COVID-19 is caused by a coronavirus called SARS-CoV-2. Many countries around the world implemented their own policies and restrictions designed to limit the spread of Covid-19 in recent months. Businesses and schools transitioned into working and learning remotely. In the United States, many states were under strict orders to stay home at least in the month of April. In recent weeks, there are some significant changes related restrictions include social-distancing, reopening states, and staying-at-home orders. The United States surpassed 2 million coronavirus cases on Monday, June 15, 2020 less than five months after the first case was confirmed in the country. The virus has killed at least 115,000 people in the United States as of Monday, June 15, 2020, according to data from Johns Hopkins University. With the recent easing of coronavirus-related restrictions and changes on business and social activity such as stay-at-home, social distancing since late May 2020 hoping to restore economic and business activities, new Covid-19 outbreaks are on the rise in many states across the country. Some researchers expressed concern that the process of easing restrictions and relaxing stay-at-home orders too soon could quickly surge the number of infected Covid-19 cases as well as the death toll in the United States. Some of these increases, however, could be due to more testing sites in the communities while others may be are the results of easing restrictions due to recent reopening and changed policies, though the number of daily death toll does not appear to be going down in recent days due to Covid-19 in the U.S. This raises the challenging question: How can policy decision-makers and community leaders make the decision to implement public policies and restrictions and keep or lift staying-at-home orders of ongoing Covid-19 pandemic for their communities in a scientific way? In this study, we aim to develop models addressing the effects of recent Covid-19 related changes in the communities such as reopening states, practicing social-distancing, and staying-at-home orders. Our models account for the fact that changes to these policies which can lead to a surge of coronavirus cases and deaths, especially in the United States. Specifically, in this paper we develop a novel generalized mathematical model and several explicit models considering the effects of recent reopening states, staying-at-home orders and social-distancing practice of different communities along with a set of selected indicators such as the total number of coronavirus recovered and new cases that can estimate the daily death toll and total number of deaths in the United States related to Covid-19 virus. We compare the modeling results among the developed models based on several existing criteria. The model also can be used to predict the number of death toll in Italy and the United Kingdom (UK). The results show very encouraging predictability for the proposed models in this study. The model predicts that 128,500 to 140,100 people in the United States will have died of Covid-19 by July 4, 2020. The model also predicts that between 137,900 and 154,000 people will have died of Covid-19 by July 31, and 148,500 to 169,700 will have died by the end of August 2020, as a result of the SARS-CoV-2 coronavirus that causes COVID-19 based on the Covid-19 death data available on June 13, 2020. The model also predicts that 34,900 to 37,200 people in Italy will have died of Covid-19 by July 4, and 36,900 to 40,400 people will have died by the end of August based on the data available on June 13, 2020. The model also predicts that between 43,500 and 46,700 people in the United Kingdom will have died of Covid-19 by July 4, and 48,700 to 51,900 people will have died by the end of August, as a result of the SARS-CoV-2 coronavirus that causes COVID-19 based on the data available on June 13, 2020. The model can serve as a framework to help policy makers a scientific approach in quantifying decision-makings related to Covid-19 affairs.