COVID-19 has become a deadly pandemic in the recent times claiming millions of lives worldwide in a grievous manner. Most of the countries in the world have limited number of medical resources (hospitals, beds, ventilators, etc.), and in the case of large outbreak, it becomes very difficult to provide treatment to every infected individual. In this study, we propound a mathematical model where we classify the infected into two subcategories—asymptomatic and symptomatic. This model further accounts for the effect of limited medical resource for infected people and using face masks in combating the pandemic. Focusing on these aspects, we analyze the model and exploit the available data for assessing the pattern in three most affected countries, namely USA, India and Brazil. The developed model is calibrated to fit data for these three countries and estimate the transmission rate of symptomatic, asymptomatic individuals. The rate at which the individuals who are quarantined recover is estimated as well. Along with these estimations, a comparative study based on the basic reproduction number estimated for the three countries is presented. Standard methods of sensitivity analysis are performed to analyze the ways in which basic reproduction number is impacted upon due to changes in different parameters of the model. Further, we obtain disease-free equilibrium and endemic equilibrium of the model. It is observed that backward bifurcation occurs if the capacity of treatment is small and bistable equilibria are shown that makes the system more sensitive to the initial conditions. Sufficient conditions for the local asymptomatic stability of the endemic equilibrium and disease-free equilibrium of the system are obtained. The results of this study imply that to curb the severity of the increasing cases of the disease in these countries, effective strategies to control disease spread should be implemented so that the basic reproduction number can be decreased below the threshold value which is certainly less than unity. The use of protective masks in public is shown to be an important preventive measure to lower disease transmission rate. Also, the quantity of medical resources should increase so that every infected person can get better treatment. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.