Transcript ppt
Fish Infectious Disease Model Case Study BSC417/517 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 lowleverage variables • To [email protected] by Thursday AM Next time • Sensitivity analysis: infectious disease model • Case analysis: infectious disease model