Multi-demographic sub-networks
So far every member of the population during a metawards model run has
been treated equally. There was no concept of different groups of individuals,
e.g. school children, hospital patients, holiday-makers etc. being
modelled any differently. The only distinction was between workers,
who made fixed movements (potentially between wards)
during the day, and random interactions within their home ward in
the evening, and players, who just made random interactions within
their home ward.
Understanding Network
The Network class models this network of workers and
players. It holds a set of Nodes that represent each
electoral ward, and a set of Links that represent the
fixed motions between wards made by the “workers”.
The Node class holds the number of players who
are susceptible to infection (S). This is held in the variable
metawards.Node.play_suscept.
The Link class contains the number of workers who are
susceptible to infection (S) who travel regularly between their
“home” ward and their “work” ward. This is held in the
variable metawards.Link.suscept.
During a model run these values will be reduced as individuals are infected and then progressed through the different disease stages.
Note
These variables are stored as double precision floating point numbers, despite representing integer values. This is because it is more efficient to use double precision numbers when they are used for calculations during a model run.
Understanding Networks
To model multiple demographics, we need to create space for multiple different
sets of workers and players. This is achieved in metawards by
giving each demographic its own Network. All of these
demographic sub-networks are merged and managed via the
Networks class.
We create a Networks object by first specifying the way
we would like to distribute the population between different demographics.
We do this by writing a demographics file, which is a simple
JSON-format
file. First, create a file called demographics.json and copy in the below;
{
"demographics" : ["red", "blue"],
"work_ratios" : [ 0.0, 1.0 ],
"play_ratios" : [ 0.5, 0.5 ]
}
This file specifies that the population will be distributed between
two demographics, red and blue, named in the demographics
field. You can have as many or as few demographics as you wish, and
can name them in any way you want.
The work_ratios lists the ratio (or percentage) of the worker population
that should belong to each demographic. For example, here all of the
workers are in the blue demographic, and none of the workers are
in the red demographic.
The play_ratios lists the ratio (or percentage) of the player population
that should belong to each demographic. For example, here 50% of the
players are in the red demographic, and 50% of the players are in the
blue demographic.
Note
You can specify the work and play ratios using either numbers between
0.0 and 1.0, or you can pass in strings that are interpreted using
metawards.Interpret.number(), e.g. “50%”, “1/4” or
“(10+15)%”. The only requirement is that the sum of ratios must
equal 1.0 (or 100%), as every individual must be assigned to one
of the demographics.
Now that you have created the demographics.json file, you can tell
metawards to use it via the --demographics, or -D,
command line argument. Run metawards using;
metawards -d lurgy3 -D demographics.json
In the output you should see lines such as;
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Specialising into demographics ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Demographics demographics.json
loaded from demographics.json
version: None
author(s): unknown
contact(s): unknown
references(s): none
repository: None
repository_branch: None
repository_version: None
demographics = [
Demographic(name='red', work_ratio=0.0, play_ratio=0.5, adjustment=None)
Demographic(name='blue', work_ratio=1.0, play_ratio=0.5, adjustment=None)
]
Seeding generator used for demographics with seed 4751828
Using random number seed: 4751828
Number of differences is 0.0 + 0.0
Specialising network - population: 56082077
red - population: 16806530
blue - population: 39275547
These show that your demographics file was read correctly. In this case,
this has specialised the Network which modelled a
population of 56082077 individuals into a Networks
which has a red population of 16806530 and a blue population of
39275547.
Warning
A fixed random number seed is used to assign left-over individuals
to a random demographic. For example, 10 individuals cannot be divided
equally between 3 demographics, so one randomly chosen demographic
will have 4 individuals, while the other two will have 3. This
division is performed by metawards in every single
Node and every single Link,
to ensure that every individual is allocated. This random seed is
hard-coded to 4751828. Or, you can set it for a demographic
by adding "random_seed" = number to the demographics file,
e.g. "random_seed" = 10859403.
Once the Networks had been specialised, the model run
was performed as before. Now, the output shows the S, E, I, R values
for both the overall total population, and also for the demographic
sub-network populations, e.g.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 0 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56082077 E: 0 I: 0 R: 0 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 1 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56082077 E: 0 I: 0 R: 0 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 2 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56082077 E: 0 I: 0 R: 0 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 3 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56082077 E: 0 I: 0 R: 0 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 4 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56082077 E: 0 I: 0 R: 0 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
Infection died ... Ending on day 5
In this case no infection was seeded, so nothing appears to happen.
We can seed an infection just as before, by using the --additional
(or -a) option, e.g. now run;
metawards -d lurgy3 -D demographics.json -a ExtraSeedsLondon.dat
You should see output similar (but not identical) to;
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 249 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56079607 E: 0 I: 2 R: 2468 IW: 0 POPULATION: 56082077
red S: 16804060 E: 0 I: 2 R: 2468 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 2
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 250 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56079607 E: 0 I: 2 R: 2468 IW: 0 POPULATION: 56082077
red S: 16804060 E: 0 I: 2 R: 2468 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 2
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 251 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56079607 E: 0 I: 1 R: 2469 IW: 0 POPULATION: 56082077
red S: 16804060 E: 0 I: 1 R: 2469 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 1
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 252 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56079607 E: 0 I: 1 R: 2469 IW: 0 POPULATION: 56082077
red S: 16804060 E: 0 I: 1 R: 2469 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 1
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 253 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 56079607 E: 0 I: 0 R: 2470 IW: 0 POPULATION: 56082077
red S: 16804060 E: 0 I: 0 R: 2470 IW: 0 POPULATION: 16806530
blue S: 39275547 E: 0 I: 0 R: 0 IW: 0 POPULATION: 39275547
Number of infections: 0
Infection died ... Ending on day 254
By default, infections are seeded into the first demographic (in this case red). This demographic are players, so only interact in their home ward via random interactions. As such, the infection did not spread beyond that home ward and so it died out quite quickly.
Seeding different demographics
You can seed different demographics by specifying the demographic in
the additional seeding file. Create a new seeding file called
ExtraSeedsLondonBlue.dat and copy in the below;
1 5 255 blue
The format of this file is a list of lines that say which wards should be seeded. In this case, there is just one line containing four values.
The first value (
1) is the day of seeding, in this case on day 1.The second value (
5) is the number of individuals to infect, in this case 5.The third value (
255) is the index of the ward to infect. You can find the index of the ward you want using theWardInfosobject, e.g. vianetwork.info.find("...").The fourth value (
blue) is the name or index of the demographic you want to seed.
Note
If you want, you could have specified the demographic in this file by
its index (1) rather than by its name (blue). It is up to you.
The blue demographic contains all of the workers, so we would expect to see a different outbreak. Perform a model run using;
metawards -d lurgy3 -D demographics.json -a ExtraSeedsLondonBlue.dat
You should see a more sustained outbreak, ending in a similar way to this;
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 147 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 16864032 E: 0 I: 1 R: 39218044 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 57502 E: 0 I: 1 R: 39218044 IW: 0 POPULATION: 39275547
Number of infections: 1
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 148 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 16864032 E: 0 I: 1 R: 39218044 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 57502 E: 0 I: 1 R: 39218044 IW: 0 POPULATION: 39275547
Number of infections: 1
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Day 149 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
S: 16864032 E: 0 I: 0 R: 39218045 IW: 0 POPULATION: 56082077
red S: 16806530 E: 0 I: 0 R: 0 IW: 0 POPULATION: 16806530
blue S: 57502 E: 0 I: 0 R: 39218045 IW: 0 POPULATION: 39275547
Number of infections: 0
Infection died ... Ending on day 150
Because the blue workers could move between wards, they were able to carry the infection across the country, meaning that most members of the blue demographic were infected.