Containment measures

Types of measures

Usually one would not let the spread of an epidemic go unchecked, rather there would be various containment measures. Some of these might arise voluntarily as people start to be more careful when interacting with others, some might have to be government enforced like travel restrictions, assembly prohibitions or lockdowns.

In the context of the simulation, all measures fall into two groups:

1) Measures restricting mobility
2) Measures restricting transmission probability

The first class of restrictions affects how many people potentially meet, the second class what they do when they meet. So a travel ban, or a canceled fair would be a class 1) measure whereas keeping safe distances, wearing masks or frequently washing hands would be a class 2) measure.

Single intervention

So, let's try to explore what the measures do. Create the following config file as the baseline epidemic:

simulation
num_timesteps 800
snapshot_interval 200
filename_base containment
random_seed 101

disease
recovery_time 7
p_transmission 0.23

population
grid_size 1000
num_classes 3

class
mobility 3
p_mobility 1.0
fraction 0.8

class
mobility 5
p_mobility 1.0
fraction 0.19

class
mobility 100
p_mobility 1.0
fraction 0.01

end

Note the random_seed keyword - sometimes we may want to explore literally the same scenario over and over. In this case, we can initialize the random number generator with a specified number (it doesn't really matter what number). Sometimes (as before) we may want to explore a range of possibilities - if the keyword is not used, the system time is used to initialize the random number generator, making every run distinct.

Now, let's try the first containment measure - after day 200, we impose a week of severe mobility restrictions.

measures
num_measures 1

measure
start 200
duration 7
mobility 2

Here the measures keyword allows to specify how many interventions we do in the following, and each intervention is headed by measure. Each measure has a starting day, a duration and allows to impose mobility and transmission values which are imposed while the measure is in force.

Unfortunately, the result is not really satisfactory - while the growth of the epidemic is stalled for a short time, it more or less picks up where it left right after the measure is over. So half-hearted measures do not work. Let's try something more substantial, prolonging the measure and in addition improving hygiene for the contacts that still take place - replace the block above by

measures
num_measures 1

measure
start 200
duration 20
mobility 2
transmission 0.05

That looks already different - note how the growth rate of infected people is tiny long after the 20 day period has ended, and when the growth finally picks up again, it never is as rapid as it used to be. So - somehow the containment measure has significantly altered the spreading pattern of the disease.

What happens if we prolong the measure further? Increasing the duration to 26 days results in very slow growth for almost 300 days before the speed starts picking up again. Prolonging yet further ends the spread for good.

So - how can the spreading pattern be changed so pronouncedly? We've seen the reason in the previous section - a hard containment measure affects lots of outlying infection hotspots in a way that the infection ends locally - leaving behind clusters of immune people. When the infection front reaches these again, it stalls.

For comparison, there are all the scenarios we discussed so far:

Comparison of different containment scenarios.

Double intervention

Given that, after a first hard measure, the spreading pattern of the disease is permanently slowed - can this be used by a two-step intervention? Let's try a hard-soft measure package where initally 20 days of increased hygiene and travel restrictions are kept, and afterwards for 400 days hygiene ist just 'a little better' than usual (people are aware of the disease) and only the large-scale travel that mixes significant fractions of the population (fairs, holiday, soccer games...) is prohibited.

measures
num_measures 2

measure start 200
duration 20
mobility 2
transmission 0.05

measure start 225
duration 400
mobility 6
transmission 0.2

Now, this actually works to stop the disease. We can also run a scenario in which we would only impose the 400 days of light restrictions (a kind of mitigation strategy), and while this would slow the spread quite a bit while it lasts, it does not stop it at all.

Comparison of a double intervention with a long mitigation phase.

Consequences

There's clearly many possible scenarios, but the main types of outcomes (which you can explore yourself) are: Too soft and short measures fail to do anything relevant, the spread afterwards is nearly as fast before. Soft and long measures mitigate the spread and slow it while the measure lasts, but do not substantially alter the dynamics afterwards. Measures that are hard enough to stop the spread in many hotspots create pockets of immune people which permanently slow down the development of subsequent waves. And finally sufficiently long and hard interventions end the spread. Especially a combination of an initial hard, followed by a soft measure can be much more powerful than either of them alone.


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