RUI: Interacting Particle Systems in Biology

9625126 Schinazi摘要 相互作用粒子系统是可数集（通常是格子）上的空间随机模型。 研究人员使用这些系统来模拟几种生物现象。这些模型中的许多已经在数学、生物学和物理学文献中被考虑过，但很少有严格的结果被证明。到目前为止，大多数关于相互作用粒子系统的数学理论都是针对单调（或吸引）系统的。当人们处理流行病时，单调性并不成立。证明非单调系统的结果是至关重要的，因为我们世界中的许多现象在任何（数学）有用的方式中都不是单调的。 相互作用的粒子系统在研究流行病方面非常有用。例如，研究者提出了以下流行病传播的模型。有一个网格的网站，每个网站要么是空的，健康或感染。健康个体和感染个体在空的最近邻站点上生育健康个体。健康的个体会被最近的邻居感染。健康人和感染者的死亡率不同。这对于像艾滋病这样的流行病来说似乎是足够的，因为感染者可能会生下健康的个体。研究者证明的一个结果是，给定一个足够大的感染率，当且仅当受感染个体的生育率足够高时，流行病才会持续下去。虽然所考虑的模型是对真实的世界的粗略简化，但它确实给出了一个有趣的想法来测试。也就是说，艾滋病流行最具破坏性的国家是否就是受感染者生育率最高的国家？

9625126 Schinazi ABSTRACT Interacting particle systems are spatial stochastic models on a countable set (usually the lattice). The investigator uses these systems to model several biological phenomena. Many of these models have already been considered in the mathematical biology and physics literature but very few rigorous results have been proved. So far most of the mathematical theory about interacting particle systems deals with monotone (or attractive) systems. When one deals with epidemics, monotonicity does not hold. To prove results for non-monotone systems is crucial since so many phenomena in our world are not monotone in any (mathematically ) useful way. Interacting particle systems are very useful in studying epidemics. For instance, The investigator proposes the following model for the spread of an epidemic. There is a grid of sites and each site is either empty, healthy or infected. Healthy and infected individuals give birth to healthy individuals on empty nearest neighbor sites. Healthy individuals get infected by infected nearest neighbors. Healthy and infected individuals die at different rates. This seems adequate for epidemics like the AIDS epidemic for which infected individuals may give birth to healthy individuals. One of the results proved by The investigator is that, given an infection rate which is large enough, the epidemic will persist if and only if the rate at which infected individuals give birth is high enough. While the model considered is a gross simplification of the real world it does give an interesting idea to test. Namely, is it true that the countries where the AIDS epidemic is the most devastating are the countries where the rate at which infected individuals give birth is the highest?