Coronavirus Disease (COVID-19) Identification Time Analysis Using Queueing Model (Preprint)

BACKGROUND The article presents an application of a model of queues in series queueing system under overloading conditions to estimate the time of detection and identification of coronavirus (COVID-19) infections. OBJECTIVE The objective is to present a simplified probabilistic model for assessing the general tendency to estimate the period of time needed to detect and identify already infected citizens before the treatment process really begins. METHODS The law of the iterated logarithm is proved for such a system, which shows that the general identification process corresponds to the law of iterated logarithm. RESULTS Some numerical examples of a different number of evaluation parameters are provided. CONCLUSIONS The modelling results showed that the sojourn time of the patient in the process of coronavirus investigation/detection/identification and treatment in the case of imbalance in the system as a whole increase in accordance with the law of the iterated logarithm. Even if the process of the treatment phases is well arranged and generally balanced, in case of the rate of investigation/detection/identification is lower than the rate of infection, the total number of already infected and unidentified citizens will increase in accordance with the law of the iterated logarithm.

ANALYSIS AND OPTIMIZATION OF BLOOD-TESTING PROCEDURES

This paper is devoted to the performance analysis and optimization of blood testing procedures. We present a queueing model of two queues in series, representing the two stages of a blood-testing procedure. Service (testing) in stage 1 is performed in batches, whereas it is done individually in stage 2. Since particular elements of blood can only be stored and used within a finite time window, the sojourn time of blood units in the system of two queues in series is an important performance measure, which we study in detail. We also introduce a profit objective function, taking into account blood acquisition and screening costs as well as profits for blood units, which were found uncontaminated and were tested fast enough. We optimize that profit objective function w.r.t. the batch size and the length of the time window.