daanvanhauwermeiren / covid19-model

SEIR model with scenario analysis and model-based predictive control to simulate the effect policies

BIOMATH COVID19-Model

Original code by Ryan S. McGee. Modified by T.W. Alleman in consultation with the BIOMATH research unit headed by prof. Ingmar Nopens.

Copyright (c) 2020 by T.W. Alleman, BIOMATH, Ghent University.

Our code implements a SEIRS infectious disease dynamics models with extensions to model the effect quarantining detected cases. Our code allows to quickly perform Monte Carlo simulations, calibrate model parameters and calculate an optimal government policies using a model predictive controller (MPC). A white paper and souce code of our previous work can be found on the BIOMATH website.

Demo

A demo of the model can be found here. This notebook can also be run in the browser through binder,

Model highlights

Model dynamics

We use an extended version of the SEIR model to model the disease at a higher resolution. This classic SEIR model splits the population into different categories, i.e. susceptible, exposed, infected and removed. We break down the latter two categories in super mild (asymptotic), mild, heavy and critical for the infected part of the population, whereas the removed population indicates the immune and dead fraction. Parameters values are (for now) based on Chinese covid-19 literature but we are seeking to closer collaborate with Belgian hospitals as more data becomes available. The dynamics are modeled using two frameworks: 1) deterministic and 2) stochastic. The deterministic model can fluently run age-structured (metapopulation) simulations naturally by changing the initial conditions. The stochastic model class is under construction but will be updated soon.

Additional capabilities

As of now (20/04/2020), the SEIRSAgeModel (deterministic model implementation with inherent age-structuring) contains 7 functions which can be grouped in two parts: 1) functions to run and visualise simulations and 2) functions to perform parameter estimations and visualse the results. 3) functions to optimize future policies using model predictive control (MPC). Also, scenario specific functions will be added over the course of next week.

As of now (20/04/2020), the SEIRSNetworkModel contains 5 functions which can be grouped in two parts: 1) functions to run and visualise simulations and 2) functions to perform parameter estimations and visualse the results. Implementing the model predictive controller is straightforward and can easily be done. However, the optimisation problem is really difficult and requires thousands of function evaluations. Given the large amount of computational resources required to run just one stochastic simulation, it is highly unlikely that the model predictive controller will ever be used to optimize government policy. The MPC functions will be implemented and their usefullness assessed after a calibration is performed. Also, scenario specific functions will be added over the course of next week.

How to use the model

A Jupyter Notebooks containing all scientific details and a tutorial of both frameworks is available in the /src folder.

Future work

Model dynamics

Future work will include a modification of the model dynamics most likely according to the flowchart below, this will be done in collaboration with hospitals. We believe these will allow to simulate the disease spread even more realisticly.

Scenario-specific functions

We will implement a function which uses the past policies to quickly recreate the Belgian ICU and hospitalisation curves up-to-date. This function will be used to quickly propose MPC optimal policies and to perform scenario analysis about the future.