Sexual network drivers of HIV and herpes simplex virus type 2 (HSV-2) transmission A comparative mathematical modeling analysis

ABU-RADDAD2,3,5 1Division of Bioinformatics, Research Center for Zoonosis Control, Hokkaido University, Sapporo, Hokkaido, 001-0020, Japan 2Infectious Disease Epidemiology Group, Weill C

Supplemental information

Sexual network drivers of HIV and herpes simplex virus type 2 (HSV-2) transmission: A comparative mathematical modeling

analysis

Ryosuke OMORI1,2,3,4* and Laith J ABU-RADDAD2,3,5

1Division of Bioinformatics, Research Center for Zoonosis Control, Hokkaido University, Sapporo, Hokkaido, 001-0020, Japan

2Infectious Disease Epidemiology Group, Weill Cornell Medicine - Qatar, Cornell University, Qatar Foundation - Education City, Doha, Qatar

3Department of Healthcare Policy and Research, Weill Cornell Medicine, Cornell University, New York, New York, USA

4JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan

5College of Public Health, Hamad bin Khalifa University, Doha, Qatar

Reprints or correspondence: Ryosuke Omori, PhD, Division of Bioinformatics, Research Center for Zoonosis Control, Hokkaido University North 20, West 10, Kita-ku, Sapporo, Hokkaido,

Japan Telephone: +(81) 11-706-7307 Fax: +(81) 11-706-7310 E-mail:

omori@czc.hokudai.ac.jp

Text S1 Definitions of key network statistics

1) Clustering coefficient

The clustering coefficient of the network is calculated as an average of the clustering coefficient for each individual in the population:

i i

q q

N

=∑

Here N denotes the total population size.

The clustering coefficient for an individual i is defined as :

qi = number of pairsof neighborsof i that areconnected

number of pairsof neighborsof i

We defined and used two clustering coefficient measures, one for only non-marital partnerships and the other for all partnerships (that is including marital ones)

2) Concurrency

Concurrency is defined as the proportion of individuals in the population that have ≥2 sexual partners at a specific time point We defined and used two concurrency measures, one for only non-marital partnerships and the other for all partnerships For the all partnerships measure, both the marital partnership as well as the non-marital partnerships are counted as sexual partnerships

3) Degree correlation

Degree correlation is defined as Pearson’s correlation coefficient of the numbers of partners between pairs of individuals connected by partnership Degree correlation for the pairs of individuals in the population can be expressed as:

sd ( ) ki sd ( ) kj

Here, k and i k are the numbers of partners of each of the two partners in the pair, cov is the j

covariance and sd is the standard deviation.

We defined and used two degree correlation measures, one for only non-marital partnerships and the other for all partnerships (that is including marital ones)

Reference

1. Newman M Networks: an introduction: Oxford university press; 2010

2 Kretzschmar M, Morris M Measures of concurrency in networks and the spread of infectious

disease Mathematical Biosciences 1996,133:165-195.<Go to ISI>://A1996UD81200003