应激作用下免疫应答的定性数学模型
A qualitative mathematical model of the immune response under the effect of stress
摘要：
在过去的几十年里，人们对大脑和身体之间联系的兴趣显著增长。例如，在心理神经免疫学中，许多研究从医学或免疫学以及生物化学的角度将来自许多不同来源和情况的压力与免疫系统的变化联系起来。在本文中，我们确定了重要的行为之间的相互作用的免疫系统和压力的医学研究，并寻求代表他们定性的一个范例，但简单的数学模型。为此，我们开发了一个微分方程模型，两个方程的感染水平和免疫系统，它集成了压力的影响作为一个额外的参数。我们能够在压力很小的情况下重现一个稳定的健康状态，在压力很大的情况下重现一个在健康和感染状态之间的振荡状态，在压力很大的情况下重现一个“精疲力竭”或稳定的生病状态。不同的动力学之间的机制是由两个鞍结在周期（SNIC）分岔控制。此外，我们的模型能够在从中等压力下降到低压力时捕获诱导的感染，并且它预测在最终达到耗尽状态之前增加感染期。
英文摘要：
In the last decades, the interest to understand the connection between brain and body has grown notably. For example, in psychoneuroimmunology many studies associate stress, arising from many different sources and situations, to changes in the immune system from the medical or immunological point of view as well as from the biochemical one. In this paper we identify important behaviours of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end we develop a differential equation model with two equations for infection level and immune system, which integrates the effects of stress as an additional parameter. We are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a "burn-out" or stable sick state for extremely high stress. The mechanism between the different dynamics is controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing before eventually reaching a burn-out state.
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