Corson S, Greenhalgh D, Hutchinson S J
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
J Math Biol. 2013 Mar;66(4-5):935-78. doi: 10.1007/s00285-012-0577-y. Epub 2012 Aug 28.
Studies of hepatitis C virus (HCV) infection amongst injecting drug users (IDUs) have suggested that this population can be separated into two risk groups (naive and experienced) with different injecting risk behaviours. Understanding the differences between these two groups and how they interact could lead to a better allocation of prevention measures designed to reduce the burden of HCV in this population. In this paper we develop a deterministic, compartmental mathematical model for the spread of HCV in an IDU population that has been separated into two groups (naive and experienced) by time since onset of injection. We will first describe the model. After deriving the system of governing equations, we will examine the basic reproductive number R₀, the existence and uniqueness of equilibrium solutions and the global stability of the disease free equilibrium (DFE) solution. The model behaviour is determined by the basic reproductive number, with R₀ = 1 a critical threshold for endemic HCV prevalence. We will show that when R₀ ≤ 1, and HCV is initially present in the population, the system will tend towards the globally asymptotically stable DFE where HCV has been eliminated from the population. We also show that when R₀ > 1 there exists a unique non-zero equilibrium solution. Then we estimate the value of R₀ from epidemiological data for Glasgow and verify our theoretical results using simulations with realistic parameter values. The numerical results suggest that if R₀ > 1 and the disease is initially present then the system will tend to the unique endemic equilibrium.
针对注射吸毒者（IDU）群体中丙型肝炎病毒（HCV）感染情况的研究表明，该群体可分为两个具有不同注射风险行为的风险组（初次注射者和有经验者）。了解这两组之间的差异以及它们如何相互作用，有助于更合理地分配预防措施，以减轻该群体中HCV的负担。在本文中，我们针对HCV在一个已按注射起始时间分为两组（初次注射者和有经验者）的IDU群体中的传播情况，建立了一个确定性的、 compartmental数学模型。我们将首先描述该模型。在推导控制方程组之后，我们将研究基本再生数R₀、平衡解的存在性和唯一性以及无病平衡（DFE）解的全局稳定性。模型行为由基本再生数决定，R₀ = 1是HCV地方流行率的临界阈值。我们将证明，当R₀ ≤ 1且HCV最初存在于群体中时，系统将趋向于全局渐近稳定的DFE，即HCV已从群体中消除的状态。我们还表明，当R₀ > 1时存在唯一的非零平衡解。然后，我们根据格拉斯哥的流行病学数据估计R₀的值，并使用实际参数值进行模拟来验证我们的理论结果。数值结果表明，如果R₀ > 1且疾病最初存在，那么系统将趋向于唯一的地方流行平衡。
