Estimating Optimum Length of Stay in a Hospital to Control the Infection Spread during an Epidemic Using Left-Right Truncated Poisson Model

Background: The unprecedented havoc of COVID-19 pandemic stressed medical infrastructure of every affected country. The developing countries were more affected as their already inadequate medical resources were strained further. Material and Methods: In order to estimate the time of onset of recovery through the period of hospitalisation stay, the retrospective data on the number of days that 83 COVID-19 patients stayed in a hospital in New Delhi, India was obtained. A Left-Right Truncated Poisson Distribution Model (LRTPD) was developed to estimate the average number of days that patients had to spend in the hospital before the onset of recovery and they were no longer infected. Left truncation is on the ‘u’ left most classes of the random variable and right truncation is after ‘v’ classes. The parametric estimates of the LOS were validated using the Monte-Carlo method. Results and Conclusion: The models suggested that if appropriate truncation limits (both the data-specific and as per expert advice) are used in case of critical medical emergencies, approximately 90 percent of the patients will be able to get hospital admission, without over-burdening the hospital infrastructure. The median recovery onset time/ Length of stay (LOS) obtained using the Kaplan-Meier estimator was consistent with the results of the parametric modeling and simulation. However, the Kaplan-Meier method overestimated the mean LOS as compared to the parametric methods.