The entire world is spreading of coronavirus -COVID-19 has increased exponentially across the globe, and still, no vaccine is available for the treatment of patients. The crowd has grown tremendously in the hospitals where the facilities are minimal. The queue theory is applied for the Single-server system and its self-similarity existence in a queue used to identify the queue time, waiting time, and Hurst parameter by different patient arrivals methods Health care center in our local area located in Hosapete, Ballari district, Karnataka. Due to more arrivals to the health care center for the identification and confirmation of disease covid-19. This study paper presents a sequential queuing model for estimating infections' detection and identification in severe loading conditions. The goal is to offer a simplified probabilistic model to determine the general behavior to predict how long the treatment cycle will diagnose and classify people already tested and get negative or positive results. For this type of Method, there are some graphical representations of the various measurement criteria. The modelling results showed that the patient's waiting period in the course of inquiries, detections, detecting, or treating COVID-19 in the event of imbalances in the system as a whole rise following the logarithm rule.