Abstract
The entire world has been affected by the outbreak of COVID-19 since early 2020. Human carriers are largely the spreaders of this new disease, and it spreads much faster compared to previously identified coronaviruses and other flu viruses. Although vaccines have been invented and released, it will still be a challenge to overcome this disease. To save lives, it is important to better understand how the virus is transmitted from one host to another and how future areas of infection can be predicted. Recently, the second wave of infection has hit multiple countries, and governments have implemented necessary measures to tackle the spread of the virus. We investigated the three phases of COVID-19 research through a selected list of mathematical modeling articles. To take the necessary measures, it is important to understand the transmission dynamics of the disease, and mathematical modeling has been considered a proven technique in predicting such dynamics. To this end, this paper summarizes all the available mathematical models that have been used in predicting the transmission of COVID-19. A total of nine mathematical models have been thoroughly reviewed and characterized in this work, so as to understand the intrinsic properties of each model in predicting disease transmission dynamics. The application of these nine models in predicting COVID-19 transmission dynamics is presented with a case study, along with detailed comparisons of these models. Toward the end of the paper, key behavioral properties of each model, relevant challenges and future directions are discussed.