Who Do You Know? A Simulation Study of Infectious Disease Control Through Contact Tracing Benjamin Armbruster and Margaret L. Brandeau Stanford University

Contact Tracing Health care provider’s perspective: 1.Infected person found (index case) 2.Treated 3.Asked for list of contacts 4.Contacts found and tested 5.If contact infected go to step 1. Standard practice for Tuberculosis (TB) Common for HIV and other STDs –called partner notification

1 54 susceptible infected ? being tested node 2 infected Contact Tracing

5 1 4 susceptible infected ? being tested node 2 infects nodes 1,4,5 Contact Tracing

5 1 4 susceptible infected ? being tested node 4 gets tested (maybe has symptoms) ? Contact Tracing

5 1 4 susceptible infected ? being tested node 4 tests positive, gets treated becomes a contact tracing index case names nodes 1,2,3,6,7 as contacts nodes 1,2,3,6,7 scheduled to be tested ? ? ? ? ? Contact Tracing

5 1 4 susceptible infected ? being tested node 3 tests negative ? ? ? ? Contact Tracing

5 1 4 susceptible infected ? being tested node 6 tests negative ? ? ? Contact Tracing

5 1 4 susceptible infected ? being tested ? ?? node 1 tests positive, gets treated becomes a contact tracing index case names nodes 2,4 as contacts node 4 already tested testing node 2 gets higher priority as named by both nodes 1,4 Contact Tracing

susceptible infected ? being tested ? ? node 2 tests positive, gets treated becomes a contact tracing index case names nodes 1,4,5 as contacts nodes 1,4 already tested node 5 scheduled to be tested Contact Tracing

susceptible infected ? being tested ? node 5 tests positive, gets treated becomes a contact tracing index case names node 2 as a contact node 2 already tested Contact Tracing

susceptible infected ? being tested node 7 tests negative Contact Tracing

Outline Details of the simulation What is the optimal contact tracing policy? Does spending more money help? Conclusions Limitations and future work

Simulation Dynamics t 1 90 days t 2 30 days t 3 90 days t 4,t 5 5 days η 1/9000 new cases/day/person d i = number of infected neighbors of node i

Network A small-word graph with n nodes: 1.Create nodes 0,...,n-1 2.Connect node i to i±1,2 (mod n) 3.Add link (i,j) with probability 1/n n =500 people

Simulation Details Each prevalence data point is the Average over many ( ) runs Error bars show 95% confidence interval Steady-state prevalence in a run: 1.Infect a random node 2.Simulate for 5 years 3.Average the prevalence at the end of day 181, day 182,...

Contact Tracing Policy Budget B Currently tracing 1.Tutankhamen 2.Frederic Chopin 3.Eleanor Roosevelt … B empty slot ? ? ? ? ?

5 9 8 Contact Tracing Policy Budget B New index case: choose k contacts to trace

5 9 8 Contact Tracing Policy Budget B New index case: choose k contacts to trace Once we have time 1.Niels Abel 2.node 2 3.node 3 4.node 7 5.…

Contact Tracing Policy Budget B New index case: choose k contacts to trace If we have resources, then trace from top of list Currently tracing 1.Tutankhamen 2.Frederic Chopin 3.Eleanor Roosevelt … B empty slot Once we have time 1.Niels Abel 2.node 2 3.node 3 4.node 7 5.…

Contact Tracing Policy Budget B New index case: choose k contacts to trace If we have resources, then trace from top of list Currently tracing 1.Tutankhamen 2.Frederic Chopin 3.Eleanor Roosevelt … B Niels Abel Once we have time 1.node 2 2.node 3 3.node 7 4.…

k=5 B=8 Which Policy is Best?

How Many Contacts to Trace per Index Case?

Increasing the Budget

What is the Best Level of Contact Tracing? α=$10,000 n = 500

Choosing α Resource allocation problem –total budget B total –budget b i for program i s.t. b 1 + · · · +b m ≤ B total –benefit f i (b i ) maxf 1 (b 1 )+ · · · +f m (b m ) s.t.b 1 + · · · +b m ≤ B total

Cost Effectiveness Resource allocation problem –total budget B total –budget b i for program i s.t. b 1 + · · · +b m ≤ B total –benefit f i (b i ) –cost effectiveness 1 / f i ′(b i ) minmax i 1 / f i ′(b i ) s.t.b 1 + · · · +b m ≤ B total α=α=

Budget Allocation 1.Choose α large 2.For each program –find b i s.t. α = 1 / f i ′(b i ) –if doesn't exist, then set b i =0 3.Calculate money spent b 1 + · · · +b m 4.If >B total, then –decrease α a bit –go to step 2 5.Else at optimal allocation

Conclusions First detailed model of contact tracing Found a better prioritization of contacts Diminishing returns to scale Cost-effectiveness should play a role when choosing a budget

Limitations / Future Work Dynamics are missing –a latent or asymptomatic stage –the male-female distinction –variety of exogenous infections Network stylized: –pairs, pair-formation needed for HIV / STDs Policy gives no priority to vulnerable contacts Genotype information Dynamic control