A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks
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1 A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks Bilal Khan, Kirk Dombrowski, and Mohamed Saad, Journal of Transactions of Society Modeling and Simulation International, SAGE, 2014). Presented by: Gisela Font Sayeras
2 Overview Network Simulation ERGM vs ABM Model Design of MABUSE, the system Validation
3 Network Simulation What is a network? What is a dynamic network? Networks in the real world Networks in simulation
4 Main network simulation strategies ERGM (Exponential Random Graph Modeling) Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M. ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of statistical software. 2008;24(3):nihpa ABM (this class)
5 Exponential Random Graph Modeling (ERGM) Real Network Stats G1 G2 G100
6 Exponential Random Graph Modeling (ERGM) Real Network Stats G1 G2 G100
7 Agent Based Model Simulation (ABM) Real Network Stats G1 G2 G100
8 Agent Based Model Simulation (ABM) Real Network Stats??? G1 G2 G100
9 ERGM vs ABM ERGM gives you realistic network-level guarantees but lacks realistic individual agency The network gets to change realistically over time What each agent is doing could be unrealistic ABM gives you lack realistic individual agency but lacks realistic network-level guarantees Each agent gets to change realistically over time What the network is doing could be unrealistic
10 MABUSE MABUSE gives you realistic network-level but lacks realistic individual agency The network gets to change realistically over time What each agent is doing could be unrealistic ABM gives you lack realistic individual agency but lacks realistic network-level guarantees Each agent gets to change realistically over time What the network is doing could be unrealistic
11 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go
12
13
14 How are the properties of individuals determined? Univariate Distribution Properties of nodes Age Gender Young (20-35) Old (36-60) Female Male
15 How are the properties of individuals determined? Univariate Distribution Properties of nodes Age Gender Young (20-35) Old (36-60) Female Male
16 How are the properties of individuals determined? Univariate Distribution Properties of nodes Make Person 1 Age Gender Young woman (22 years old) Young (20-35) Old (36-60) Female Male
17 Population 1
18 How are the properties of individuals determined? Univariate Distribution Properties of nodes Age Gender Young (20-35) Old (36-60) Female Male
19 How are the properties of individuals determined? Univariate Distribution Properties of nodes Age Gender Young (20-35) Old (36-60) Female Male
20 How are the properties of individuals determined? Univariate Distribution Properties of nodes Make Person 2 Age Gender Old man (50 years old) Young (20-35) Old (36-60) Female Male
21 Population 1 2
22 Population
23 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go
24
25 How individuals choose who to form relationships with? Who is 1 going to choose?
26 How is the choice going to be made? Bivariate Distribution Aggregator Gender: 0.8 Age: 0.3 (from ERGM)
27 How is the choice going to be made? 1 2 Aggregator Gender: 0.8 Age: 0.3 (from ERGM)
28 How is the choice going to be made? Calculate Propensity 1 2 Aggregator Gender: 0.8 Age: 0.3 (from ERGM)
29 How is the choice going to be made? Calculate Propensity 1 2 Propensity 1-2 = 0.25* *0.3 = 0.32 Aggregator Gender: 0.8 Age: 0.3 (from ERGM)
30 How is the choice going to be made? 2 Calculate Propensity
31 How is the choice going to be made? 2 Calculate Propensity
32 How is the choice going to be made? Normalize = / 2.2 = 0.14
33 How is the choice going to be made? 2 Random Selection
34 How is the choice going to be made? 2 Random Selection
35 Drug layer: sharing needles Sex layer
36 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go
37 Drug layer: sharing needles Sex layer
38 Every node has an "ideal degree" Univariate Distribution Properties of nodes Age Gender Ideal Degree Young (20-35) Old (36-60) Female Male Low (0-3) Med (4-8) High (9-19)
39 Every Relationship has a "longevity" Properties of edges Edge Longevity Transient (7-30) Steady (30-50)
40 How do network edges change? Ideal Degree =
41 How do network edges change? Day 7: Relationship 1-2 ends Ideal Degree =
42 How do network edges change? Day 7: Relationship 1-2 ends 2 1 Ideal Degree = 4 Actual Degree =
43 How do network edges change? Ideal Degree = Actual Degree = 3 10
44 How do network edges change? Person 1 starts new relationship Ideal Degree = Actual Degree = 4 10
45 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go
46 Every node has a risk interval" Univariate Distribution Properties of nodes Age Gender Ideal Degree Risk Interval Young (20-35) Old (36-60) Female Male Low (0-3) Med (4-8) High (9-19) Low (1-3) Med (4-8) High (9-19)
47 What are the people doing? Risky things 1) Wake up 2) Choose a neighbors 25 3) Engage in risk act with them Risk Interval = 2 (days between risk act) 10
48 Disease transmission during a risk act Case
49 Disease transmission during a risk act Case
50 Disease transmission during a risk act Case Transmission probability
51 Disease transmission during a risk act Case Transmission probability
52 The "natural history" of disease HIV 1 25 =0.004 in acute = in chronic Transmission probability
53 The "natural history" of disease HCV 1 25 Transmission probability
54 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go
55 How are people coming and going? Univariate Distribution Properties of nodes Young (20-35) Age Old (36-60) Gender Female Male Ideal Degree Low (0-3) 0.3 Med (4-8) Risk Interval High (9-19) Low (1-3) 0.2 Med (4-8) Node Longevity Min (20-35) High (9-19) Max (36-60)
56 How are people coming and going? Longevity = 26 10
57 How are people coming and going? Day 26: Person 1 dies Longevity = 26 10
58 How are people coming and going? Day 26: Person 1 dies Longevity = 26 10
59 How are people coming and going? Day 26: Person 1 dies Now all these people have Actual degree < Ideal degree and the population shrank.
60 How are people coming and going? New Person is made
61 How are people coming and going? New Relationships are made Longevity = 50 19
62 Outline of MABUSE Model INITIALIZATION 1. Nodes are made (including some infected) 2. Edges are made SIMULATION RUN 3. Edges change over time 4. Risk acts happen with neighbors 5. Nodes come and go Now, putting it all together
63 One layer, one pathogen scenario Network Layer Drug layer Transmission probability #1
64 Multi-layer scenario Network Layer #1 Drug layer Transmission probability #1 Network Layer #2 Sex layer Transmission probability #1
65 Multi-pathogen scenario Network Layer Drug layer Transmission probability #1 Transmission probability #1
66 Multi-pathogen Multi-layer scenario Network Layer #1 Drug layer Transmission probability #1 Transmission probability #1 Network Layer #2 Sex layer Transmission probability #1 Transmission probability #1
67 Design of MABUSE Key features Dynamic network simulation Multiple (dynamic) node attributes Multiple (dynamic) edge layers Multiple simultaneous pathogens Stochastically defined node agency E.g. risk activity along network edges on different layers is what drives the flow of multiple pathogen types
68 How is the implementation going to be validated? Validate Network Dynamism Validate Pathogen Flow
69 Validation of Network Simulation 1. Take a real network. Compute statistics A. Structure (univariates and bivariates) B. Dynamism (ideal degrees, longevity) 2. Use 1A+1B to do a 10 year simulation. At the end, Compute statistics A. Structure (univariates and bivariates) B. Dynamism (ideal degrees, longevity) Is 1A "close" to 2A? Is 1B "close" to 2B? Use Shannon-Jensen divergence to measure the "distance" between distributions
70 Real social network Model extraction Structural model Dynamism model
71 Real social network Model extraction Structural model Dynamism model Network generator Artificial social network (Initial)
72 Real social network Model extraction Structural model Dynamism model Network generator Network simulator Artificial social network (Initial) Artificial social network
73 Real social network Model extraction Structural model Dynamism model Network generator Network simulator Artificial social network (Initial) Artificial social network Artificial social network
74 Real social network Model extraction Structural model Dynamism model Network generator Network simulator Divergence calculator Artificial social network (Initial) Artificial social network Artificial social network
75 Shannon-Jensen divergence Shannon-Jensen divergence Results Time
76 Validation of Pathogen Take Base Scenario Single Layer Single Pathogen Compare Base Scenario with the following Artificial Scenarios
77 Artificial Scenario 1 Base Scenario 40% l = 2 24% 40% %of60 = = 64 l = 3 24% 40% 16% % of 36 = = 77.8
78 Artificial Scenario 2
79 Artificial Scenario 3
80 Artificial Scenario 4 40/3 40/3 40/3
81 Multi Actor-Based Universal Simulation Engine MABUSE is stochastic, agent-based, discrete event simulator for epidemics in dynamic networks. The simulator runs on specialized highperformance hardware and is capable of running simulations of dynamic networks having 1,000,000+ nodes, and handling approximately 800 million discrete events per second.
82 Conclusion MABUSE allows us to simulate Multiple (dynamic) node attributes Multiple (dynamic) edge layers Multiple simultaneous pathogens A realistic dynamic network From the POV of an agent (micro, ABM-style) From POV of the network (macro, ERGM-style) Model where each agent takes into account its own properties and the properties of other agents to make connections, and act on those connections
83 Thank you Any Questions?
84 Jensen-Shannon Divergence Real D 1 : M 55% F 45% 30 D 1 : M 75% F 25% Mid: M 65% F 35% SJ D1, D2 = 1 [KL D1, M + KL D2, M ] 2 KL D1, M = i=m,f D1 i log( D1 i Mid i ) = 0.55 log log( )
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