29th March 2020 | Last updated: 3rd April 2020

Individual-based epidemiological model including ‘social distancing’, occult immunisation and finite ICU capacities

David J. Jörg, PhD

Preamble

I'm not an epidemiologist; my background is in non-equilibrium physics and the theory of biological systems. Nevertheless, after having read a few COVID-19 related modelling papers, I started thinking about an epidemiological modelling system that combines those effects on epidemiological dynamics that have been in the focus of attention (at least in the media) in recent weeks,

Since I am not an expert in this field at all, I don't know whether similar or equivalent model frameworks already exist. If they do exist and you are aware of them, I would be very happy about a short e-mail. For now it is an interesting exercise for me to put together a corresponding theoretical framework. Most likely, I will not have the time to fully unfold its dynamics as a side project. Therefore I would simply like to put it out there—in case someone else might find it interesting or even useful. On the other hand, if a more experienced researcher in this field would find the approach interesting, I would be equally willing to think about a (small-scale) collaboration.

Since all parts of this projects are preliminary, I currently refrain from uploading any materials to repositories such as arXiv or GitHub. All available materials can be downloaded from this website.

Model overview

In the spirit of traditional SIR-type models, I propose an individual-based epidemiological model describing four populations:

Each individual exists in a spatial domain in which it can move (unless it is under quarantine). Such motion should not be interpreted as genuine motion in real space. Rather, it provides an effective representation of a time-dependent contact topology between individuals that includes a notion of locality—this may incorporate the (very coarse-grained) effects of motion in real space as one contributing factor.

Individuals perform random walks with a specific motility and have the ability to keep a certain distance to each other through a ‘behavioural force’ related to ‘social distancing’; the degree of social distancing depends on the individual's conformity and the imposed distance.

The rate of infection of a susceptible individual depends on its proximity to infectious individuals. Infectious individuals may freely move around unless they are detected and placed under quarantine; upon detection, they are hospitalised and/or quarantined and are suspended from the spatial domain. Hence, they stop contributing to spreading the disease. Both (undetected) infectious individuals and hospitalised individuals recover with a state-specific rate. Once quarantined individuals have recovered, they re-enter the spatial domain and resume their motion.

We consider a certain fraction of the hospitalised/quarantined individuals (Q) to undergo intensive care. If the total number of individuals under intensive care exceeds ICU capacities, the death rate jumps to a higher value.

Important caveats:

A formal summary of the model is available as a pdf.

Simulation of typical scenarios

The following plots show example model outputs for four different scenarios.

Example realisations: time evolution



Reference scenario
(without social distancing)

With social distancing

Example realisations: overall infection dynamics

Please be aware that these are toy examples designed to illustrate the qualitative impact of different mechanisms in the model.

What could be pursued...

Simulation source code

The simulation is implemented in Fortran 90. It computes the individual-based dynamics on a square-like 2D domain with periodic boundary conditions.

Version 1.0.0 (Sunday, 29th March 2020) — Source code and instructions for compilation

Other useful links (like it's 1999)

crowdfight COVID-19 initiative

Contact

mail@davidjorg.com | @david_joerg on Twitter