Fish Infectious Disease Model

Case StudyBSC417/517

Today

• Exploratory analysis• Problem statement• Conveyors• Model validity: structural and predictive• High/low leverage variables (& example)• Endogenous and exogenous variables defined• More on sensitivity analysis and case analysis

Steps in exploratory analysis• Problem definition– What questions are we trying to answer? These must be

explicitly stated. A purpose statement can be useful for this exercise.

• Model validation– Whether the model as designed can give reasonable

predictions and explanations of the system– Structural validity– Predictive validity

• Exploratory analysis: “playing around” with the model– System perturbation– Sensitivity analysis

• Case analysis– Testing scenarios or hypotheses

Understanding the system• Defining each system element, its units, its relationship

to other units– What role does each unit play in the system?

• Which system elements dominate system behavior? Why? What factors are less important to the problem at hand?

• What synergies exist that may exert large influences on the system?

• How does the system respond to perturbations of various kinds?

• Under what conditions will we see collapse or runaway behavior?

Elements of a purpose statement

• 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

Purpose statement: example• “We wish to model the spread of disease X

through our fish population over a two year period. Under normal conditions (ie, no infected fish are present), the fish population exhibits a stable size over time. We wish to predict how the makeup of the population of fish will change over time as a result of recurrent epidemics of disease X. We will use the model to evaluate two options for responding to an epidemic of this type: (1) repeated capture and removal of infected fish and (2) introduction of a new, resistant strain of fish for which the infectiousness of disease X will be reduced by 50%.”

Conveyors

• Transit time: amount of time individuals or material entering will remain before flowing to next step

• Flow through: the outflow through which individuals exit from the conveyor after residing for a time

• Leakage: optional outflow from which individuals can “leak” from conveyor before transit time is complete

• Leakage fraction: fraction of individuals that leak out over the transit time.

• Conveyors are useful in modeling transformations as processes

Validity testing

• 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

Case analysis

• Using real world scenarios as inputs to a model

• Each case is different• Run multiple models for comparability

purposes

Assignment: fish model, HW8

• Build in user interface• Define units for all quantities• Label variables endogenous or exogenous• Identify probable high-leverage and low-

leverage variables

• To bsc417@gmail.com by Thursday AM

Next time

• Sensitivity analysis: infectious disease model• Case analysis: infectious disease model