论文标题
药物使用的数学建模：两种成瘾性药物的单物质依赖的动力学
Mathematical Modeling of Drug Use: The Dynamics of Monosubstance Dependence for Two Addictive Drugs
论文作者
论文摘要
根据在该领域所做的以前的工作，我们建立了一个动态系统，该系统描述了孤立人群中的药物成瘾的变化，同时可以同时获得两种成瘾性物质。然后，我们使用我们的模型来研究系统是否捕获了切换毒品习惯的用户的过程。该项目的动机之一是数学地检查被猜想的猜想是，沉迷于较不成名的物质将有效地导致个人依赖更令人上瘾和可能更危险的药物。 我们介绍了其他假设，根据该假设，我们的模型被简化为竞争性的Lotka-Volterra系统。这个动力学系统具有三个或四个固定点，然后稳定性就对成瘾性物质之间的竞争结果以及人群中个人的命运产生了含义。从对还原模型的分析中，我们确定实际上存在捕获以下动态的参数状态：取决于药物偏好的初始分布；两种药物的使用都会消失，其中一种药物的使用将变得普遍，或者对两种药物的成瘾都将共存。
Based on previous work done in this field, we build a dynamical system that describes changes in drug addiction in an isolated population when two addictive substances are available simultaneously. We then use our model to investigate whether the system captures the process of users switching drug habits. One of the motivations for this project is to mathematically check the conjecture that being addicted to a less-addictive substance will effectively lead individuals to become dependent on more addictive and potentially more dangerous drugs. We introduce additional assumptions, under which our model is reduced to a competitive Lotka-Volterra system. This dynamical system has three or four fixed points, stability of which then gives an implication about the outcomes of the competition between addictive substances and, therefore, the fate of individuals in the population. From the analysis of the reduced model, we determine that there actually exist parameter regimes that capture the following dynamics: depending on the initial distribution of the drug preference; either the use of both drugs will die out, the usage of one of the drugs will become prevalent, or addictions to both drugs will coexist.
