due
• Reading
• Eisenberg et al. 2002, readings in text