Bulletin of Mathematical Biology

, Volume 68, Issue 3, pp 525–550

# Modeling the HIV/AIDS Epidemic Among Injecting Drug Users and Sex Workers in Kunming, China

Original Article

DOI: 10.1007/s11538-005-9051-y

Bacaër, N., Abdurahman, X. & Ye, J. Bull. Math. Biol. (2006) 68: 525. doi:10.1007/s11538-005-9051-y

## Abstract

This paper presents a mathematical model of the HIV/AIDS epidemic in Kunming,the provincial capital of Yunnan, China. The population is divided into several groups, with individuals possibly changing group. Two transmission routes of HIV are considered: needle sharing betweeninjecting drug users (IDUs) and commercial sex between female sex worker(FSWs) and clients. The model includes male IDUs who are also clients and female IDUs who are also FSWs. Groups are split in two—risky and safe—according to condom use and needle sharing. A system of partialdifferential equations is derived to describe the spread of the disease. For the simulation, parameters are chosen to fit as much as possibledata publicly available for Kunming. Some mathematical properties of the model—in particular the epidemic threshold R0 which determines the goal of public health interventions—are also presented. Though the model couples two transmission routes of HIV, the approximation $$R_0\simeq \max\{R_0^{{\rm IDU}},R_0^{{\rm sex}}\}$$, with closed formulas for $$R_0^{{\rm IDU}}$$ and $$R_0^{{\rm sex}}$$, appears to be quite good. The critical levels of condom use and clean needle use necessary to stop both the sexual transmission and the transmission among IDUs can therefore be determined independently.

### Keywords

HIV/AIDS Kermack-McKendrick epidemic model R0 Female sex workers Injecting drug users China

92C60 35Q80

## Authors and Affiliations

• Nicolas Bacaër
• 1
• 4
• Xamxinur Abdurahman
• 2
• Jianli Ye
• 3
1. 1.Institut de Recherche pour le Développement (IRD)BondyFrance
2. 2.College of Mathematics and System SciencesXinjiang UniversityUrumqiP.R. China
3. 3.Center for Public Health Surveillance and Information ServicesChinese Center for Disease Control and Prevention (CCDC)BeijingP.R. China
4. 4.IRDBondy CedexFrance