This paper presents a novel model to detect the COVID-19 infected person from a Markovian feedback persons in a limited department capacity. The persons arrive one by one to the department and the balking and the retention of reneged person approaches are considered. There exists one server presents the service to these persons according to first-come, first-served (FCFS) discipline. An efficient and novel algorithm is presented to get the exact value of the probability of n persons in the department at any time interval. This algorithm depends on the Laplace transform to solve a probabilistic dynamical system of differential equations. By considering the exponential detection function and if the probability of the infected person in the department is equal to the probability of each one, then this algorithm is useful to obtain the detection probability of the infected one. Under steady state, the detection probability of the infected person is described. The usefulness of this model is illustrated for different capacities by using a numerical example to describe the behavior of probabilities of the persons in the department, the detection probabilities of the infected person as functions in time, and the mean time to detection.

中文翻译：

---

基于概率动态系统开发 COVID-19 感染者检测模型

本文提出了一种新颖的模型，用于在有限的部门能力中从马尔可夫反馈人员中检测 COVID-19 感染者。人员一一到达部门，并考虑拒绝和保留拒绝人员的方法。存在一个服务器根据先到先服务 (FCFS) 规则向这些人提供服务。提出了一种高效新颖的算法来获得n的概率的精确值任何时间间隔内的部门人员。该算法依赖于拉普拉斯变换来求解概率动力系统的微分方程。通过考虑指数检测函数，如果科室感染者的概率等于每个人的概率，那么该算法对于获得感染者的检测概率是有用的。在稳态下，描述了感染者的检测概率。通过数值例子来描述该模型在不同能力下的有用性，描述了部门人员的概率行为、感染者的检测概率作为时间函数以及平均检测时间。