Since quarantine and isolation have been identified as key factors for the recovery of any individual tested positive for coronavirus disease 2019 (COVID-19), in this study the dynamics modelling quarantine and isolation are formulated. By considering the principles of dynamics modelling quarantine and isolation with respect to COVID-19 spread, we derive, extend, and analyze, the formulation of the quarantine and isolation scenario with the aim of clarifying the implications that may arise from the process of quarantine and isolation, depending on the day a host tested positive for COVID-19. Thus, our formulation is extended to a system of fractional parabolic partial differential equations (FPPDEs) to enable us to present adequate and unique information of our formulation through a well-posed numerical method. Therefore, we hope our contribution in this study is helpful to the society at large.