A Time-dependent mathematical model for COVID-19 transmission dynamics and analysis of critical and hospitalized cases with bed requirements

A time-dependent SEAIHCRD model is the extension of the SEIR model, which includes some new compartment that is asymptomatic infectious people, hospitalized people, critical people, and dead compartments. In this article, we analyzed six countries, namely the United States, Brazil, India, South Africa, Russia, and Mexico. A time-dependent SEAIHCRD model calculates the magnitude of peaks for exposed people, asymptomatic infectious people, symptomatic infectious people, hospitalized people, the number of people admitted to ICUs, and the number of COVID-19 deaths over time. It also computes the spread scenario and endpoints of disease. The proposed model also involves asymptomatic infectious individuals. To estimate the various parameters, we first collect the data and fit that using the Lavenberg-Marquardt model for death cases. Then we calculate infection rate, recovery rate, case fatality rate, and the basic reproduction number over time. We calculate two types of case fatality rates: one is the daily case fatality rate, and the other is the total case fatality rate. The proposed model includes the social distance parameter, various age classes, hospital beds for severe cases, and ICU beds or ventilators for critical cases. This model will be useful to determine various essential parameters such as daily hospitalization rate, daily death rates, including the requirement of normal and ICU beds during peak days of infection.