Investigating the impact of Circular Migrations on HIV ... - CBR Wiki

The QuestionHow do circular migrations affect <strong>the</strong> dynamics<strong>of</strong> HIV transmission through a population?3

The QuestionHow do circular migrations affect <strong>the</strong> dynamics<strong>of</strong> HIV transmission through a population?• Frequency <strong>of</strong> migrant return• Sexual behaviour <strong>of</strong> migrants and non-migrants +partner(s)• Recency <strong>of</strong> transmission.• Concurrent partnerships4

Outline1. Motivation - The Research Question2. Background3. Mechanisms4. Modeling5. Discuss!5

Lurie et. al. (2003)• 196 migrant men + 130 rural partners• 64 non migrant men + 98 rural partners• Detailed questionnaire + Blood samples9

• 25.9% migrant men + 12.7% non migrant menHIV+• 21% <strong>of</strong> partners <strong>of</strong> migrant men, 17% partners <strong>of</strong>nonmigrant men.• Female partner infected in ≈ 1/3rd <strong>of</strong> discordantpartnerships.• Greater likelihood <strong>of</strong> being infected from outsideprimary relationship.• <strong>Investigating</strong> Bi-directionality is crucial.10

Outline1. Motivation - The Research Question2. Background3. Mechanisms4. Modeling5. Discuss!11

Major Factors1. Migrants’ high risk sexual behaviour.2. Bi-directionality <strong>of</strong> disease transmission3. Concurrent Partnerships4. Recency <strong>of</strong> transmission12

Concurrent Partnerships: Relationships that overlap intime.13

Definition <strong>of</strong> Concurrency(Morris, Kretzcshmar)Serial Monogamy12345timeConcurrency1234514

Population Level Structure(Morris and Kretzschmar)monogamyconcurrencyVirus Perspective: Less time locked in samepartnership.15

Simulating Impact <strong>of</strong> Concurrency(Morris and Kretzschmar, 1997)Number <strong>of</strong> Infected500 1000 15000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Concurrency16

Major Factors1. Migrants’ high risk sexual behaviour.2. Bi-directionality <strong>of</strong> disease transmission3. Concurrent Partnerships4. Recency <strong>of</strong> infection17

Outline1. Motivation - The Research Question2. Background3. Mechanisms4. Modeling5. Discuss!18

Social Networks: Why use this paradigm?• Social Networks provide a framework to keep track<strong>of</strong> all nodes and <strong>the</strong> ties <strong>the</strong>y are involved in.• Conducive to an agent-based investigation <strong>of</strong> relationaltiming and connection to concurrency19

A Social Network is defined as a set <strong>of</strong> n social actorsand a relationship between each pair <strong>of</strong> factors (Handcock,2008).Define a sociomatrix Y with 1, . . . , n actors. ThenY ij ={1 if relationship exists from actor i to actor j0 elseNote: The tie is <strong>the</strong> variable <strong>of</strong> interest.Fundamental Problem:P (Y = y).Specifying a distribution for20

Exponential Random Graph Model:P (Y = y) = 1 κ exp {∑ A η A g A (y)}• General class <strong>of</strong> models.• Summation is over all possible configurations.• η A parameter corresponding to configuration A.• g A (y) = ∏ y ij ∈A y ij ={1 if configuration exists in network0 else}• κ is normalizing quantity21

Estimation: κ makes estimation difficult.Consider transformation:log⎡⎣ P (Y ij = 1|y c ij )P (Y ij = 0|y c ij⎤⎦ =∑A(Y ij )η A d A (y)• Sum over all configurations A that contain Y ij• η A corresponds to configuration A.• d A (y) = change statistic: Switch toggled from onto <strong>of</strong>f.22

Bernoulli Random Graph (Erdos-Renyi Model).⎛ ⎞P (Y = y) = 1 κ exp η ij y ij⎠⎝ ∑ i,j• Every possible edge Y ij is a configuration• Parameter η ij is a parameter for each configuration• Statistic g ij (y) = y ij indicates existence <strong>of</strong> configuration.23

Rural Women Urban WomenMigrant Men ̌ ̌NonMigrant Men ̌ ✘24

• Village, Town, and <strong>Migrations</strong> between.• Identify Change Statisticsso part-• Population reaches a “stationary” state:nerships have formed.• Simulate transmission <strong>of</strong> <strong>the</strong> disease through <strong>the</strong>network.• About 3 months later - migrants return home and anew batch <strong>of</strong> migrants go to mine. Process repeats.25

Take Home Messages• Not much is known about <strong>the</strong> <strong>impact</strong> <strong>of</strong> migrationon how STI’s travel through populations.• Good data on sexual behaviour is hard to find.• Process based models can help us gain insight intothis problem with <strong>the</strong> goal <strong>of</strong> effective interventionstrategies.26

Thanks:• Steven Goodreau and Susan Cassels• <strong>the</strong> UW NetModeling Group• QERMies• Anderson Lab27