In the end of 2019, the emergence of COVID-19 was reported and confirmed for the first time, and it triggered an international pandemic. In Japan, the strong tendency to spread of infection is still continuing. The Japanese Government has been raised two concepts to overcome this difficulty. One is the thorough measures to control of the spread of infection and the other is the economic recovery. The government has carried out the corresponding two policies: the use of COVID-19 Contact-Confirming Application (COCOA) and the application of “GoTo Travel Campaign”. We focus on these two policies and study an ideal situation, which enables us to balance more economic recovery and control of the spread of infection. To pursue this goal, we propose a mathematical model to estimate these policies’s effects and conduct simulations of 28 scenarios. In addition, we analyze each result of the simulation and investigate characteristics of each situation. As a result, we clearly find that it required that not only the increasing the using rate of COCOA but also a positive change of people’s behaviors and awareness.