Model discussion

[FHell]

We need a better disease and counter measure model. Prime candidate is:

https://arxiv.org/pdf/2011.11413.pdf

ideally augmented with B117 and vaccination, but turned into a stochastic model.

If we build the stochastic infection dynamics on the negative binomial distribution, to capture effects of overdispersion, (e.g. as in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7338915/) we also have to estimate the impact of measures on the variance, not just on the reproduction number.

[FHell]

Also note this interesting simulator:

https://covidsim.org/v3.20210119/?place=gb

[FHell]

An alternative to a highly detailed SEIR + TTI model would be to make use of the fact that we are doing a discrete time stochastic model to directly model the onset of infectiousness as a time delay. But this quickly becomes complicated, too. So some expert input at this point would be needed.

[FHell]

After a brainstorming session with @oskarddfa the decision for the second Prototype is to have an SEIR model with Em and Im for the mutation, and model the reduced effectiveness of TTI as an I dependent \Delta R_TTI

[FHell]

In 0e785784ab0bf17cd167929e9910b870e2fae643 I have implemented the SEIR model with TTI of varying strength and negative binomial infection dynamics. (S to E transition is negative binomial with mean = R_0 I S / total, E to I and I to R are simple constant probability transitions)

[oskarpfeffer]

It came to my mind that we could also try to model adherence to regulations? Actually, that was a thought that I had some time ago, and it is a bit different from what the model is right now, but maybe it is an interesting idea.

The idea would be to model adherence to regulations using MCMC, where the regulations are set in the property (energy) function and the adherence to regulations is modeled through the tunable genericity. This is in my opinion a good approach to tuning the adherence since it resembles a physical system connected to a heat bath at temperature (inverse adherence) T. However, this modeling is not easy to implement into the current system and maybe is still a project on its own. I think the best implementation would be on a temporal network of interactions between people, meaning that the network is changing constantly (passing of time, people meet other people) and this rewiring of interactions is done through MCMC, where the regulations are within the cost function, where no regulations is a constant cost function. Then the epidemic spreads through SEIR at every time step, where 1 time step is equal to a whole MCMC step intended as the iteration of MCMC N times, N being the number of vertices.

Does not really have much to do with the current model of the COVID-Game, but I just wanted to share this thought and maybe someone has an idea how to implement some part of this idea.

[FHell]

Interesting but yes, I don't think this is related to the game. :) Generally adherence also would be part of the counter measure modeling (I made an issue for that).

[FHell]

So the stochastic SEIR model now has the following aspects:

• incubation period (and thus delay of measures)
• super spreading and handling very small number of infected correctly (I hope)
• TTI only being effective until some threshold
• more infectuous mutant
• background infection rate
• travel between regions with arbitrary travel matrix (prototype)

and on a technical side we save the trajectory, so we can display the 7 day incidence rather than the instantaneous infectuous.

This is not fully debugged and when the number of infected becomes large this implementation is very inefficient. But this is relatively straightforward to fix because for large number of infected we can simplify the distributions.