Evaluation of different mobility models in equation-based infectious disease dynamics

Abstract

Compartmental models based on ordinary differential equations (ODEs) are among the earliest and most widely used epidemiological models for describing disease dynamics within a population. Given the extensive research on these models, they represent well-established methods for analysis and benefit from their comparatively low computational cost.

However, they are based on the assumption that the population is ``well-mixed'', implying that all compartments mix in a homogeneous pattern. While individuals in different compartments can have different properties concerning the transmission of the disease, the ``well-mixed'' assumption describes the absence of geographical or social barriers within the population. This assumption is not only overly simplified, particularly on a large scale, it also results in the loss of spatial information regarding the population. To address some of these limitations, we examine models that take the spatial heterogeneity of the regions into consideration. Spatially resolved models allow for the evaluation of regional interventions and interventions connected to the movement of individuals.

In this thesis, we will study two different approaches on integrating mobility to a model. The first approach is represented by a model based on ODEs that incorporates the effect of mobility directly in its equations. In the second approach, the authors proposed to connect decoupled ODE systems for the local regions through a graph. We evaluate these two approaches on metapopulation models, extend the first approach and analyze all three approaches with regard to practicability, complexity, and predictions.