Model (B) Assumption Information （※Case of scenario with a low rate of severe illness)
・Assumes 14 million people in Tokyo
・Multilayer network comprised of 5,000 households ≒ 10,000 agents
・One agent has the weight of 1,400 people to match the population of Tokyo
・The model uses the artificial synthetic data of Professor Murata of Kansai University, which was resampled and synthesized based on the population composition of the census
・This data includes information such as household composition, age, gender, occupation and address, and uses that information to generate network layers such as “family layer,” “school layer,” “workplace layer,” “neighborhood community layer” and “random (holidays, travel, etc.) layer”
・The frequency and extent of contact (how many people are met) can be set for each layer. For example, this model can be used as reference information for policy decision-making, such as advance estimates of the effects of telework targets through the Japan Business Federation, etc., advance estimates of the effects of school closures and remote classes by the Ministry of Education, Culture, Sports, Science and Technology, and estimates of the effects of requests for self-restraint from traveling or eating out, etc.
・Although not incorporated into the current model, it could be expanded for estimates of the economic effects due to the decrease in meeting people in addition to trends in the number of infected people.
Model (B) Multilayer Concept
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.
Model (B) of MultiLayer-MultiAgent for SEIR Flow
※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)
Model (B) of MultiLayer-MultiAgent for SEIR: Settings
・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
Model B Results: Number of Newly Infected People
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 encourage a reasonable degree of self-restraint on actions and that state continues, the number of newly infected people may have already peaked out and we may be on the way to bringing infections under control.
As W increases, the peak will be higher and come earlier.
As a result, when an increased W is suppressed, the peak comes earlier and then lowers.
Model B Results: Number of Newly Infected People (beta = 0.4 only / 2*2 cells expanded in the lower right of the previous section)
If the extent of contact is suppressed and the frequency of meeting is kept to a certain level and excluding the upper left scenario, even with the strong infectivity of beta 0.4, it is expected that a level of about 50,000 newly infected people a day will continue until about mid-March, following which the situation will move towards bringing infections under control gradually. If there is the strong self-restraint mode as in the bottom right, now is the peak and there is also a sense of expectation that infections will be brought under control.
Model B Results: Cumulative Number of Infected People
In the upper left scenario, infections are controlled in a state of near-herd immunity.
Model B Results: Number of Infected People with Severe Illness (Moderate or Higher Level)
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 and depending on the scenario, the number may reach several tens of thousands of people, peaking in the first week of March.
In other words, “moderation” rather than “abstinence” is the essence
KeyGraph: Black (●) Nodes Are High-Frequency, Red (●) Nodes Are Low-Frequency but Bridging Elements
Let’s Try Adding a Few Nodes.
♦ Reference ♦ Suggestions for Vaccination Planning in the Distribution of Urban Human Interaction
Results: A: W=2m0+2, B: W=2m0-2, C: W=m0+2, D: W=m0-2, and vaccinated in two stages of 0.3 percent of the population per day, in the order:
① A→B→C→D ② B→C→D→A ③ C→D→A→B ④ D→C→B→A
*A: 1-12 weeks, B: 13-24 weeks, C: 25-36 weeks, D: 37-48 weeks, with 2% of the population per week each. In the graph below, except for the two colors near W=m0 (green and ochre), the values are large from the large curve of W-2m0 (the graph shows m0=8, but the same trend is observed for m0=6, etc.)
※ 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.
・Layers that form cliques by household
・Combine all identical household_id
・Layer that forms a constrained network based on industry_W and industry_m_0
・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)
・Layer where school children form a constrained network based on school_W and school_m_0
・school_W: Maximum number of connections to other people (school_W - only school_m_0 accepts other people's hands)
・school_m_0: The number of hands extended by the individual
・Generation logic (pseudo code)
・Layer that forms a constrained network from distances based on distance_W and distance_m_0
・distance_W: Maximum number of connections to others (distance_W - distance_m_0 to accept others' hands)
・distance_m_0: The number of hands extended by the individual
・Generation logic (pseudo code)
・Layers created by random graphs
・p: Probability of edge selection
・Decide which edge to adopt with probability p from n(n - 1) / 2 edges and generate a graph