Hybrid Mathematical-Epidemiological Models for Infectious Disease Dynamics

Kurzfassung

Epidemiology is the study of infectious diseases, including their origin, spread and prevention. A useful tool to predict the spread of such diseases or assess preventative measures, are mathematical models. Current stateof-the-art models that arose due to the COVID-19 pandemic include agentbased models [1, 2], metapopulation models [3, 4, 5, 6, 7] as well as equationbased models [8, 9]. The different types of models each have their own drawbacks and benefits. For example, while agent-based models tend to reflect reality better than metapopulation or equation-based models by describing the population on a microscale, the computational cost is relatively high and scales poorly with larger populations. This is alleviated by using metapopulations, that is considering the population at a mesoscale level instead. On the other hand, Equation-based models using systems of ordinary differential equations are purely deterministic, by assuming the population is homogeneously mixed, but the cost for solving the equations is low and independent of the population size, making it ideal for parameter studies. In this thesis, we present the infectious disease models introduced by [10], starting with a general formulation for an agent-based model, which will be successively reduced to a metapopulation model and a piecewise equationbased model. The agent-based model allows precise predictions by a bottomup approach, that is by modelling the population as individuals. This is the finest granularity model, followed by the metapopulation model grouping agents together. Finally, the piecewise equation-based model approximates the size of agent groups by deterministic equations, which is the coarsest granularity and allows for top-down modelling.