Mathematical Epidemiology 
Spread of Covid-19 


COVID-19 Epidemiological Modelling Project

The COVID-19 Epidemiological Modelling Project is a spontaneous mathematical modelling project by international scientists and student volunteers. It is a contribution of science to solve some of the current problems related to the pandemic, first of all in relation to the spread of the disease, the epidemiological aspect. However, as the understanding of disease spread is intimately linked to stratgic decision making in the financial, economic and political spheres, we have eventually discuss the links appropriately. In the end, we like to give informed risk analysis, in order to give the most likely scenarios and strategic option based on scientific evidence.

Epidemiological Mathematical Modelling

Epidemiological Mathematical Modelling

There are currently many mathematical models and data collection strategies in relation to the Covid-19 pandemic starting and running, with different purpose and success. As mathematicians and mathematically interested scientists we like to avoid at all cost that the public misunderstands the relevance and impact of research results in this area.

Comparison and Ranking

It is therefore one of the most urgent aims of this project to compare and discuss current modelling stratgies and results. For this purpose we will collect scientific experts in an interdisciplinary spirit to discuss current mathematical modelling and data collection strategies, most with respect to how they can establish and support successful policy options.

The Project's Own Model

The project will establish and give advice to science and public. The long-term goal is to establish a modern interdisciplinary expert system for a better risk analysis and support of future strategic decisions related to Covid-19.

The need to establish such an expert system was described in a recent blog.

There are many epidemiological models excisting, that can of course be applied to Covid-19. We like to review these models and their corresponding implementations, give a critical review, but also try out some alternatives. Like in climate change modelling, we can only come closer to the truth if we can establish several parallel modelling attemps, and investigate their strength and weaknesses.

Aim 1 - Structural Model of COVID-19 spread.

In a first modelling step is to establish a structural model of the disease. In case of Covid-19, it is a complex multi-scale social group formation underlying the spread of the disease. Human individuals in general have, due to sociological and economic reasons, a number of social group memberships, determining the contact patterns of individuals.

Aim 2 - Dynamic Stochastic Modelling

In order to predict future number of infected cases, we need to establish a dynamic model based on the structural model established in aim 1. Because the number of infected individuals relative to susceptible individuals is still a small number, we use an event based reaction-type formalism, at least initially. Mass-action type differential equations are still not adequate from a mathematical modelling perspective.

Aim 3 - Epidemiological Simulation of COVID-19 spread.

We like to test spatial and non-spatial stochastic simulation algorithms. Non-spatial and spatially explicit models of coronavirus spread can be established on different scales. The scales for non-spatially explicit models range from local, regional to national social groups, for example single, family, neighbourhood, shops, cars, trains, restaurants, schools, to hospital, companies, villages to cities, metropols to nations. Each of these entities is assumed to be a reaction chamber for the disease. In a spatially explicit model, all of these reaction chambers are assumed to have spatial coordinates, and therefore can have a location on a geographical map with different resolution.

Aim 4 - Statistics, Data Analysis and Machine Learning Applied to COVID-19 spread.

The disease spread model is used to be paramtrised with real data on different scales, from local to national to international.

Aim 5 - Review on Epidemiological Models Relevant for Covid-19

We like to invite a number of international experts to review existing models of epidemiological models in order of their relevance for Covid-19 spread predictions.