From vaccination planning to life context networks

Effective reproduction number Rt

<< R0 calculation policy: The objective is to obtain a method to estimate R0 while the data is still midway >>
Rt increase due to new variants is subtracted from what has been factored in so far, and the increase is taken into account from the beginning (increase only in the future)
(b) Vaccine use is also reflected in the conversion from Rt to R0

(1) After an emergency declaration t0, the change is maintained at the previous level for t0 +5 days, and then by t0 +5+dt (dt≒1mo), it decreases by { (the minimum value of 2w immediately before t0 +5) - (the minimum value of 2w immediately before t0 +5)}/2. Then converge to near 1 over dt.
(3) For Rt, historical data was used up to 7/6 (because it may be revised later), and then "divided by the portion of the s function up to 7/6 (approx. maximum) that eventually grows 1.5 times (100% of the Delta variant/infectivity as of April) in about 2.5 months from the beginning of June" to get Rt before the Delta variant, and then multiplied by the same s function for the entire period to obtain Rt for the entire period.
(3) For pv, N/S was obtained by preliminary simulation using data up to 7/17 (N/S of 7/17 is used thereafter), and Rt was converted to R0.
* The preliminary SM converged to a sufficient accuracy (no change in 3 significant digits) in 5 iterations

Basic reproduction number R0

Even with the best effort, the peak will reach 1,500-2,000*, but an increase is expected to continue for a while if vaccination is abandoned again
*Considering this kind of simulation, the numerical values are less important than the qualitative explanation, however if the approximate increase or decrease matches the data within an error range of 10-20%, the reliability of the method can be recognized

●Why a network model is required (only the third is a review of the previous)
　○Hc (equality of distribution) maximization is extremely effective as a first aid until pv (vaccination speed) is accelerated
　○Maximizing mean R0 in vaccinated areas is effective at low pv speeds but counterproductive at Δ variant spread
　○Errors accumulate when regions are combined and simulated (then tested theoretically with mathematical model experts)

●Basic Concept and Model Overview of MultiLayer-MultiAgent Model
　○Local nature of the network, enabling it to reflect the context of life in micro-macro interactions
　○Report of the current calculation parameters and examples of calculation results
　○Future Schedule
　○Appendix
　　■ Order distribution of each layer
　　■Generation logic of each layer of MLN (separate document)

SEIR circuit lattice model with inflow and outflow in and out of the region
（Ohsawa & Hayashi 2021 https://arxiv.org/abs/2104.09719)

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. Consideration is given to local circumstances rather than the full mean field method.

A rather large mean-field SEIR model problem ・Differences may widen depending on the amount of vaccine allocated ・The central section of the graph of (Hc, total number of infected persons) (←Hc affects the vaccination effect no less on the speed of vaccination 2104.09719.pdf (arxiv.org)) shows little error, so Hc is safe to use

Research Background
It is difficult to "predict" the spread of Covid infections because unknown causes, such as changes in people's lifestyles (how and where they eat, contact with other people, etc.) and virus mutations, keep coming into play. For this reason, assumptions such as a similar temporal change in the effective reproduction number as in previous years were used as necessary to predict the spread of infection, but people's lives may change due to the appearance of mutated variants or major events such as the Olympics. On the other hand, Ohsawa et al. have used simulations to suggest that SwC is intrinsic to the strategy of vaccine tilting and the strategy of phasing out self-restraint. The youth-first, activity-first, and urban-first principles can be placed in that system.

Purpose of Research
Rather than the accuracy of predictions about the spread of infection, we will develop qualitative understanding of the causes and explanatory knowledge about the effects of infection, and methods to acquire this knowledge. For example, last year, we presented action guidelines such as "Stay with Your Community (SwC)" and "Avoid traveling to remote areas (where you don't usually go), but only interact with people you mutually recognize as necessary". But this year, we will develop action guidelines that involve diverse contact among people (by occupation, attribute, region, etc.).

Method
・A survey on contact with people and objects was conducted with guidelines based on SwC principles and an accountable self-restraint plan was developed, developing a wider range of locations and situations than last year
・The social network model developed in the previous year was extended to a hierarchical model in which (a) work relationships, (b) friendships, and (c) other layers are interconnected. (1) Expansion of synthetic population composition data by Kansai University (Murata), (2) Use of questionnaire survey data that closely examines human interaction in each level
・Last year, due to machine constraints, calculations were performed on a network of up to 10,000 agents, but in order to run simulations with a more realistic number of agents, the network was connected to the SEIR lattice, as shown in the conceptual diagram on the right, and we will consider the feasibility of a hybrid approach of micro and macro where interactions between individuals with faces and hands can be analyzed in multi-people and multi-region.

Expected Results
・Hierarchical infection network model. Multi-people and multi-region effect verification by integrating micro and macro
・Qualitative understanding of the causes of the spread of infection and the explanatory knowledge of its impact
・By the above development of policy messages (Example: rather than "Don't go out drinking", show the real reason "SwC deviation is high in bars" and consider bar design to reduce risk)

Philosophy

● Model for observing the macroscopic effects of microscopic human activities
　✓ By using multiple layers, it is possible to simulate complex events while reducing the number of parameters compared to a single layer network, because basic statistics are set and calculated for each layer

●Interactions between different activities can be observed by modeling them as different layers and overlapping them
　✓ Infection in the family, in the workplace, in the community, and at school
　✓ Infection due to travel, participation in events, etc.

● Can be extended to perform policy-based external operations for each Layer
　✓ Workplace Layer: Parameters can be changed according to guidelines from Keidanren and supervisory authorities, etc.
　✓ School Layer: Parameters can be changed by guidelines from Ministry of Education, Culture, Sports, Science and Technology, Ministry of Health, Labor and Welfare, etc.
　✓ Travel & Events Layer:　Some parameters can be changed by declaring a state of emergency, etc.

Model Overview

⚫ Infection transmission model
　✓ A general multi-agent based SEIRS model was adopted

⚫ The model allows for adjustment of the coupling relationship of the edges of each layer for each iteration
　✓ Can be thinned out, not all edges connected
　✓ The thinning out rate can be adjusted on a layer-by-layer basis (awareness of emergency declarations, school closures, guidance to companies on telework rate targets, etc.)

⚫ Vaccination
　✓ Can be set to vaccinate or not at each node
　✓ It is possible to set a rule to reduce the transition probability to E of a node in the state of S by ▲X% by vaccination
　✓ Manipulation such as gradual dosing using age and latitude/longitude information (Dr. Murata's synthetic data) is possible

● Lowest number of infected people in networks with small W/m0 and low edge sufficiency (green line)
● The network with the largest W/m0 and the highest edge sufficiency (purple line) has the most infected people, and almost all of them are infected
● The effect of the edge sufficiency ratio is larger than the effect of W/m0 (the relationship between blue and purple, red and yellow, green and light blue)

Current settings
⚫ Initial number of infected persons: Calculated at 1% of the population
⚫ S -> Transition Probability of E: 20%
⚫ E -> Transition probability of I: 30%
⚫ I -> Transition probability of R: 10%
⚫ R -> Transition probability of S: 10%

Meaning of 0_5000_x_y_z:
・x: Random number seed (1,2,3),
・y: Setting of W and m0,
・z: Setting of edge thinning rate for each layer