Based on the situation around April 28, we simulated the future spread of COVID-19 infection in New York City and Tokyo using MATLAB.
Absent any particular progress, such as the development of an effective vaccine or a more aggressive lockdown, the number of infected people will have risen to 280,000 in eight months' time and the number of deaths will exceed 150,000 in NY. In the case of Tokyo, the "voluntary restraint (Stay at Home campaign)"(*) during the Golden Week (29 April ~6 May) was effective and the number of infected people increased or decreased somewhat after the holidays, but the number of infected people and the total number of deaths was limited to about 600 and 700 by the beginning of the next year, respectively.
The mathematical model used in this paper is the so-called SEIR model with time delay. The key to the simulation is how to set up the dozen or so parameters of the model. In general, the main purpose of the mathematical model analysis is to provide such qualitative questions as
(1) Does the model have an equilibrium point?
(2) The stability of multiple equilibrium points (whether they converge to some value over time or diverge).
(3) Does a periodic phenomenon appear?, etc.
Quantitative analysis (e.g., electrical circuits) is sometimes performed precisely, but social phenomena or ecological models tend to be qualitative because the parameters are difficult to quantify. However, even in the qualitative analysis, the results are sufficiently informative for us. Therefore, the simulation in this paper means that the parameters of the model were found based on the real data. It is better to understand the transition of the future variables as a quadratic outcome.
　 It must be a researcher's effort to create "collective knowledge" for the unknown. The reader is expected to make better calculations and predictions using the attached MATLAB code.

(*) Because Japan lacks an enforceable legal system, the head of the government has not been given an enforced policy of lockdown like USA.