Sabbatino Michela, De Reggi Simone, Pugliese Andrea
Department of Mathematics, University of Trento, Via Sommarive 14, Povo, 38123, Trento, Italy.
CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100, Udine, Italy.
Bull Math Biol. 2025 Jan 3;87(2):22. doi: 10.1007/s11538-024-01387-w.
One of the strategies used in some countries to contain the COVID-19 epidemic has been the test-and-isolate policy, generally coupled with contact tracing. Such strategies have been examined in several simulation models, but a theoretical analysis of their effectiveness in simple epidemic model is, to our knowledge, missing. In this paper, we present four epidemic models of either SIR or SEIR type, in which it is assumed that at fixed times the whole population (or a part of the population) is tested and, if positive, isolated. We find the conditions for an epidemic to go extinct under such a strategy; for these types of models we provide an appropriate definition of , that can be computed either analytically or numerically. Finally, we show numerically that the final-size relation of SIR models approximately holds for the four models, over a large parameter range.
一些国家用于控制新冠疫情的策略之一是检测与隔离政策，通常还会结合接触者追踪。此类策略已在多个模拟模型中进行了研究，但据我们所知，在简单疫情模型中对其有效性的理论分析尚付阙如。在本文中，我们提出了四个SIR或SEIR类型的疫情模型，其中假设在固定时间对全体人口（或部分人口）进行检测，若检测呈阳性则进行隔离。我们找出了在此类策略下疫情灭绝的条件；对于这些类型的模型，我们给出了一个合适的基本再生数（$R_0$）定义，其既可以通过解析方法计算，也可以通过数值方法计算。最后，我们通过数值方法表明，在较大的参数范围内，SIR模型的最终规模关系在这四个模型中大致成立。
