A risk-based model for predicting the impact of using condoms on the spread of sexually transmitted infections Asma Azizi a, * , Karen Ríos-Soto b , Anuj Mubayi c, d , James M. Hyman a a Department of Mathematics, Tulane University, New Orleans, LA, 70118, United States b Department of Mathematical Sciences, University of Puerto Rico, Mayaguez, PR, 00610, United States c School of Human Evolution and Social Change, Arizona State University, Tempe, AZ, United States d Simon A. Levin Mathematical Computational Modeling Science Center, Arizona State University, Tempe, AZ, United States article info Article history: Received 7 November 2016 Received in revised form 16 February 2017 Accepted 24 February 2017 Available online 1 March 2017 Keywords: Mathematical modeling Sexually transmitted infection (STI) Biased (preferential) mixing Random (proportional) mixing Condom-use Risk (number of partners) abstract We create and analyze a mathematical model to understand the impact of condom-use and sexual behavior on the prevalence and spread of Sexually Transmitted Infections (STIs). STIs remain significant public health challenges globally with a high burden of some Sexually Transmitted Diseases (STDs) in both developed and undeveloped countries. Although condom-use is known to reduce the transmission of STIs, there are a few quantitative population-based studies on the protective role of condom-use in reducing the incidence of STIs. The number of concurrent partners is correlated with their risk of being infectious by an STI such as chlamydia, gonorrhea, or syphilis. We develop a Susceptible-Infectious-Susceptible (SIS) model that stratifies the population based on the number of concurrent partners. The model captures the multi-level heterogeneous mixing through a combination of biased (preferential) and random (proportional) mixing pro- cesses between individuals with distinct risk levels, and accounts for differences in condom-use in the low- and high-risk populations. We use sensitivity analysis to assess the relative impact of high-risk people using condom as a prophylactic intervention to reduce their chance of being infectious, or infecting others. The model predicts the STI prevalence as a function of the number of partners of an individual, and quantifies how this distribution of effective partners changes as a function of condom-use. Our results show that when the mixing is random, then increasing the condom-use in the high-risk population is more effective in reducing the prevalence than when many of the partners of high-risk people have high risk. The model quantifies how the risk of being infected increases for people who have more partners, and the need for high-risk people to consistently use condoms to reduce their risk of infection. © 2017 KeAi Communications Co., Ltd. Production and hosting by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction There are approximately 19.7 million new Sexually Transmitted Infections (STIs) every year in the United States of America (Satterwhite et al., 2008). More than half of the people in the U.S. will have an STI at some point in their lifetime (Koutsky, 1997). Mathematical models can provide frameworks to understand the underling epidemiology of STI and how they are * Corresponding author. E-mail address: aazizibo@tulane.edu (A. Azizi). Peer review under responsibility of KeAi Communications Co., Ltd. Contents lists available at ScienceDirect Infectious Disease Modelling journal homepage: www.keaipublishing.com/idm http://dx.doi.org/10.1016/j.idm.2017.02.004 2468-0427/© 2017 KeAi Communications Co., Ltd. Production and hosting by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/). Infectious Disease Modelling 2 (2017) 100e112