No need to be afraid of infection numbers – Towards post-corona era #2

Assumed layer characteristics
・Households: A network that is fully integrated within a household and completely isolated from other households.
・Occupations: A network of people in the same occupation who adhere to a W-m0 relationship and are connected.
・Schools: Children in the same area and grade level, while adhering to the W-m0 relationship. Network linking them
・Neighbors: A network of agents who are close to each other and adhere to the W-m0 relationship.
・Random: A network that is connected to n people randomly without any specific rules.

Reasons for separating layers
・The loosely and tightly coupled relationships of the network and the concentration and frequency of contact will differ depending on the context of how people are connected.
・It can be installed and removed in different contexts, and can be thinned and amplified, making it easy to use as a material for implementing emergency declarations and examining economic stimulus policies.
・Multi-layered formats are very useful for modeling such events.

※1. v1_det = min(v1, v1 – weeks elapsed since first vaccination* v_det_rate / v_det_term)
※2. v2_det = min(v2, v2 - weeks elapsed since second vaccination * v_det_rate / v_det_term)
※3. v3_det = min(v3, v3- weeks elapsed since third vaccination * v_det_rate / v_det_term)

・Data: Artificial synthesis data from Professor Murata of Kansai University
・Infection transmission model:
　✔️Adopted the SEIRS model after considering multi-agent based vaccine effectiveness.
　✔️Considered the transition of status I from mild to serious illness, and then from serious illness to death
　✔️Calculated when each layer is thinned in half
　✔️One time step was changed to one day based on the average incubation period of the Omicron variant
・Vaccination: Vaccination reduces the transition probability of S/V1/V2/V3 nodes to E by -X%. Vaccine effectiveness declines gradually

The model was revised significantly and one time step was changed to one day. Various parameters were reviewed in association with that. The timing and height of the peaks vary depending on the “extent of contact” and the “frequency of meeting.” If measures to prevent the spread of infections lead to a reasonable degree of self-restraint on actions, the peak is expected from the latter half of February.

If the extent of contact is suppressed and the frequency of meeting is kept to a certain level, even with the strong infectivity of beta 0.4, a peak of about 100,000 people per day, excluding the upper left scenario, is expected, towards bringing infections under control.

In the upper left scenario, infections are controlled in a state of near-herd immunity.

If there is a small risk of severe illness (1/10 that of Delta), the number of people with severe illness in any scenario is expected to be several thousand at most. On the other hand, in the case of large risk, the number may reach 10,000 to 20,000 people after peaking in the latter half of February.

Stay Home -> Stay with Your Community was understood
However, what is the home of Stay Home?

Stay with Your Community
・𝑊 is the upper limit on the maximum number of people met, 𝑚_0 is the number of people met intentionally
→ If 𝑊 increases, the number of infected people increases
→ It is possible to prevent an explosive increase in the number of infected people by establishing communities with people met intentionally (keeping 𝑊 below 2𝑚_0)
= Contact with people outside of the community is dangerous

Previous studies have focused on relationships between people -> also on the risk of infection due to the facility where people are staying
Going to facilities people do not normally go to = change in visited facilities = increase in contact (including indirect contact) with people outside of the community

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

Assumptions
・People’s actions are “movements from facility to facility”
・The characteristics of visited facilities are determined by people’s attributes (occupation x awareness of self-restraint)
Occupations: Divided into the four classifications of university students, employed people, housewives or unemployed people
Awareness of self-restraint: 0, 1, 2, random (With *1, all respondents’ awareness of self-restraint is classified into three stages)

Settings
・People’s attributes (occupation x self-restraint) are
Occupations: Divided into the four classifications of university students, employed people, housewives or unemployed people
Awareness of self-restraint: 0, 1, 2, random (With *1, all respondents’ awareness of self-restraint is classified into three stages)
・Actual number of facilities in Tokyo and its population (*2) multiplied by 1/10,000
・Question about visited facilities (*1):
One day is divided into 11 time zones.
Choose the facility you stayed at during each time zone from 17 options.

※１）Results of a questionnaire survey of 1,288 residents of Tokyo and Kanagawa Prefecture collected by this Ohsawa Group project last fiscal year
※２）

① Decide the action to take that day
Select one at random from the actions classified for the attributes the same as yours (occupation, awareness of self-restraint)
When the visited facility changes is when awareness of self-restraint changes
Changes in awareness of self-restraint are expressed like 0_0_0, +2_+1_-1, r_r_r
(From the left changes in awareness of self-restraint of people with “high,” “medium” and “low” awareness: 0  No change, +n (-n)  n steps up (down) r  select the visited facility randomly)

② Calculation performed for each time step (= 1 day) × 11 times → ①

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

Settings
・Change is r_r_r: Decide visited facility regardless of awareness of self-restraint
・Rate of change of visited facility from 0 to 1 in increments of 0.1
・Changes in visited facilities when infections are spreading and when infections are declining

Insights
・The higher the rate of change, the higher the peak in the number of newly infected people
・The higher the number of people who change their actions, the higher the cumulative number of people infected

The figures in the legend show the proportion of people who changed the facilities they visited, and the changes in visited facilities took 50 days from day 130 to complete.

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

Settings (same as ①)
・Change is r_r_r: Decide visited facility regardless of awareness of self-restraint
・Rate of change of visited facility from 0 to 1 in increments of 0.1
・Changes in visited facilities when infections are spreading and when infections are declining

Insights
・The direction of change is the same as when infections are spreading
・However, the change in the number of infected people in the zone where the rate of change is low is small

The figures in the legend show the proportion of people who changed the facilities they visited, and the changes in visited facilities took 50 days from day 230 to complete.

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

Settings
・Change is x_y_y: Change is dependent on awareness of self-restraint as in the legend below

Insights
・The number of infected people increases when awareness of self-restraint is lowered, like -2_-1_0 or r_-1_0
・The number of infected people decreases when awareness of self-restraint is raised, like 0_0_+ 1 or 0_+1_r
・There is no change when 0_+1_+2

Changes in visited facilities took 50 days from day 130 to complete

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

Settings (same as ③)
・Change is x_y_y: Change is dependent on awareness of self-restraint as in the legend below

Insights
・The number of infected people increases when awareness of self-restraint is lowered, like -2_-1_0 or r_-1_0
・The number of infected people does not decrease even when awareness of self-restraint is raised, like 0_0_+ 1 or 0_+1_r

Changes in visited facilities took 50 days from day 230 to complete

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

From the results of ① and ②
・Before the changes in visited facilities: Most of the people met are people with the same awareness of self-restraint or the same occupation
・After the changes in visited facilities (action regardless of awareness of self-restraint): The frequency of meeting people with different awareness of self-restraint or occupation increases, deviating from Stay with Your Community (SWC) → The number of infected people increases rapidly

From the results of ③ and ④
・There is no change in the number of infected people even if awareness of self-restraint changes to 0_+1_+2:
Awareness of self-restraint is concentrated at one level, and the suppressive effect is offset by the increased risk of infection due to the increase in population density
・Changes in visited facilities are the same as ① and ②: Keeping SWC is the most universal strategy
・Awareness of self-restraint ↓: Normally, number of infected people ↑
・Awareness of self-restraint ↑: When infections are spreading = number of infected people ↓, when infections are declining = number of infected people ↓ = ↑

Summary
・When infections are spreading: Loose communities are not formed -> The effect of reducing the risk of infection at visited facilities is excellent
・When infections are declining, infections occur across loose communities and the effect of “changing destination” is virtually eliminated
・Staying in facilities normally used contributes to preventing the spread of infections more than meeting people not normally met in facilities with a low risk of infection

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

・Actions that a lot of people do such as Action 2 (office), Action 9 (theme park) and Action 13 (train) spread infections. When α (the probability of an infected person infecting a specific person with whom they have had contact) is low, the number of infected people increases relatively with actions that have a very small number of people but a low rate of mask wearing and a long time lapse, such as Action 12 (accommodation)

Tatsuya Matsuura: Ohsawa Laboratory Graduation Thesis

・Household
・Occupation
・School
・Distance
・Random

※ Data sampling of data is done by randomly sampling a specified number of households, so the number of households can be specified, but the number of nodes cannot be specified.

・Overview
　・Layers that form cliques by household
・Parameter
　・None
・Generation logic
　・Combine all identical household_id

・Overview
　・Layer that forms a constrained network based on industry_W and industry_m_0
・Parameter
　・industry_W: The maximum number of connections to others (industry_W - industry_m_0 is the maximum number of connections that can be accepted from others)
・industry_m_0: The number of hands extended by the individual
・Generation logic (pseudo code)

for node_i in {grouping of nodes (in ascending order by node number)}:
　　for node_j in {the grouping of nodes with the same industry_type_id as node_i, excluding node_i (in random order)}:
　　　　if industry_degree(node_j) <= industry_W - industry_m_0:
　　　　　　{grouping of edges}.append((node_i, node_j))
　　　　break if {number of edges appended} >= industry_m_0

・Overview
　・Layer where school children form a constrained network based on school_W and school_m_0
・Parameter
　・school_W: Maximum number of connections to other people (school_W - only school_m_0 accepts other people's hands)
　・industry_m_0: The number of hands extended by the individual
・Generation logic (pseudo code)

for node_i in {grouping of nodes (in ascending order by node number)}:
for node_j in {the collection of nodes of the same age and in the same area as node_i, excluding node_i (in random order)}:
if school_degree(node_j) <= school_W - school_m_0:
{grouping of edges}.append((node_i, node_j))
break if {number of edges appended} >= school_m_0

・Overview
　・Layer that forms a constrained network from distances based on distance_W and distance_m_0
・Parameter
　・distance_W: Maximum number of connections to others (distance_W - distance_m_0 to accept others' hands)
　・industry_m_0: The number of hands extended by the individual
・Generation logic (pseudo code)

for node_i in {grouping of nodes (in ascending order by node number)}:
for node_j in {grouping of nodes other than node_i (in random order)}:
if distance_degree(node_j) <= distance_W - distance_m_0:
if 1/(ε + distance(node_i, node_j)) >= random(0, 1):
{grouping of edges}.append((node_i, node_j))
break if {number of edges appended} > = distance_m_0

・Overview
　・Layers created by random graphs
・Parameter
　・p: Probability of edge selection
・Generation logic
　・Decide which edge to adopt with probability p from n(n - 1) / 2 edges and generate a graph

↓Actual population of each occupation and settings in simulation

↓Actual number of each facility and settings in simulation