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Modeling the HIV/AIDS epidemic among injecting drug users and sex workers in Kunming, China. (English) Zbl 1334.92389
Summary: 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 between injecting drug users (IDUs) and commercial sex between female sex workers (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 partial differential equations is derived to describe the spread of the disease. For the simulation, parameters are chosen to fit as much as possible data publicly available for Kunming. Some mathematical properties of the model – in particular the epidemic threshold $$R_0$$ which determines the goal of public health interventions – are also presented. Though the model couples two transmission routes of HIV, the approximation $$R_0\simeq \max\{R^{\mathrm{IDU}}_0, R^{\mathrm{sex}}_0\}$$, with closed formulas for $$R^{\mathrm{IDU}}_0$$ and $$R^{\mathrm{sex}}_0$$, 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.

##### MSC:
 92D30 Epidemiology 35Q92 PDEs in connection with biology, chemistry and other natural sciences