SEIR model in which infected people flow in from the outside

Extended SEIR model with inflow and outflow for each state (Susceptible S / Exposed E / Infectious I / Recovered R). However, differences in condition between travelers and local people cannot be taken into account.

SEIR circuit lattice model with inflow and outflow in and out of the region

（Ohsawa & Hayashi 2021 https://arxiv.org/abs/2104.09719)

Point (1) Consider the possibility that the movement of people in any state may affect the spread of infection at the destination. In addition, we have developed a SEIR circuit lattice model that can take into account the difference in the state of the travelers and the local people.

## ※Results when using the S/E/I/R ratio of the departure area as the S/E/I/R of the destination at the initial stage, but even with a more realistic reset, the following trends do not change.

Point (3) If the vaccination speed is increased, the risk of interprefectural movement will be significantly reduced (If the condition of point (2) is observed, the effect of suppressing the spread of infection was discovered at the boundary of 0.4% / day of the population)

## Q & A

Q1: Shouldn't the number of infected cases increase as the number of incomers increases?

A: It's just a preconceived idea. A model that overlooks the effect that the increase in the number of infected cases "may diminish" due to incoming group of people who have been vaccinated and have a low proportion of infected persons (In the settings where a: departure area, b: destination area, Number of susceptible people S, Number of exposed people E, Number of infectious people I, and Number of population N, the rate of increase of E should be Rt Sa Ib /(Na+Na→b), not Rt Sa Ib / Na, otherwise it doesn't make sense) accumulates errors and sees the result that the number of infected cases are more than it actually is. In the setting where vaccination speed pv >0.4%/day, it "may diminish", not "diminishes", so the trend that the number of infected cases decreases as incomers increase is not significant (p>0.2). It is a weaker correlation than in the setting where pv <0.4%/day, "the number of infected cases increases as incomers increase" (p>0.05).

Q２: Is the increase in the number of people from overseas and the interprefectural movement modeled in the same way?

A: This is also different. People’s interprefectural movement is set to return in about 2~3 days after the movement, and since they are a part of the total population of the country, they are included in the population parameter of cumulative infected cases here. On the other hand, people from overseas stay for about 3 weeks and are not included in the cumulative infected cases because they will leave Japan when they return home. These things are shown as differences in the method of giving initial values and the method of aggregation.

Q3：What is the practical significance of these results?

A：The same level of vaccination can significantly suppress the spread of infection by maximizing the average value of Rt in the focus area when the vaccination speed is slow, or by maximizing the conditional entropy Hc when the speed gets faster. In particular, Hc can be easily calculated if the population distribution is known. Predicting Rt is more difficult than estimating Hc.

A:If the vaccination speed pv is increased, economic activities including interprefectural movement can be activated, and the policy-making equation "appropriate action of the people = f (pv)" can be taken into consideration.