Epidemic Modeling with Discrete Space Scheduled Walkers: Possible Extensions to HIV/AIDS

Transcription

1 Epidemic Modeling with Discrete Space Scheduled Walkers: Possible Extensions to HIV/AIDS 2008 ICSEng Maciej Borkowski Blake W. Podaima Robert D. McLeod Internet Innovation Centre (IIC) Dept. Electrical and Computer Engineering University of Manitoba IIC, July 2008 Internet Innovation Center

2 Overview Part One: Motivation The Model Where, Who, When, What Implementation Demonstration Questions Part Two: Limitations Related Work Possible Extensions Internet Innovation Center 1

3 Motivation Response to a Programming Challenge: General Interests in Complex Systems Internet Innovation Center 2

4 BSERC: Loose Specification for Epidemic Modeling Basis idea: Data mine where possible the basic tenets of people-people interactions. Topology: Data mined from maps Behaviour: Data mined from demographics Our approach develops models based on real network topologies and scheduled walkers. The goal of the research is to shed additional light on the problems associated with very complicated phenomena through data-driven modeling and simulation. Internet Innovation Center 3

5 Epidemiology Disease modeling of a pandemic-proportion epidemic is an important area of study. There are widely-held beliefs that a local disease epidemic or global pandemic in the general population is overdue. This idea is derived from analysis of previous epidemics and catastrophes that puncture the equilibrium (the black swan phenomenon). Internet Innovation Center 4

6 The Model Data mining is a common theme in modern information technology: Analytical methods may not exist or are overly complex. Data does exist and can be readily extracted. Statistical methods can now more easily deal with the vast amount of data that is available. Our work is an attempt to help promote data-driven epidemic simulation and modeling: Where data is available we demonstrate its utility, where unavailable we demonstrate how it would be utilized. Unavailable data refers to practical or political limitations on access, rather than technical or theoretical availability. Internet Innovation Center 5

7 Where One of the first things needed is topology data, or physical network data that is, where are we attempting to apply the study of epidemic spread? These are primarily real places, such as homes, institutions, businesses, industry, schools, hospitals, and transport, within cities of all types. Much of this information in mineable, more so now than ever. Internet Innovation Center 6

8 Topological Data Sources Google Earth with Overlays Google Maps Internet Innovation Center 7

9 Who Of similar importance to location (where), is the agents (who) are being infected. This is data that is generally technically available but practically unavailable. (An approach) Collaborate with organizations that house and take census data. Data mining these sources are not technical issues but rather political or policy issues and require the will of government to make this data available for simulations such as these. Our model attempts to illustrate how the data would be used if available. Internet Innovation Center 8

10 When An agents schedule (when) is also of critical importance. This data is more typically inferred rather than explicitly available, but as we are primarily creatures of habit reasonable assumptions can be made. Many of us operate on fairly routine weekday schedules, punctuated by more flexible weekends. As such, this scheduled data (for the sake of the simulation) can be associated with an agent, modified by slight variations in arrival and departure times. Internet Innovation Center 9

11 When For example, a school-aged child spends the period between 8:00 am and 4:00 pm at a local school with a reasonably high probability. Typically, they would be home at 4:00 pm, spending perhaps some of an evening at a community centre or sports facility. The weekend schedule likely includes periods at home and periods locally within the neighborhood. While this profile retains a large degree of simplicity, it is likely sufficient to represent the role of schedule in our simulation. Internet Innovation Center 10

12 What In addition to where, who, and when, we also need to address what. The what here is typically a disease, either bacterial or viral, communicated with an associated probability of contraction when in contact with an infectious agent. These parameters are adjustable and represent an aspect of the current simulation with the greatest uncertainty in terms of their validity, and could benefit from collaboration or input from an epidemiologist. Internet Innovation Center 11

13 Extensions Each of these simulation aspects (where, who, when) can be extended to include a multitude of cities, weakly coupled by institutions such planes, trains, automobiles, supporting agent movement. In addition, seasonal variation has also be incorporated, accounting for seasonal prevalence of particular diseases (e.g., influenza). Behaviour: Low mobility when sick or getting sick. Internet Innovation Center 12

14 Implementation Based on the model as described above, it should be clear that our underlying simulation model is that of a Discrete-Space Scheduled Walker (DSSW), in contrast to other models that are more traditionally based on random or Brownian walkers on artificial topologies. We attempt to capture the most important aspects of real-people networks, incorporating (by construction) notions such as small world networks. Internet Innovation Center 13

15 Object Model Internet Innovation Center 14

16 Where - Topological Data Sources This is starting point for locating various institutions. Winnipeg is used to illustrate the use of map information as input for generating our underlying topology of institutions, where people (agents) potentially come into contact and infect one another. Business Homes Mall Transportation Etc. School Internet Innovation Center 15

17 Implementation: Where Object Template: Institution Properties: Geographical location Probability of contracting a disease Special types: Home Bus Car Φ i Internet Innovation Center 16

18 Implementation: Who Object Template: Agent Properties: Probability of contracting a disease Probability of using a car Working institutions Leisure Institutions Working schedule Leisure Schedule Part of: Family, Community Λ j Internet Innovation Center 17

19 Who A population in a city is generated based on types and locations of families: A family is a group of agents living in one home. Each family type can consist of any number of various agents. Each family has an assigned percentage that sets the percentage of such families in the entire population of a given city. The actual number of agents in a city is a resultant of creating homes with families of a given type. Each home can be occupied by only one family. The geographical location of families within a city is random. Internet Innovation Center 18

20 Who Internet Innovation Center 19 City of Winnipeg, population: 635,869

21 Implementation: When Object Template: Schedule Properties: Activity start time Activity lasts for Institution where the activity takes place Probability of choosing given activity Special Types: Working schedule, Leisure schedule Part of: Agent, Community Internet Innovation Center 20

22 When - Schedules Sample working schedule: 8:00 8:00 WI 98 17:00 2:00 Mall 30 17:00 2:00 LI 50 Meaning: 98% chances that agent will spend 8h at working institution starting from 8:00 am 30% chances that agent will spend 2h shopping starting from 5:00 pm or 50% chances that agent will spend 2h at any of its leisure institutions (Cinema, Restaurant, etc.) 8:00 2% 16:00 17:00 30% 35% Mall 19:00 98% 35% Working Institution Leisure Institution Internet Innovation Center 21

23 Implementation: What Object Template: Virus Properties: Probability of contracting the virus Incubation period Infecting period starts Infecting period ends Sickness (low mobility) lasts Extra resistance boost Extra resistance lasts Extensions: Ψ Seasonal Variations, Mutation Internet Innovation Center 22

24 Seasonal Variations Internet Innovation Center 23

25 Infection probability #_of_infectious_agents( Si, Ti ) I prob ( i, j, d) = Ti Φi Λ j Ψ d ( d) m #_of_agents( S, T ) i i Variable I i j d prob d m S i T i Φ i Λ j Ψ d m (d ) Meaning probability of being infected institution index agent index day mutation day i th institution time spent in i th institution probability of being infected in i th institution probability of being infected for j th agent probability of being infected by a given virus probability of being infected in day d Internet Innovation Center 24

26 Simulating a day Once scheduling is completed, simulation enters the phase in which agents perform their activities. First, the wall clock is set to 0:00. Iteration through all time steps then begins. For each time step a list of activities scheduled for this time is iterated and agents are moved to their destination institutions. After the above have been performed for all activities for a given time step, the time is incremented by a time increment value and the processing of activities continues. The algorithm stops when the 24 hour limit is reached. After this point the day counter is incremented and the next day is scheduled. Internet Innovation Center 25

27 Simulating a day Scheduling For each agent, a list of activities for a given day is generated from agent's schedule Processing At each time increment Agents are moved between institutions Home Bus/Car Bus/Car Institution Institution Bus/Car Bus/Car Home Home Bus/Car Institution Internet Innovation Center 26

28 Public Transportation Internet Innovation Center 27

29 The User Interface to DSSW Parameters for simulation are set up in a number of files and the user can step or loop through the simulation at any given rate. During the simulation, a number of plots and statistics are collected and logged to a web server where the user can then further analyze the simulation run. Internet Innovation Center 28

30 Analysis Some data that is available on the corresponding web server Internet Innovation Center 29

31 Seasonal Variations Seasonal variations are well known and provide fairly well labeled data for comparison The figure illustrates the type of data available Comparison allows for a tuning of parameters to more closely reflect actual data collected for a particular disease Internet Innovation Center 30

32 Mutations tipping point A mutation to a deadlier strain or a sudden variation in the mode of transmission (perhaps the virus has become airborne) Other uses of the simulator would be in helping to evaluate the extent of inoculations or policies in the event of a simulated outbreak. This will allow for epidemiologists to partially close the loop when evaluating policy Internet Innovation Center 31

33 Summary: DSSW Part One This presentation introduced a reasonable method of epidemic modeling, taking advantage of opportunities for data mining and scheduled walkers. The basic characteristic of the model is to extract and combine real topographic and demographic data. This work shows that model creation using real data is indeed feasible, and will likely result in better characterization of the actual dynamics of an epidemic outbreak. Further work will focus on refining the model, and validating the afore-mentioned conjecture. Internet Innovation Center 32

34 Demonstration Internet Innovation Center 33

35 Questions Internet Innovation Center 34

36 Part Two: Extensions and limitations of potential relevance to HIV/AIDS Current limitations of the DSSW simulation engine Extensions in behavioral pattern extraction Often from potentially unexpected sources Related work Summary Internet Innovation Center 35

37 Limitations of DSSW Agree All models are wrong but some models are useful. George E.P. Box, Statistician Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things. Sir Isaac Newton Perhaps truth can actually be found in the multiplicity and confusion of things! Maciej, Blake and Bob Ref: Wikipedia Internet Innovation Center 36

38 Limitations of DSSW (Cont d) One city Two types of schedules: work and leisure Actual demographics are more complex Much of this information is available Some of which will be have to be derived from disparate and unexpected sources At present DSSW appears mainly well suited to egalitarian type diseases Internet Innovation Center 37

39 Extensions: Hierarchy Incorporate Hierarchy Intracity and Intercity Basic modality remains: data-driven models of discrete space- and time- walkers, mined from available sources. Cities are largely autonomous Allows for the problem to remain tractable and allows for efficient modes of computation (hence, parallelism can be exploited). Internet routing algorithm analog Internet Innovation Center 38

40 Extensions: Key Sources for Extracting Patterns of Behaviour Patterns of people s behavior (i.e., monitoring): taken from tracking and locating technologies that are already in place albeit not mined for use in epidemic modeling. Monitoring for missing persons, illegal activities, including (Bio)- terrorist threats: e.g., i) Video surveillance and security cameras ii) GPS and RFID tracking and location technologies Obstacle: Privacy concerns/acts e.g., i) PIPEDA Personal Information Protection and Electronic Documents Act ii) HIPPA Health Insurance Portability and Accountability Act Internet Innovation Center 39

41 Related Research: Key Sources for Extracting Patterns of Behaviour (cont d) Financial Transaction Profiling. Usually mined to detect fraud Cell phone tracking, where are you services. By default the service provider already knows where you are, even more precisely with GPS. Consumer wireless electronics: MAC snooping and tracking. Bluetooth headsets (ingress and egress of signalized arterials) (ref: in paper) Similar protocols for WiFi Device-enabled Kiosks and vending machines (via Handhelds or Cell phones) Internet Innovation Center 40

42 Related Research: Key Sources for Extracting Patterns of Behaviour (cont d) Tracking transit ridership. Token data mining of ridership (ref: in paper) Objective: Scheduling; (Bio)-terrorism impact (ref: in paper) Method: RFID implanted or Bar-code tokens Mining online transportation information systems E.g., Helsinki public transport (ref: in paper) Objective: to provide real-time location information for riders; our application would utilize this data to model the movement of people within a city for disease modeling (and its possible spread) Method: vehicle GPS mapping overlay with Internet Browser Internet Innovation Center 41

43 Real-time Helsinki Public Transportation Information Internet Innovation Center 42

44 Related Research: Key Sources for Extracting Patterns of Behaviour (cont d) Video Surveillance Cameras: tracking and locating The Toronto Transit Commission has plans to photograph the faces of every commuter (ridership). Objective: Scheduling, (Bio)-terrorism impact (ref: in paper) Method: to utilize Autonomous Face-recognition City of Edmonton Traffic Monitoring: tracking and locating Objective: Reporting of congestion; Removal of disabled vehicles; Avoidance of bottlenecks Method: (we propose) to utilize Autonomous Vehicle License Plate- or ID- recognition Internet Innovation Center 43

45 Ubiquitous Real-time Traffic Monitoring Cameras Ref: Internet Innovation Center 44

46 Related Research: Extracting Patterns of Behaviour (RFID tracking) Although not as explicit or readily attainable, the potential to extract patterns of behavior and interactions of agents at critical institutions such as hospitals can be made more feasible through the use of RFID tracking. As RFID sensor networks move from inventory solutions to enhanced applications, data collected from RFID tracking at clinics and hospitals can be envisioned as an input to DSSW. Internet Innovation Center 45

47 Related Research: Extracting Patterns of Behaviour (Economic Impact) Economic Impact: Costs associated with implementing policy. (ref: in paper) Specifically, the economic impact of restricting air travel as a policy in controlling a flu pandemic. Not directly related to HIV/AIDS But models global air travel and estimates impact and cost associated with travel restrictions. E.g. 95% travel restriction required before significantly impairing disease spread Overall area of research denoted: Agent Based Modeling Internet Innovation Center 46

48 Related Research: Extracting Patterns of Behaviour (Economic Impact) Internet Innovation Center 47

49 Related Research: Surveillance Based Modeling UNAIDS initiatives: (ref: in paper) Curve fitting empirical data to models Potentially could be data sources for DSSW Data collection itself is a daunting task Maybe useful in regulation the simulations More likely of somewhat limited utility for DSSW Internet Innovation Center 48

50 Related Research: Surveillance Based Modeling Internet Innovation Center 49

51 DSSW Shortcomings wrt HIV/AIDS However the DSSW simulator is conceptually useful in predicting the spread of HIV/AIDS as it places emphasis on patterns of behavior and data mining. With our limited knowledge of patterns of behavior (e.g., cultural values/attitudes, social morals, effects of poverty, etc.) for HIV much of our simulation would be pure conjecture. This contrasts diseases such as influenza which really have no predisposed target group. Influenza is more who -agnostic than HIV. Internet Innovation Center 50

52 Other sources or information Occasional mass gatherings E.g. Olympics or other special that may perturb an overall or global simulation E.g. The Hajj Largest mass pilgrimage in the world an estimated 2 million people participated. Conditions are difficult and thus it offers an opportunity for a large scale disease such as influenza to take hold. These people then disperse to their home countries, many via public transport, and could easily influence the spread and outbreak of the disease. Internet Innovation Center 51

53 Other modeling considerations We may be able to model the effectiveness of timely vaccination and/or inoculations Typically vaccinations are more likely to take place relatively large institutions throughout a city (school, community centre, etc.) or through other programs offered through the work place or regional health authorities. These services would have considerable consequence in perhaps limiting the rate at which disease could spread and modeling would also indicate potential bottlenecks in delivery, particularly if the vaccine were of limited supply. Internet Innovation Center 52

54 Other modeling considerations Having an effect on the spread of disease (and the modeling therein) are the wide spread usage of anti-viral and anti-retroviral medications: Some anti-viral medications are specifically designed to mitigate the effects of the flu and the associated symptoms, reducing the amount of time an individual may be infectious. Many patients of HIV are now receiving anti-retroviral therapy. This treatment appears to aid in the prevention of mother-tochild transmission and may therefore have a significant impact on the overall spread-of-disease model. Nanomedicines are currently under development that use nanoparticles of gold in combination with previously failed HIV drugs to rekindle the drug s ability to stop the virus from invading the body s immune system and gaining a cellular foothold (ref. J. of the American Chemical Society). Internet Innovation Center 53

55 Summary Presented an Agent Based Modeling approach to epidemic simulation. Emphasis on data mining of spatial topologies and agent behavior patterns Denoted Discrete Space Scheduled Walkers Presented several indirect data sources Often no obvious connection to virus modeling Presented potential extensions to HIV/AIDS modeling More difficult as the virus is not who -agnostic Extracting patterns of behavior is difficult. Internet Innovation Center 54

56 Thank-you Comments and suggestions very welcome. Next year we hope to offer two more BSERC programming challenges. Topics under consideration Introduce a panic behavior in light of an epidemic Incorporate a mass gathering Suggestions from the workshop Internet Innovation Center 55

57 IIC Contact Maciej Borkowski, Blake W. Podaima, Robert D. McLeod Internet Innovation Center E3-416 EITC University of Manitoba Winnipeg, Manitoba R3T 5V6 {maciey, bpodaima, Tel: (204) Fax: (204) Internet Innovation Center 56