In the wake of the novel coronavirus, SARS-CoV-19, the world has undergone a critical situation in which grave threats to global public health emerged. Among human populations across the planet, travel restraints, border enforcement measures, quarantine, and isolation provisions were implemented in an attempt to control and limit the spread of the contagion. Decisions on how to implement and enforce various control policies should be determined based on available real-world evidence and theoretical prediction. In this study, we propose a novel exportation- importation epidemic model associated with the quarantine and hospitalized-isolation policies by considering the two-body system: a source country of a contagious disease and a neighboring country that is initially disease-free. The model is first applied to the original COVID-19 data in China, Italy, and the Republic of Korea (ROK) and observed through consistent fitting results with equivalent goodness-of-fit. Then, the data are estimated per the fitting parameters. Driven by these parametric settings and considering the normalized population, the numerical analysis, and epidemiological exploration, this work further elucidates the substantial impact of quarantine policies, healthcare facilities, and the public counter-compliance effect.

In the promptness of the COVID-19 outbreak, it would be very important to observe and estimate the pattern of diseases to reduce the contagious infection. To study this effect, we developed a COVID-19 analytical epidemic framework that combines with isolation and lockdown effect by incorporating five various groups of individuals. Then we analyze the model by evaluating the equilibrium points and analyzing their stability as well as determining the basic reproduction number. The extensive numerical simulations show the dynamics of a different group of the population over time. Thus, our findings based on the sensitivity analysis and the reproduction number highlight the role of outbreak of the virus that can be useful to avoid a massive collapse in Bangladesh and rest of the world. The outcome of this study concludes that outbreak will be in control which ensures the social and economic stability.