Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., H-6720 Szeged, Hungary.
Math Biosci Eng. 2019 May 21;16(5):4506-4525. doi: 10.3934/mbe.2019225.
In this paper we consider a model for the spread of a sexually transmitted disease considering sexual transmission and spread via infected needles among intravenous drug users. Besides the transmission among drug users, we also consider sexual contacts between intravenous drug users and non-drug users. Furthermore, the needles are considered as a vector population. For several European countries, a sharp increase of sexually transmitted diseases was reported and several others are rated as endangered based on the number of syringes given out per intravenous drug users per year. The main purpose of the paper is to investigate the dynamics of this model including the effect of needle exchange and study the risk of an increased transmission among non-drug users, induced by the reduction of the needle exchange program. Following the determination of the basic reproduction number R it is shown that all solutions tend to the unique disease-free equilibrium if R < 1. We also prove that the disease persists in the human population if R > 1. Our numerical simulations, based on real life and hypothetical data for HIV, suggest that a decrease in the rate of the distribution and discharge rate of new needles might imply that the considered disease is becoming endemic in the considered human population of drug users and non-drug users. A variant of our model with time- variable needle distribition parameter is fitted to recent HIV data from Hungary to give a forecast for the number of infected in the following years.
在本文中，我们考虑了一个性传播疾病传播模型，该模型考虑了性传播以及静脉注射吸毒者之间受感染的针头传播。除了吸毒者之间的传播之外，我们还考虑了静脉注射吸毒者与非吸毒者之间的性接触。此外，针头被视为一个载体种群。有几个欧洲国家报告了性传播疾病的急剧增加，而根据每年每个静脉注射吸毒者分发的注射器数量，其他几个国家的情况被认为是危险的。本文的主要目的是研究该模型的动力学，包括针具交换的效果，并研究由于减少针具交换计划而导致非吸毒者之间传播风险增加的情况。在确定基本繁殖数 R 后，我们证明如果 R < 1，则所有解都趋于唯一的无病平衡点。我们还证明，如果 R > 1，则疾病会在人群中持续存在。我们基于 HIV 的真实生活和假设数据的数值模拟表明，新针头分配和排放速度的降低可能意味着所考虑的疾病在考虑的吸毒者和非吸毒者人群中成为地方病。我们对具有时变针头分布参数的模型进行了变体拟合，以根据匈牙利最近的 HIV 数据对未来几年的感染人数进行预测。
