Nathaniel Osgood CMPT

Transcription

1 System Dynamics Modeling: Overview & Causal Loop Diagrams Nathaniel Osgood CMPT

2 What is System Dynamics? A feedbackoriented perspective A broad, evolving methodology to help Conceptualize Describe Analyze Manage feedback systems

3 System Dynamics offers Qualitative & quantitative components A defined, incremental and iterative modeling process that delivers value throughout Timehoned techniques for working with diverse interdisciplinary stakeholders Evolved software permitting focus on the what is being described not how it is run A rigorous mathematical foundation A rich set of analysis tools Techniques for interfacing closely with cognate areas (e.g. statistics, decision sciences, evidencebased practices, applied mathematics, other modeling approaches, etc.)

4 Differences in Framing the Issues Modeling methodologies are often distinguished more fundamentally by the questions being asked than by the answers being given Such methodologies will often be most distinguished by the way in which they frame problems In comparing, we must be conscious of these differences

5 Engagement in the Human Theatre Uses of SD Models [Hovmand]

6 [Modeling] Power to the People: Fostering Participatory Discourse To empower participatory modeling, System Dynamics tends towards simpler formalisms Capturing qualitative understanding Easy understanding by stakeholders: Simulation model Inspection Dialogue Manipulation Declarative ( programming free ) specification Intuitive graphical representation Features support high stakeholder involvement in model conceptualization, formulation & analysis

7 Stages of the System Dynamics Mothers Overweight Babies Born from GDM Pregnancy Overweight Babies Born to Pregnant Normal Weight Mothers Overweight Babies Born from NonGDM Mother with History of GDM Normal Weight Babies Born to Overweight Mothers without GDM Normal Weight Babies Born to Mothers without GDM Normal Weight Babies Born from T2DM Pregnancy Normal Weight Deaths Normal and Underweight Weight Developing Obesity T2DM Oveweight Babies Born from T2DM Mothers Overweight Individuals Developing T2DM T2DM Deaths Completion of Pregnancy for Mother with T2DM Overweight T2DM Pregnant with T2DM History of GDM Normal Weight Babies Born from GDM Pregnancy <Birth Rate> Pregnancies of NonOverweight Women Completion of Pregnancy to NonOverweight State Shedding Obesity Completion of Pregnancy Duration Pregnancies of Overweight Overweight Women Deaths Pregnant Women with GDM New Pregnancies from Mother with T2DM Pregnant Normal Weight Mothers with No GDM History Overweight/Obesity Pregnant Overweight Pregnancies to Overweight Mothers with No Mother Developing GDM GDM History Women with History of GDM Developing T2DM Developing GDM GDM Pregnant with GDM History of GDM Completion of GDM Pregnancy Pregnancies for Women with GDM History of GDM GDM History Pregnant with PreExisting History of GDM Modeling Process A Key Deliverable! Model scope/boundary selection. Model time horizon Identification of key variables Reference modes for explanation Causal loop diagrams Stock & flow diagrams Policy structure diagrams Group model building Contacts of Susceptibles with Infectives Susceptibles Specification of Qualitative & Semiquantitative insights Infectives Waiting Times New Infections People Presenting for Treatment Health Care Staff Overweight Babies Born from Pregnant Overweight Reference mode reproduction Parameter sensitivity analysis Specification & investigation of intervention scenarios Investigation of Parameters Matching of Crossvalidation intermediate time Quantitative causal series Robustness&extreme case hypothetical external relations tests conditions Matching of Decision rules observed data point Unit checking Crossscenario Initial conditions Problem domain tests comparisons (e.g. Constrain to sensible CEA) bounds Formal analysis Structural sensitivity analysis Normal Weight Individuals Developing Normal Weight Babies Born from NonGDM Mother with Pregnancy to Overweight State that Continue on to Postpartum T2DM Pregnancies to NonOverweight Mother Pregnant Women Developing Persistent Deaths from NonT2DM Women with History of Completion of NonGDM Pregnancy for Woman with Pregnancies Developing GDM from Mother with I I ( S I) h I 2 h 2 ( S I) h I 2 h Baseline 50% 60% 70% 80% 90% 95% 98% 100% Average Variable Cost per Cubic Meter Learning environm ents/micr oworlds/f light simulator s 0.3 Quantitative insights

8 Value of the Modeling Process Often the modeling process itself rather than the models created offers the greatest value Modeling as theory building: Refinement of mental models Reflecting on Mental models What is & is not known / data Different perspectives

9 Benefits of Rich Stakeholder Participation Developing rich, grounded understanding Building community capacity Critiquing model behavior Fostering stakeholder cooperation Implementing policy recommendations Facilitating data collection design Aiding in replanning Keeping model updated Empowering community selfguidance Dignity of Risk [Hovmand]

10 Group Model Building [Hovmand]

11 Group Model Building [Hovmand]

12 Model Conceptualization: Feedback Loops Loops in a causal loop diagram indicate feedback in the system being represented Qualitatively speaking, this indicates that a given change kicks off a set of changes that cascade through other factors so as to either amplify ( reinforce ) or push back against ( damp, balance ) the original change Loop classification: product of signs in loop (best to trace through conceptually) Balancing loop: Product of signs negative Reinforcing loop: Product of signs positive

13 Example: Physical Systems With & Without Feedbacks Balancing Driving / flying Thermic regulation: Hot blooded (homeothermy) vs. cold blooded (ecothermic) animals Introducing a feedback can fundamentally alter a system s behaviour

14 Recall: A Common Problem: Overly Narrow Mental Models Most decisions are based on mental models Frequently the failure to anticipate & account for policy resistance is due to narrow mental models Deleterious effects are blamed on side effects of anticipated process Failure to consider interactions between diverse pieces of system (each of which may be well understood) System dynamics seeks a broader understanding of the underlying system

15 Examples of Deleterious Feedbacks Cutting cigarette tar levels reduces cessation Cutting cigarette nicotine levels leads to compensatory smoking Targeted antitobacco interventions lead to equally targeted coupon programs by tobacco industry Charging for supplies for diabetics leads to higher overall costs by increases costs due to reduced selfmanagement, faster disease progression ARVs prolong lives of HIV carriers, but lead to resurgent HIV epidemic due to lower risk perception Saving money by understaffing STI clinics, leads to long treatment wait, greater risk of transmission by infectives & bigger epidemics Antibiotic overuse worsens pathogen resistance Antilock breaks lead to more risky driving Natural feedback: Intergenerational Vicious Cycles

16 Causal Loop Diagram Food Ingested Hunger Focuses on capturing causality and especially feedback effects Indicates sign of causal impact ( vs. ) x y indicates x y indicates y x y x 0 0

17 Causal Loop Diagram An arrow with a positive sign (): all else remaining equal, an increase (decrease) in the first variable increases (decreases) the second variable above (below) what it would otherwise have been. An arrow with a negative sign (): all else remaining equal, an increase (decrease) in the first variable decreases (increases) the second variable below (above) what it otherwise would have been.

18 Reasoning about Link Polarity Easy to get confused regarding link polarity in the context of a causal chain Tips for reasoning about link polarity for X Y Reason about this link in isolation Do not be concerned about links preceding X or following Y Ask if X were to INCREASE, would Y increase or decrease? Increase in Y implies,decrease in Y implies If answer is not clear or depends on value of X, need to think about representing several paths between X and Y

19 Tips Variables should be noun phrases Variables should be at least ordinal Links should have unambiguous polarity Remember factors involving people Avoid megadiagrams Label loops Distinguish perceived and actual situation

20 Ambiguous Link Ambiguous Link: Sometimes, sometimes Overtime Replace this by disaggregating causal pathways by showing multiple links Work Accomplished per Day Overtime Fatigue Greater Incorporation of Outside Tasks at Work Efficiency Work Accomplished per Day More Time Working

21 Feedback Loops Loops in a causal loop diagram indicate feedback in the system being represented Qualitatively speaking, this indicates that a given change kicks off a set of changes that cascade through other factors so as to either amplify ( reinforce ) or damp ( balance ) original change Loop classification: product of signs in loop (best to trace through conceptually)

22 Substance Abuse Stigmatization Capacity for Productive Work Nutrition Risk of Injury & Accidents Health Costs Employability Poverty Impulse towards SelfMedication Dysphoria & Stress Reinforcing (positive) feedback Balancing (negative) feedback

23 Advantages of Recognizing Feedback Balancing Feedback (Stability) Reinforcing feedback (Instability) Desirable Undesirable Securing resiliency Individual selfregulation Structure interventions (and system) to achieve this and prevent this Preventing policy resistance & adverse lock in effects Low tar & nicotine cigarettes Risk perception for Infectious diseases Enabling rapid intervention success Viral approaches, peer messaging, rapid social change Heading off rapidly growing vicious cycles Addictions, cycle of poverty, SAVA

24 Gates Comments The biggest advantage we have is that As [NT] got more applications, NT good developers like to work with good servers got more popular. As it s developers gotten more popular, we ve got [Cusumano&Selby, 95] more applications. Most people don t get millions of Computer Reseller News, people giving them feedback about their [T] he more users [the internet] products We have this whole group of gets, the more content it gets, the [2000] people in the US alone that takes more users it gets. phone calls about our products and logs Red Herring, everything that s done. So we have a It s all about scale economies and better feedback loop, including the market share. When you re market shipping a million units of Windows [Cusumano&Selby, 95] software a month, you can afford to spend $300 million a year improving it and still sell at a low price. [Fortune, ]

25 Examples: Vicious/Virtuous Cycles Positive (reinforcing) feedback can lead to extremely rapid changes in situation Existing Users Number of Connections to Music Download Server New Users Discovering Site Likelihood of Cross Listing and Listing on Search Engines Length of Time Per Download Likelihood of User Starting Multiple Simultaneous Downloads Confusing Code Customers Word of Mouth Sales Ease of Understanding where to Make a Change Confusing Additions

26 Simple Causal Loops Change Requests Remaining Work Project Duration Overbearing PM M anagement Style Willingness of Project Particip ants to share info with PM Changes to Schedule Job Rhy thm Estimated Design Costs beyond Target Budget Target Budget PM Suspicion Aggregate Productivity Design Scope

27 Example Balancing Loops Balancing loops tend to be selfregulating Aggregate Computer Responsiveness Programs Run Simultaneously Virtual Memory Swapping Mistakes Learning from Mistakes

28 Risk Management Schedule Disruptions Unmanaged Risks Time taken for Risk Assessment and Management

29 Longer Term Cost of Pressure: Cutting Corners

30 Vicious Cycles

31 Turnover Vicious Cycle Developer Fatigue Morale Backlog of Work Resignations Team Productivity Extra Hiring Related Work Work per Team Member

32 Reinforcing Loop Dynamics: Exponential Growth Example Customers Word of Mouth Sales Site Popularity Likelihood of Cross Listing and Listing on Search Engines Dynamic implications 20,000 15,000 10,000 5,000 Graph for Stock Time (M onth) Stock : Current

33 Causal Loop Dynamics: Goal Seeking (Balancing Loop) Treshold for Policy Dissatisfaction to Lead to Action Threshold Hunger to Motivate Eating Example: Food Ingested Dynamic behavior Hunger

34 Causal Loop Dynamics: Oscillation (Balancing Loop with Delay) Causal Structure Dynamic Behavior:

35 Growth and Plateau Loop structure: Reinforcing Loop Balancing Loop Customers Word of Mouth Sales Potential Customers Existing Users New Users Discovering Site Likelihood of Cross Listing and Listing on Search Engines Internet Users Yet to Discover Site Dynamic Behavior: 100,000 75,000 Graph for Customer From Tsai 50,000 25, Time (Month) Customer : Current

36 Regulatory Mechanisms

37 Perverse Incentives Under Stress

38 Elaborating Causal Loops Work Pressure Work Remaining Productivity Work Pressure Fatigue Work Remaining Productivity

39 Elaborating Causal Loops 2 Project Performance Managerial Desire to Blame Information Availability Quality of Management Decision Making Project Performance Managerial Desire to Blame Developer's Trust of Manager Managerial Trust of Developers Information Availability Quality of Management Decision Making

40 Exercise 1: Link & Loop Polarity Label the polarity of each link in this diagram Time per Download Population of Downloading Users What factor is missing? Bandwidth Available Per Connection Is the feedback positive or negative? Bandwidth Available to Server

41 Exercise 2: Unanticipated Side Effects Seeking modest investment in Blackberries for productivity enhancement Muddied by unanticipated side effects

42 Exercise 3: Link & Loop Polarity Create one or more causal loops relating Project Morale Project Turnover Workload Project delay Are these loops positive or negative? Do these loops all have the same time to kick in (time constants)?

43 One Set of Loops Developer Fatigue Morale Backlog of Work Resignations Team Productivity Extra Hiring Related Work Work per Team Member

44 Recall: Dealing with Symptoms vs. Causes Our focus is often on undesirable symptoms (high cost, schedule delay, poor quality) rather than on underlying causes Often a project is in severe trouble by the time these obvious (and easily quantifiable) symptoms appear Often choices of interventions fail to consider broader (and perhaps less quantifiable) effects of actions

45 A Consulting Case

46 Managerial Pressure Narrow mental model aims for this goal Unanticipated side effects push back vs. time savings & cause quality problems

47 New Hiring A Bigger Picture Familiarity of Workers with Codebase Fraction of Staff that is New to Project Training Needs Resignations Morale Project Lateness Work Accomplished per Day Managerial Pressure Multiplexing of Tasks Overtime Time for Bug Fix Task Coordination and Degree of Thought for Fixes Fatigue Pressure for "Quick and Dirty" Fixes Thoroughness of Testing Reliability of Bug Fixes Debugging Work to be Done Quality of Released Product Defects Resolution Rate Total Patent or Latent Defects New Defect Resolution Rate

48 Path Dependence/Network Effects & LockIn In the presence of positive feedback, can get lock in effects Similar early conditions result in divergent outcomes (instability) Example: Product largely in balance vs. continuously in turmoil

49 Unstable, Critical, and Subject to Lockin Software Quality Trust Respect Morale

50 Elaborating Causal Loop Diagrams: Most Basic Feedbacks

51 With Recovery (& Waning Immunity)

52 With Risk PerceptionDriven Behavioral Change

53 Public Health System Screening & Treatment Responses

54 and Vaccination As Well

55 Blowback: Perverse Evolutionary & Behavioural Feedbacks

56 Incorporating Some Determinants of Health

57 Structure as Shaping Behaviour System structure is defined by Stocks Flows Connections between them (yielding feedbacks) Nonlinearity: The behaviour of the whole is more than the sum of the behaviour of the parts Emergent behaviour would not be anticipated from simple behaviour of each piece in turn Stock and flow structure (including feedbacks) of a system determines the qualitative behaviour modes that the system can take on (parameters determine particulars) Changes to the feedback structure can change behaviour in fundamental ways

58 Causal Loop Structure: Dynamic Implications Each loop in a causal loop diagram is associated with qualitative dynamic behavior Most Common SingleLoop Modes of Dynamic Behavior Exponential growth Goal Seeking Adjustment Oscillation When composed, get novel behaviors due to shifting loop dominance Behaviour of system more than sum of parts e.g. Growth & Plateau, Boom & Bust, Lockin

59 Causal Loop Dynamics: Exponential Growth (First Order Reinforcing Loop) Examples # of Infectives # New Infections Weight Perceived as Normal Individual Target Weight Mean Weight in Population Dynamic implications # of Susceptibles

60 Causal Loop Dynamics: Goal Seeking (Balancing Loop) Treshold for Policy Dissatisfaction to Lead to Action Threshold Hunger to Motivate Eating Example: Food Ingested Dynamic behavior Hunger

61 Causal Loop Dynamics: Oscillation (Balancing Loop with Delay) Causal Structure Dynamic Behavior:

62 Growth and Plateau Loop structure: Reinforcing Loop Balancing Loop Customers Word of Mouth Sales Potential Customers Existing Users New Users Discovering Site Likelihood of Cross Listing and Listing on Search Engines Internet Users Yet to Discover Site Dynamic Behavior: 100,000 75,000 Graph for Customer From Tsai 50,000 25, Time (Month) Customer : Current

63 State of the System: Stocks ( Levels, State Variables, Compartments ) Stocks (Levels) represent accumulations These capture the state of the system These can be measured at one instant in time Stocks start with some initial value & are thereafter changed only by flows into & out of them There are no inputs that immediately change stocks Stocks are the source of delay in a system In a stock & flow diagram, shown as rectangles

64 Example Model: Stocks

65 The Critical Role of Stocks in Dynamics Stocks determine current state of system Stocks often provide the basis for making choices Stocks central to most disequilibria phenomena (buildup, decay) Lead to inertia Give rise to delays

66 State Changes: Flows ( Fluxes, Rates, Derivatives ) All changes to stocks occur via flows Always expressed per some unit time: If these flow into/out of a stock that keeps track of things of type X (e.g. persons), the rates are measured in X/(Time Unit) (e.g. persons/year, $/month, gallons/second) Typically measure over certain period of time (by considering accumulated quantity over a period of time) e.g. Incidence Rates is calculated by accumulating people over a year, revenue is $/Time, water flow is litres/minute Can be estimated for any point in time

67 Example Model: Flows

68 Key Component: Stock & Flow Flow Stock Flow Stock Stocks Determine Flows Flows Dictate Change in Stocks

69 Auxiliary Variables Auxiliary variables are convenience names we give to concepts that can be defined in terms of expressions involving stocks/flows at current time Adding or eliminating an auxiliary variable does not change the mathematical structure of the system Critical for model transparency Can be reused at many places References to auxiliary variables prevents need for modeler to think about all of details of definition Enhanced modifiability: Single place to define Convenient for reporting (graphing, tables) & analyzing model dynamics

70 Example Model: Auxiliary Variables

71 Constants & Time Series Parameters For similar reasons to auxiliary variables, we give names to Model constants Time series

72 Example Model: Parameters

73 xample System Structure, Illustrating Feedbacks

74 Handling Heterogeneity Step 1: Test (via scenarios) if heterogeneity is likely to have substantive impact on results Step 2: Where necessary, disaggregate model according to heterogeneity Small model: Duplicate stocks Larger model: Subscripting Step 3: Express intergroup contact patterns via mixing & preference matrices

75 <Susceptible (X16m)> <Force of Infection (lambda16m)> <Infected (Y16m)> <Susceptible (X16fb)> <Infected (Y16fb)> new male infections infective years males Cumulative male infective years new female infections <Force of Infection (lambda16fb)> infective years females Cumulative number of males with infections <Female Mortality Rate> <Male Mortality Rate> Cumulative number of female with infections YearsInAgeCategory (band i) Mortality Rate by Sex Age SmokingStatus <Population Growth Rate q> <Babies Born by Sex> Male Mortality Rate Cumulative female infective years <Babies Born by Sex> Female Births Female Mortality Rate Male Births Mean Time Until Age Progression by Sex SmokingStatus AgeCategory Female Children 0 to 4 Male Children 0 to 4 Deaths of Male Children 0 to 4 Mortality Rates for Children 0 to 4 by Sex Male Aging to Age 5 Mean Time Until Age Progression for Females Years in Years 0 to 4 <Mean Time Until Age Progression for Females> Initial fraction of males vaccinated Aging of vaccinated males () Male Children 5 to 9 Initial Children 0 to 4 by Sex Initial Children 5 to 9 by Sex Deaths of Female Children 0 to 4 Female Aging to Age 5 <Mortality Rates for Children 0 to 4 by Sex> Mean Time Until Age Progression for Males Deaths of Male Children 5 to 9 Mortality Rates for Children 5 to 9 by Sex Aging of vaccinated females () <muscc death> <mutciss death> <Total population of females by SmokingStatus SexualActivityGroup AgeCategory CervicalScreeningCategory> Female Children 5 to 9 Male Aging to Age 10 Years in Years 5 to 9 <muccl death> <muicin3 death> <muicis1 death> <muicis2 death> <mutcins death> Fraction of male population vaccinated Vaccinated (V16m) Mean Duration of Sexual Activity <mucin1 death> muvm death Male Children 10 to 11 <muccr death> <muicin2 death> <mucin2 death> Fraction of female population vaccinated Vaccinated (V16fb) Female Aging to Age 10 <Total population of males by AgeCategory SmokingStatus muvfb death SexualActivityGroup> Deaths of Male Children 10 to 11 Mortality Rates for Children 10 to 11 by Initial Children 10 to 11 by Sex <Years in Years 0 to 4> <Years in Years Deaths of Female Children 5 to 9 <Mortality Rates for Children 5 to 9 by Sex> Sex 5 to 9> <Male Mortality Rate> <muvfb death> Fraction of Population in Sexual Activity Category Initial population of males (Nm) <Female Mortality Rate> Initial fraction of females vaccinated Recovered from Treated & Infected Carcinoma s2 Annual likelihood of vaccination for males <Mean Time Until Age Progression for Males> <muccd death> <muicin1 death> <mucin3 death> Female Total Deaths <mudccl death> Fraction of Females never undergoing cervical screening Fraction of Females entering cervical screening category (tadpole b) category (tadpole b) Vaccination females Female Children 10 to 11 Annual likelihood of vaccination for females muzfb death Vaccination males Male new Entrants into Sexually Active Population Total Male new entrants per year Years in Years 10 to 11 (cap betam) <Mean Time Until Age Progression for Females> Rate of waning from vaccine protection (sigmavm) Aging of suceptible males () <mudcis1 death> <mucis1 death> Initial Population by Sex SmokingStatus AgeCategory Initial Population by Sex SmokingStatus SexualActivityCategory and AgeCategory Initial population females (Nf) by AgeCategory SmokingStatus SexualActivityGroup CervicalScreeningCategory Deaths of Female Children 10 to 11 Aging of immune females () <mudccr death> <mudcis2 death> Initial population females (Nf) by AgeCategory SmokingStatus SexualActivityGroup <Mortality Rates for Children 10 to 11 by Sex> <Female Mortality Rate> <Regression CIN3 to Infected Rate (tau16fbs3)> <Rate of Recovery from infection wtih HPV (gamma16f)> <Fraction of Population in Sexual Activity Category> <Fraction of children that initiate smoking by 12 years old by Sex> Rate of waning from vaccine protection (sigmavf) <YearsInAgeCategory (band i)> <mucis2 death> <muzfb death> <mudcin1 death> Recovered from Detected CIN3 waning vaccination (m) Susceptible (X16m) <mudcin3 death> <mudcin2 death> Recovered from Treated & Infected Carcinoma s1 muxm death <mudccd death> <muyfb death> waning vaccination (f) Immune (Z16fb) <muxfb death> Recovery (f) <Fraction of CINs regressions clearing CIN that also clear infection (gamma bar16f)> <Mean Time Until Age Progression for Females> <Force of Infection (lambda16m)> <Male Mortality Rate> Recovered from Treated & Infected CIN3 <Female Mortality Rate> Incidence (m) <Mean Time Until Age Progression for Females> Mean duration of acute HPV infection females <Female Total Deaths> <Mean Duration of Sexual Activity> <Rate of Recovery from infection wtih HPV (gamma16f)> <Female Mortality Rate> <Mean Time Until Age Progression for Females> Aging of detected local () Aging of infected males () <Mean Time Until Age Progression for Males> <Years in Years 10 to 11> <Regression CIN3 to Infected Rate (tau16fbs3)> Recovered from Undetected CIN3 <Fraction of CINs regressions clearing CIN that also clear infection (gamma bar16f)> mudccl death <Fraction of Population in Sexual Activity Category> <Fraction of Females entering cervical screening category (tadpole b)> <Female Mortality Rate> Aging of susceptible females () Aging of undetected carinoma s2 () Aging of undetected local () Total Female new Entrants per Year <Mean Time Until Age Progression for Females> mucis2 death Regression from Treated & Infected CIN3 to Undetected CIN3 Reoccurence of CIN3 (thetars3) muccl death Per Contact Risk of Infection (betam) Infected (Y16m) <Female Mortality Rate> Progression from Undetected Local to Detected Local Undetected Local to Detected Local Rate (upsilonl) muym death <Male Mortality Rate> Total population of males <Infected (Y16fb)> Fraction of children that initiate smoking by 12 years old by Sex Regression from Detected CIN3 to Infected <Mean Time Until Age Progression for Females> Detected Local (DCCL16fb) Mean duration of acute HPV infection in males Total population of males by SmokingStatus <Fractional Prevalence Males> Female new Entrants flow Aging of undetected carcinoma s1 () Susceptible (X16fb) <Female Mortality Rate> Recovered from Undetected CIN1 Per Contact Risk of Infection (betaf) <Female Mortality Rate> Regression CIN3 to Infected Rate (tau16fbs3) Undetected Carcinoma s2 (CIS216fb) Progression from Undetected Carcinoma s2 to Undetected Local Undetected Local (CCL16fb) Progression from Detected Local to Cancer Survivors muxfb death Progression from Immune to Susceptible (f) Detected Local Cancer Survivor Rate (omegal) Recovery (m) Total population by SmokingStatus Total population of males by SmokingStatus SexualActivityGroup Incidence Rate of waning natural immunity (sigmazf) Aging of undetected CIN3 () <Undetected CIS1 Rate (pi16fs4)> mucin3 death Recovered from Detected CIN1 Undetected Carcinoma s1 (CIS116fb) Undetected CIS1 Rate (pi16fs4) Immune (Z16m) Infected (Y16fb) Progression from Infected to Undetected CIN3 Undetected CIN3 Rate (theta16fbs3) Undetected CIN3 (CIN316fb) Progression from Undetected CIN3 to Undetected Carcinoma s1 Progression from Undetected Carcinoma s1 to Undetected Carcinoma s2 Progression from Detected Carcinoma s1 to Undetected Progression from Undetected Local to Cancer Death Aging of immune males() Total population of males by AgeCategory SmokingStatus muyfb death Regression from Undetected CIN3 to Infected Carcinoma s2 SexualActivityGroup <Immune (Z16m)> <Mean Time Until Age Progression for Females> <Force of Infection (lambda16fb)> <Mean Time Until Age Progression for Females> Aging of detected carinoma s1 () <Mean Time Until Age Progression for Males> <Total population of females by SmokingStatus> Aging of infected females () <Mean Time Until Age Progression for Females> Undetected CIS2 Rate (pi16fbs5) LCC death rate (chil) <Susceptible (X16m)> <Detected CIS2 Rate (kappa16fbis5)> Undetected CIN3 Rate (pi16fbs3) Detected Carcinoma s1 (DCIS116fb) Progession from Detected Local to Cancer Death Reoccurence of CIS2 (thetars5) Recovered from Treated & Infected CIN1 Undetected CIN1 Rate (theta16fbs1) Progression from Undetected Carcinoma s1 to Detected Carcinoma s1 mudcis1 death Undetected CIN2 Rate (theta16fbs2) Regression CIN3 to CIN1 Rate (tau16fbs31) Undetected CIN2 Rate (pi16fbs2) Treated and Cured TCISs (TCISs16fb) Progression from Undetected Carcinoma s2 to Detected Carcinoma s2 Cure Rate of CIS s2 (capgamma s5) Progression from Infected to Undetected CIN1 Progression from Undetected CIN2 to Undetected CIN3 % CIS s1 infected after treatment (psis4) Detected CIN1 Rate (kappa16fbis1) Detected CIN2 Rate (kappa16fbis2) Detected CIN3 Rate (kappa16fbis3) Detected CIS1 Rate (kappa16fbis4) Detected CIS2 Rate (kappa16fbis5) Regression CIN1 to Infected Rate (tau16fbs1) Regression from Undetected CIN3 to Undetected CIN2 Regression from Undetected CIN3 to Undetected CIN1 Regression CIN2 to Infected Rate (tau16fbs2) Regression from Undetected CIN2 to Infected Progression from Undetected CIN3 to Detected CIN3 Progression from Detected Carcinoma s1 to Treated & Cured TCISs Regression from Treated & Infected Carcinoma s2 to Undetected Carcinoma s2 Progression from Detected Carcinoma s2 to Undetected Local <Mean Time Until Age Progression for Females> <Mean Time Until Age Progression for Females> Progression from Undetected Local to Undetected Regional Undetected Local to Undetected Regional <LCC death rate (chil)> Rate (pil) muscc death muzm death <Infected (Y16m)> <Vaccinated (V16m)> Fraction of CINs regressions clearing CIN that also clear infection (gamma bar16f) <Mean Time Until Age Progression for Females> Initial Infected Aging of detected carcinoma s2 () Aging of undetected regional () Aging of cancer survivors() <Male Mortality Rate> Liquidbased cytology sensitivity (papsn s) for CIN1 Fraction of Initial Population that Starts Infective Liquidbased cytology sensitivity (papsn s) for CIN2 CIN3 CIS1 CIS2 <Mean Time Until Age Progression for Females> Regression from Undetected CIN1 to Infected Progression from Infected to Undetected CIN2 Progression from Detected CIN3 to Undetected RCC death rate (chir) <Female Mortality Rate> Carcinoma s1 mucis1 death <Mean Time Until Age Progression for Females> <muvm death> Aging of undetected CIN1 () <Mean Time Until Age Progression for Females> Aging of undetected CIN2 () Aging of detected CIN3 () mudcin3 death <Detected CIS1 Rate (kappa16fbis4)> <Detected CIS1 Rate (kappa16fbis4)> <Female Mortality Rate> Regression CIN3 to CIN2 Rate (tau16fbs32) Cure Rate of CIS s1 (capgamma s4) Progression from Detected Carcinoma s2 to Treated & Cured TCISs Detected Carcinoma s2 (DCIS216fb) Undetected Regional (CCR16fb) Progression from Undetected Regional to Cancer Death Cancer Survivors (SCC) Progression from Immune to Susceptible <muzm death> <Regression CIN1 to Infected Rate (tau16fbs1)> <Mean Time Until Age Progression for Females> Aging of treated and infected CIN3 () (m) <Detected CIN3 Rate (kappa16fbis3)> <Female Mortality Rate> Cancer Death Undetected CIN1 (CIN116fb) Regression from Undetected CIN2 to Undetected CIN1 Undetected CIN2 (CIN216fb) mucin2 death Recovered from Undetected CIN2 <Female Mortality Rate> Progression from Detected Carcinoma s1 to Treated & Infected Carcinoma s1 mutciss death Male Total Deaths <muym death> Rate of Recovery from infection wtih HPV muccr death Rate of waning natural immunity (sigmazm) (gamma16f) <Female Mortality Rate> Detected CIN3 (DCIN316fb) Progression from Undetected CIN1 to Undetected CIN2 Regression CIN2 to CIN1 Rate (tau16fbs21) Treated and Infected CIN3 (ICIN316fb) muicin3 death Aging of treated and cured TCISs () Cancer Death by SmokingStatus and <Female Mortality Rate> % CIS s2 infected after treatment (psis5) <Female Mortality Rate> Undetected Regional to Undetected Distant Rate (pir) CervicalScreeningCategory <Cancer Death by AgeCategory SmokingStatus and CervicalScreeningCategory> Routine Screening coverage by Age and Cervical Screening Category (cover i) mucin1 death <Mean Time Until Age Progression for Females> <Regression CIN1 to Infected Rate Progression from Undetected Regional to Undetected Distant Undetected Regional to Detected Regional Rate (upsilonr) <muxm death> (tau16fbs1)> mudcis2 death Progression from Undetected Regional to Detected Regional Cancer Death by CervicalScreeningCategory <DCC death rate (chid)> Progression from Detected Distant to Cancer Survivors Progression from Undetected CIN1 to Detected CIN1 Undetected CIN1 Rate (pi16fbs1) Progression from Undetected CIN2 to Detected CIN2 Progression from Detected CIN1 to Undetected CIN2 Recovered from Detected CIN2 Regression from Detected CIN3 to Detected CIN2 Progression from Detected CIN3 to Treated & Infected CIN3 Progression from Detected Regional to Cancer Death <Female Mortality Rate> <RCC death rate (chir)> DCC death rate (chid) Progression from Detected Distant to Cancer Death Aging of detected CIN1 () Regression from Detected CIN1 to Infected <Detected CIN2 Rate Aging of (kappa16fbis2)> detected CIN2 () <Mean Time Until Age Progression for Females> Aging of undetected distant () Cancer Death by SmokingStatus <Detected CIN1 Rate (kappa16fbis1)> <Mean Time Until Age Progression for Females> <Mean Time Until Age Progression for Females> <Regression CIN3 to CIN2 Rate (tau16fbs32)> <Female Mortality Rate> <Female Mortality Rate> Progression from Detected CIN3 to Treated & Cured TCINs % CIN3 infected after treatment (psis3) Detected CIN1 (DCIN116fb) Detected CIN2 (DCIN216fb) Cure Rate of CIN3 (capgamma s3) Regression from Treated & Infected Carcinoma s1 to Undetected Carcinoma s1 Treated and Infected Carcinoma s1 (ICIS116fb) Progression from Detected Carcinoma s2 to Treated & Infected Carcinoma s2 <% CIS s2 infected after treatment (psis5)> Cancer Death Total over Population Progression from Undetected Distant to Cancer Death Aging of detected regional () <Mean Time Until Age Progression for Females> Detected Distant Cancer Survivor Rate (omegad) mudcin1 death Regression from Detected CIN2 to Infected <Cure Rate of CIS s2 (capgamma s5)> Regression from Detected CIN2 to Detected CIN1 <Fraction of CINs regressions clearing CIN that also clear infection (gamma bar16f)> Aging of treated and infected carcinoma s1() Undetected Distant (CCD16fb) <Regression CIN2 to Infected Rate (tau16fbs2)> Recurrence of CIN1 (thetars1) % CIN1 infected after treament (psis1) Progression from Detected CIN1 to Treated & Infected CIN1 Treated and Cured TCINs (TCINs16fb) Reoccurence of CIS1 (thetars4) <Mean Time Until Age Progression for Females> Aging of detected distant () <Total Infectives (f) by Age SmokingStatus Sexual Activity Group and Screening Category> <Regression CIN2 to Infected Rate (tau16fbs2)> Regression from Treated & Infected CIN1 to Undetected CIN1 Cure Rate of CIN1 (capgammas1) Cure Rate of CIN2 (capgamma s2) <Cure Rate of CIN2 (capgamma s2)> Treated and Infected Carcinoma s2 (ICIS216fb) Recurrence of CIN2 (theta rs2) % CIN2 infected after treatment (psis2) Progression from Detected CIN2 to Treated & Infected CIN2 Regression from Treated & Infected CIN2 to Undetected CIN2 Progression from Detected CIN2 to Treated & Cured TCINs Detected Regional (DCCR16fb) Detected Distant (DCCD16fb) mudccd death <Total population of females by SmokingStatus SexualActivityGroup AgeCategory CervicalScreeningCategory> <Total population of males by AgeCategory SmokingStatus SexualActivityGroup> <Regression CIN2 to CIN1 Rate (tau16fbs21)> Fractional Prevalence Males mudcin2 death muicis1 death muccd death mutcins death <Female Mortality Rate> <Female Mortality Rate> muicis2 death <Female Mortality Rate> Progression from Detected Regional to Cancer Survivors Fractional Prevalence Females Total Infectives (f) by SmokingStatus Sexual Activity Group Age <Detected CIN1 (DCIN116fb)> <Detected CIN2 (DCIN216fb)> <Detected CIN3 (DCIN316fb)> <Detected Carcinoma s1 (DCIS116fb)> <Detected Carcinoma s2 (DCIS216fb)> <Detected Local (DCCL16fb)> <Detected Regional (DCCR16fb)> <Detected Distant (DCCD16fb)> Aging of treated and infected CIN1 <Mean Time Until Age Progression for Females> <% CIN2 infected after treatment (psis2)> <Female Mortality Rate> <Female Mortality Rate> <Female Mortality Rate> <Female Mortality Rate> mudccr death Total Infectives (f) by Age Total Infectives (f) by SmokingStatus Age <Cancer Survivors (SCC)> Aging of treated and infected CIN2 () Detected Regional Cancer Survivors Rate (omegar) <Undetected CIN3 (CIN316fb)> <Mean Time Until Age Progression for Females> <Undetected CIN1 (CIN116fb)> Treated and Infected CIN1 (ICIN116fb) <Fraction of CINs regressions clearing CIN that also clear infection (gamma bar16f)> <Mean Time Until Age Progression for Females> Aging of treated and cured TCINs () Fractional Prevalence by Sex SmokingStatus Sexual Activity Group and Age Fractional Prevalence Females Across All Screening Groups <Total Initial Partnership Changes for Sex and Age Category> Age Category Mixing Parameter Epsilon 1 Age Category Identity Matrix small delta ij Total Infectives (f) by Age SmokingStatus Sexual Activity Group and Screening Category <% CIN1 infected after treament (psis1)> <Cure Rate of CIN1 (capgammas1)> Treated and Infected CIN2 (ICIN216fb) <Female Mortality Rate> Recovered from Treated & Infected CIN2 Aging of treated and infected carcinoma s2 () Undetected Distant to Detected Distant Rate (upsilond) Progression from Undetected Distant to Detected Distant <Fraction of Total Initial Partnership Changes for Sex Occuring with Activity Category Identity Matrix small delta lm Age Category Mixing Parameter Epsilon 2 Total Infectives (f) by SmokingStatus Sexual Activity Group Contacts with Infectives between People of Potentially Different SmokingStatus Contacts with Infectives between People of Potentially Different SmokingStatus and Ages <Undetected CIN2 (CIN216fb)> muicin1 death <Rate of Recovery from infection wtih HPV (gamma16f)> <Mean Time Until Age Progression for Females> Contacts with Infectives between People of Potentially Different SmokingStatus Sexual Activity Groups and Ages People in a Given Sexual Activity Group> SmokingStatus Identity Matrix small delta ef <Undetected Carcinoma s1 (CIS116fb)> <Infected (Y16fb)> Fraction of Total Initial Partnership Changes for Sex Occuring with People in a Given Age Category Fraction of Contacts by someone of Age Category and Sex to assume that SmokingStatus Mixing Parameter Epsilon 3 (Level of Nonassortivity in mixing) take place with people of each Age Category Total Infectives (f) by SmokingStatus Progression from Detected CIN1 to Treated & Cured TCINs muicin2 death Contacts with Infectives for Person of Given Sex SmokingStatus Sexual Activity Group and Age Fraction of Total Initial Partnership Changes for Sex Occuring with People in a Given Sexual Activity Group Fraction of Contacts by someone of a specific Sexual Activity Group and Sex to assume that take place with people of each Sexual Activity Group Fraction of Total Initial Partnership Changes for Sex Occuring with People in a Given SmokingStatus Group Fraction of Contacts by someone of a specific SmokingStatus and Sex to assume that take place with people of each SmokingStatus <Undetected Carcinoma s2 (CIS216fb)> <Undetected Regional (CCR16fb)> <Undetected Distant (CCD16fb)> <Female Mortality Rate> Force of Infection for Person of Given Sex SmokingStatus Sexual Activity Group and Age Total Infectives (f) Regression from Detected CIN3 to Detected CIN1 <Treated and Cured TCINs (TCINs16fb)> <Undetected Local (CCL16fb)> <Per Contact Risk of Infection (betam)> Fraction of Total Initial Partnership Changes for Activity Group Total Initial Partnership Changes for Sex Fractional Prevalence Among Females by SmokingStatus <Treated and Cured TCISs (TCISs16fb)> <Treated and Infected Carcinoma s1 (ICIS116fb)> <Treated and Infected Carcinoma s2 (ICIS216fb)> <Treated and Infected CIN1 (ICIN116fb)> <Regression CIN3 to CIN1 Rate (tau16fbs31)> Transmission Probability Beta Force of Infection (lambda16fb) Force of Infection (lambda16m) Relative Partner Acquisition Rate for SmokingStatus Relative Partner Acquisition Rate for Sexual Activity Category (pc i) <Treated and Infected CIN2 (ICIN216fb)> <Treated and Infected CIN3 (ICIN316fb)> <Per Contact Risk of Infection (betaf)> Is Age Category among Ages 18 through 59 Total Initial Partnership Changes for Sex and Activity Group Capital B Mixing Matrix Elements rho <Fraction of Total Initial Partnership Changes for Sex Occuring with People in a Given Sexual Activity Group> Fractional Prevalence Among Females Relative Partner Acquisition Rate for Age Category (pa i) <Sexual Partner Change Rate c sub keli> <Total population of females by SmokingStatus SexualActivityGroup AgeCategory CervicalScreeningCategory> Total population of females Initial Total Population Weighted by pc and pa by Sex SmokingStatus and Age Sexual Partner Change Rate c sub keli for Ages 18 through 59 Total Initial Partnership Changes for Sex and SmokingStatus <Total Infectives (f) by Age> Total population of females by SmokingStatus Mean partner acquisition rate for age category (c j Sexual Partner Change Rate c sub keli Adjusted Sexual Partner Change Rate ckeflmij Theta bar) Sexual Partner Change Rate c sub keli for SingleAge Group Categories Total population of females by SmokingStatus Age and Sexual Activity Group Fractional Prevalence of Infection in Females by Age Total population of females by SmokingStatus SexualActivityGroup Initial Total Population by Sex SmokingStatus Age and Sexual Activity Group Total Initial Partnership Changes for Sex and Activity <Treated and Infected CIN1 (ICIN116fb)> <Treated and Infected CIN2 (ICIN216fb)> Group and Age Category Total Population by Sex SmokingStatus Age and Sexual Activity Group <Total population of males by AgeCategory SmokingStatus SexualActivityGroup> Total Initial Partnership Changes for Sex and SmokingStatus and Activity Group Total Population of females by AgeCategory Total Population of females by SmokingStatus AgeCategory Total population of females by SmokingStatus SexualActivityGroup AgeCategory <Treated and Cured TCISs (TCISs16fb)> <Treated and Cured TCINs (TCINs16fb)> <Treated and Infected Carcinoma s2 <Cancer Survivors (SCC)> (ICIS216fb)> Total Initial Partnership Changes for Sex and SmokingStatus and Activity Group and Age Category <Total population of males> <Total population of females> <Detected Distant (DCCD16fb)> Initial Total Population by Sex SmokingStatus and Age Fertility Rate per 1000 for SmokingStatus Age Category Fertility Rate per Capita for SmokingStatus Age Category Babies Born to Mother in SmokingStatus and AgeCategory <Treated and Infected Carcinoma s1 (ICIS116fb)> <Treated and Infected CIN3 (ICIN316fb)> <Undetected Distant (CCD16fb)> <Vaccinated (V16fb)> <Immune (Z16fb)> Total population Babies Born <Detected Carcinoma s1 (DCIS116fb)> <Undetected Carcinoma s1 (CIS116fb)> Total population of females by SmokingStatus SexualActivityGroup AgeCategory CervicalScreeningCategory <Susceptible (X16fb)> Population Growth Rate q <Total Infectives (f) by Age> <Undetected Carcinoma s2 (CIS216fb)> <Undetected Regional (CCR16fb)> <Fraction of Babies who are of a given sex> Babies Born by Sex <Detected Carcinoma s2 (DCIS216fb)> <Detected CIN1 (DCIN116fb)> <Detected CIN2 (DCIN216fb)> <Detected CIN3 (DCIN316fb)> <Detected Regional (DCCR16fb)> <Infected (Y16fb)> <Undetected CIN1 (CIN116fb)> <Undetected CIN2 (CIN216fb)> <Undetected CIN3 (CIN316fb)> <Undetected Local (CCL16fb)> <Detected Local (DCCL16fb)> A Subscripted Male Population Model Mixing Matrix Female Population Male Population Cu Totals Cumulative Counts Female Population Stratified by: 17 age categories 2 cervical screen. groups 3 sexual activity groups 2 smoking statuses 2 sexes Each visual stock represents 408 distinct underlying stocks

76 Example Mixing Preferences

77 Sources for Parameter Estimates Surveillance data Controlled trials Outbreak data Clinical reports data Intervention outcomes studies Calibration to historic data Expert judgement Systematic reviews Anderson & May

78 Introduction of Parameter Estimates Frequently System Dynamics models will provide much more detail on networks of factors shaping these rates, but ultimately there will be constants requiring specification Annual Likelihood of Becoming Diabetic <Annual Likelihood of NonDiabetes Mortality for Asymptomatic Population> <Annual at Risk Births> undx uncomplicated dying other causes <Annual Not at Risk Births> Annualized Mortality Rate for obese population Being Born Non Obese Non Obese General Population Annual Likelihood of Becoming Obese Becoming Obese Being Born At Risk Obese General Population Obese Mortality Developing Diabetes Undx Prediabetics Recovering Annual Likelihood of Undx Prediabetic Recovery Dx Prediabetics Recovering Undx Prediabetic Popn Diagnosis of prediabetics Dx Prediabetic Popn Annualized Probability Density of prediabetic recongnition Annual Likelihood of Dx Prediabetic Recovery NonObese Mortality Annual Mortality Rate for non obese population Annual Likelihood of NonDiabetes Mortality for dx uncomplicated dying otehr causes

79 Scenarios for Understanding How Does X affect System

80 Single Model Matches Many Data Sources one of

81 Example Aggregate Model Structure Population Size Immigration Rate Contacts per Susceptible Per Contact Risk of Infection Fractional Prevalence Average Duration of Infectiousness Immigration Susceptible Incidence Infective Recovery Recovered

82 Mathematical Notation M Immigration Rate Immigration of Susceptibles Susceptible Per Contact Risk of Contacts per Infection Fractional Susceptible Prevalence c Incidence Population Size Absolute Prevalence Mean Time with Disease S I R N Recovery Recovered

83 Underlying (Ordinary) Differential Equations I S M c S N I I c S N I R I

84 Model Mathematical Analysis System Linearization (Jacobian) FixedPoint Criteria I S c ˆ S R 0 N I ˆ I I c S 0 N I h I R R 0 I h State space diagram (reasoning about many scenarios at once) Eigenvalues (e.g. for stability analysis around fixedpoint)

85 Some Uses of Formal Approaches Explaining observed behavior patterns Identifying possible behavior modes over a wide variety of possible scenarios (e.g. via eigenspace & phase plane analysis) Identifying how behavior depends on parameters (stability, location of equilibria) Creating selfcorrecting models (via control theory) Formal calibration methods

86 Feedbacks Driving Infectious Disease Dynamics Contacts between Susceptibles and Infectives Susceptibles Infectives New Infections New Recoveries

87 Example Dynamics of SIR Model (No Births or Deaths) 2,000 people 600 people 10,000 people SIR Example 1,500 people 450 people 9,500 people 1,000 people 300 people 9,000 people 500 people 150 people 8,500 people 0 people 0 people 8,000 people Time (days) Susceptible Population S : SIR example Infectious Population I : SIR example Recovered Population R : SIR example people people people

88 Shifting Feedback Dominance 2,000 people 600 people 10,000 people 1,500 people 450 people 9,500 people Contacts between Susceptibles and Infectives Susceptibles Infectives New Infections SIR Example 1,000 people 300 people 9,000 people 500 people 150 people 8,500 people 0 people 0 people 8,000 people Contacts between Susceptibles and Infectives Susceptibles Infectives New Recoveries New Infections New Recoveries Contacts between Susceptibles and Infectives Susceptibles Infectives New Recoveries Time (days) New Infections Susceptible Population S : SIR example Infectious Population I : SIR example Recovered Population R : SIR example people people people

89 Dynamic Uncertainty: Stochastic Processes (Stochastic Differential Equations) Baseline 50% 60% 70% 80% 90% 95% 98% 100% Average Variable Cost per Cubic Meter

90 Stakeholder Engagement with Created Models Team Meetings Mabry, 2009, Simulating the Dynamics of Cardiovascular Health and Related Risk Factors

91 Varied Applications of System Dynamics Aggregate populationlevel models Stratified models Models of an individual Models of interactions of two or more individuals Stochastic models

92 Key TakeHome Messages on SD Focuses on feedbacks as the fundamental shapers of dynamics Models are consciously specific to purpose Includes both qualitative & quantitative components Offers strong stakeholder focus Group model building Stakeholder learning laboratories Can be applied at diverse levels of granularity Department of Computer Science Models admit to formal reasoning & analysis

93 System Science Methodologies: Highly Complementary No one system science methodology offers a replacement for the others Significant synergies can be secured by using combinations of methodologies to address the same problem As crosschecks on understanding where two or more can be applied Exploiting competitive advantages

94 MultiFramework Modeling We have found the use of multiple frameworks most effective Coevolving multiple models for Crossvalidation Asking different sorts of questions Within a single model (cf Multiscale modelling) Critical that dynamic models leverage with nondynamic modeling tools Decision trees Game theory Biostatistical analyses

95 Multiple Modeling Types System Dynamics Deriving calibrated parameter estimates for lowlevel model Focusing AB exploration Inspiring key initial structure of agentbased models Diagramming out highlevel drivers of behaviour Description of continuous individuallevel evolution Agent Based Modeling Social Network Analysis

96 Network Embedded Individuals <Population Size> <Population Size> Uninfected Cell Replentishment Rate Uninfected Cell Replentishment Mean Uninfected Cells Uninfected Cells 1 Person Uninfected Cell death Mean Viral Load Likelihood Density of Infection by Single Virion New Cell Infections Mean Uninfected Cell Lifetime Virion Production From Infected Cells Infected Cells Infected Cell Death Virus Load Mean Infected Cell Lifetime Virion Production Rate if Non Quantized Infection infected cell death by CTLs Virion Clearance Virion Production Rate Per Contact Virions Rate Mean Infected Cells Mean Virion Lifetime Mean of Viral Load of Neighbors Per Infected CellVirion Production Rate <Population Size> rate which infected cells are killed by CTLs CTL responsiveness immune response to infected cells CTLs CTL turnover Mean CTL lifespan