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

Supplemental information Sexual network drivers of HIV and herpes simplex virus type (HSV-2) transmission: A comparative mathematical modeling analysis Ryosuke OMORI1,2,3,4* and Laith J ABU-RADDAD2,3,5 Division of Bioinformatics, Research Center for Zoonosis Control, Hokkaido University, Sapporo, Hokkaido, 001-0020, Japan Infectious Disease Epidemiology Group, Weill Cornell Medicine - Qatar, Cornell University, Qatar Foundation - Education City, Doha, Qatar Department of Healthcare Policy and Research, Weill Cornell Medicine, Cornell University, New York, New York, USA JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan College 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: q= ∑q i i 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 are connected 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: r= ( cov ki ,kj ) ( ) sd ( ki ) sd kj Here, ki and k j are the numbers of partners of each of the two partners in the pair, cov is the 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 Newman M Networks: an introduction: Oxford university press; 2010 Kretzschmar M, Morris M Measures of concurrency in networks and the spread of infectious disease Mathematical Biosciences 1996,133:165-195.://A1996UD81200003 ... Here, ki and k j are the numbers of partners of each of the two partners in the pair, cov is the covariance and sd is the standard deviation We defined and used two degree correlation measures,... 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... 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