Lecture 9 BSC 417

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

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

More on Q2 Losing resistance = (1/ResistanceTime)*Resistant Fish

Other points to digest on last time’s 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

Background to homework What is meant by structural validity of a model? How do we model predictive validity?

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?

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

Sensitivity analysis Identifying variables that are: – High leverage variables – Low leverage variables

High leverage variables Variables that have a high impact on the system’s behavior When values of these variables are changed, the system behavior changes a great deal The system is “sensitive” to changes in this variable

Why are high leverage variables important? This is where we want to focus our mitigation strategies These are the keys to the model

John Snow’s “natural experiment” Cholera outbreak in London

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

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

Low leverage: Initial number of sick fish? Others?

Short-term carbon cycle

Steps in the sensitivity analysis 1. Identify exogenous variables – Use a bull’s 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

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

Examples

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

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