Analyzing the effects of quarantine, isolation, and vaccination on the spread of COVID-19 via a mathematical model

The main COVID-19 control strategies presently practiced are maintaining social distancing, quarantining suspected exposures, and isolating infectious people. In this paper, a deterministic compartmental mathematical model is proposed considering these three control strategies. Based on the proposed model the effect of vaccination on the suppression of the disease is discussed. Critical vaccination rate and vaccinated population size relevant to disease suppression are determined based on the proposed mathematical model. Different forms of the most used key term in infectious disease modelling, reproduction number, are determined relevant to the proposed model. Sensitivity analysis of the reproduction numbers is done to identify model parameters mostly affecting the spread of the disease. Based on the reproduction number of the model disease controlling parameter regions are determined and graphical representations of those parameter regions are presented. Based on the results of the proposed mathematical model, it is observed that earlier implementation of the vaccination process is helpful to better control the disease. However, it takes considerable time to invent successful vaccinations for newly out-breaking diseases like COVID-19. Therefore, it took considerable time to start the vaccination process for COVID-19. It is observed that after starting a vaccination process at a particular rate it should continue until the vaccinated population reaches a critical size.