We propose a simple deterministic, differential equation-based, SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two populations of susceptible persons, one which obeys confinement and for which the infection rate does not exceed 1, and a population which, being non confined for various imperatives, can be substantially more infective. The model, initially formulated as a differential system, is discretised following a specific procedure, the discrete system serving as an integrator for the differential one. Our model is calibrated so as to correspond to what is observed in the COVID-19 epidemic, for the period from February 19 to April 16.

Several conclusions can be reached, despite the very simple structure of our model. First, it is not possible to pinpoint the genesis of the epidemic by just analysing data from when the epidemic is in full swing. It may well turn out that the epidemic has reached a sizeable part of the world months before it became noticeable. Concerning the confinement scenarios, a universal feature of all our simulations is that relaxing the lockdown constraints leads to a rekindling of the epidemic. Thus, we sought the conditions for the second epidemic peak to be lower than the first one. This is possible in all the scenarios considered (abrupt or gradualexit, the latter having linear and stepwise profiles), but typically a gradual exit can start earlier than an abrupt one. However, by the time the gradual exit is complete, the overall confinement times are not too different. From our results, the most promising strategy is that of a stepwise exit. Its implementation could be quite feasible, with the major part of the population (perhaps, minus the fragile groups) exiting simultaneously, but obeying rigorous distancing constraints.

我们提出了一个基于确定性，基于微分方程的简单SIR模型，以研究各种限制策略对最致命的流行病的影响。当前的COVID-19大流行激发了我们的方法。主要假设是存在两个易感人群，其中一个服从限制并且其感染率不超过1，并且该人群不受各种命令的限制，实际上具有更大的感染力。最初公式化为微分系统的模型按照特定的过程离散化，离散系统充当微分系统的积分器。我们的模型经过校准，以对应于2月19日至4月16日期间COVID-19流行病中观察到的情况。

尽管我们模型的结构非常简单，但仍可以得出几个结论。首先，不可能仅通过分析流行病全面爆发时的数据来查明流行病的成因。很有可能事实证明，这种流行病在变得明显之前就已经传播到世界相当大的一部分。关于禁闭情景，我们所有模拟的一个普遍特征是放宽锁定约束会导致该流行病重新燃起。因此，我们寻求使第二个流行病高峰低于第一个流行病高峰的条件。在所有考虑的情况下（突然或逐步退出，后者具有线性和逐步分布），这都是可能的，但是通常逐渐退出可以比突然退出更早开始。但是，当逐步退出完成时，整体禁闭时间没有太大差异。从我们的结果来看，最有希望的策略是逐步退出的策略。它的实施可能是相当可行的，同时大部分人口（也许减去脆弱的群体）同时退出，但要遵守严格的距离限制。