This article reviews the essential role of mathematical models in understanding and combatting the pandemic of novel coronaviruses, in particular focusing the advance in the use of mathematical models in disease control in Japan. Highlighting the integral role of mathematical models in public health, the article introduces a model that factors in the heterogeneity of infectious contacts, concentrating on the effectiveness of testing and isolation, alongside a model that involves economic losses. The models exhibit how, given such heterogeneity, milder behavioral restrictions can still achieve suppression, rigorous testing and isolation can effectively curb the spread, and containment measures can mitigate economic losses. These models aid in grasping the complicated dynamics of disease transmission and optimizing interventions. The knowledge of population ecology is also considered effective for public health in statistical analysis, organizing concepts using dynamic mathematical models, which lead to policy proposals and deepen understanding. Evolution theory may help the understanding of virulence subject to change. However, effective prevention necessitates not only models but also the practical implementation of efficacious measures. The cooperation of various disciplines is particularly crucial in achieving a balance between health measures, economic interests, and human rights. Moreover, the article acknowledges the limitations of models and underscores the significance of real-world execution. Overall, the article advocates for a broader outlook to tackle future pandemics and related challenges, underscoring the importance of ongoing academic cooperation and global governance to effectively address emerging infectious diseases and their far-reaching implications.