The novel coronavirus, referred to as SARS-COV 2, originated in Wuhan, China in December 2019. Since many Health Care Workers (HCW) and general public lost their lives. The only thing which can prevent from being infected is social distancing and wearing of mask (N95) and wearing of mask has its own adverse effects. This is a retrospective study conducted in the

COVID-19 disease has emerged as one of the life threatening threat to the society. It is caused by a novel beta coronavirus. It began as unidentified pneumonia of unknown aetiology in Wuhan City, Hubei province in China emerged in December 2019. No vaccine has been produced till now. Mathematical models are used to study impact of different measures used to decrease pandemic. Mathematical models have been designed to estimate the numbers of spreaders in different scenarios in the present manuscript. In the present manuscript, three different mathematical models have been proposed with different scenarios such as screening, quarantine and NPIs for estimating number of virus spreaders. the analysis shows that the numbers of COVID-19 patients will be more without screening the peoples coming from other countries. Since, every people suffering with COVID-19 disease are spreaders. The screening and quarantine with NPIs have been implemented to study their impact on the spreaders. It has been found that NPI measures are able to reduce number of spreaders. The NPI measures reduces the growth of the spread function and providing decision makers more time to prepare with in dealing of the disease.

COVID-19 is well known to everyone in the world. It has spread around the world. No vaccine or antiviral treatment is available till now. COVID-19 patients are increasing day by day. All countries have adopted social distancing as a preventive measure to reduce spread. It becomes necessary to estimate the number of peoples going to be affected with COVID-19 in advance so that necessary arrangements can be done. Mathematical models are used to provide early disease estimation based on limited parameters. In the present manuscript, a novel mathematical model with a social distancing parameter has been proposed to provide early COVID-19 spread estimation. The model has been validated with real data set. It has been observed that the proposed model is more accurate in spread estimation.

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.

We have proposed a new mathematical method, the SEIHCRD model, which has an excellent potential to predict the incidence of COVID-19 diseases. Our proposed SEIHCRD model is an extension of the SEIR model. Three-compartments have added death, hospitalized, and critical, which improves the basic understanding of disease spread and results. We have studied COVID-19 cases of six countries, where the impact of this disease in the highest are Brazil, India, Italy, Spain, the United Kingdom, and the United States. After estimating model parameters based on available clinical data, the model will propagate and forecast dynamic evolution. The model calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries' age-category scenario. The model calculates two types of Case fatality rate one is CFR daily, and the other is total CFR. The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection. The SEIHCRD model outperforms the classic ARX model and the ARIMA model. RMSE, MAPE, and R squared matrices are used to evaluate results and are graphically represented using Taylor and Target diagrams. The result shows RMSE has improved by 56%-74%, and MAPE has a 53%-89% improvement in prediction accuracy.