Griffiths J, England T, Williams J
School of Mathematics, Cardiff University, UK.
IMA J Math Appl Med Biol. 2000 Dec;17(4):295-310.
For many years compartmental models have provided useful insights into the spread of epidemics. Such models are usually fairly easy to set up, but even the simpler models have the disadvantage that they are intractable to analytic solution. In this paper we examine models of the HIV/AIDS epidemic, and show that the equations may be linearized in a piecewise manner over time, thus allowing analytic solutions to be obtained. Indications of the usefulness of this approach are provided. In particular, an analytic solution gives insight into the mechanism of the epidemic, together with a clearer picture of the sensitivity of results to changes in parameter values. Further, the processes of parameter estimation and the methodology of back-calculation also benefit from the provision of functional forms for the state variables.
多年来， compartments 模型为传染病传播提供了有用的见解。这类模型通常相当容易建立，但即使是较简单的模型也有一个缺点，即难以得到解析解。在本文中，我们研究了艾滋病毒/艾滋病疫情模型，并表明这些方程可以随时间以分段方式线性化，从而能够得到解析解。本文提供了这种方法有用性的相关迹象。特别是，解析解能深入了解疫情的机制，同时更清楚地了解结果对参数值变化的敏感性。此外，参数估计过程和反向计算方法也因状态变量函数形式的提供而受益。
