Algebraic Biology
Algebraic Biology
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代数生物学
DOI：
10.1007/978-3-540-85101-1_11
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
McCaig C
中科院分区：
文献类型：
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作者：
McCaig C
众所周知，人口不可能无限制地增长，限制增长的是个人之间对资源的竞争。尽管几个世纪以来人们都很感兴趣，但如何最好地模拟密度依赖的人口增长这个问题仍然没有明确的答案。我们在这里通过使用过程代数WSCCS表示的一些基于个体的种群模型来解决这个问题。这些模型的优点是，它们可以明确地基于对个体相互作用的观察。从我们的概率模型中，我们使用一种正式和严格的基于重写的方法推导出表达总体种群动态的方程。这些方程很容易与传统上使用的确定性常微分方程模型进行比较，并允许对那些ODE模型进行评估，挑战它们对系统动力学的假设。此外，该方法还应用于流行病学，将人口增长与疾病传播结合起来。
It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread.