Computational Modeling, Parameterization, and Evaluation of the Spread of Diseases

Abstract: Computer simulations play a vital role in the modeling of infectious diseases. Different modeling regimes fit specific purposes, from ordinary differential equations to probabilistic formulations. Throughout the COVID-19 pandemic, we have seen how the results from these computational models can come to dictate our daily lives and the importance of reliable results. This thesis aims to address the challenge of exploiting the increase in available computational power to build accurate models with well-understood uncertainties. The latter is essential when basing decisions on any model predictions.Data collection relevant to epidemiology is expanding, and methods to incorporate models in data fitting need to follow suit. This thesis applies the Bayesian framework connecting data with models in a probabilistic setting. We propose simulation-based inference methods that allow for the use of complex models otherwise excluded due to their intractable likelihoods. Our computational set-up exemplifies how modelers can deploy Bayesian inference in large-scale, real-world data environments.The thesis includes four papers relevant for modelers considering dynamic systems, approximate Bayesian inference, or epidemics. Paper I finds the approximate posterior of a complex chemical reaction network and estimates the prior and posterior uncertainties using the pathwise Fisher information matrix, thus framing our methodology in a fully synthetic setting. Paper II constructs a disease spread model for the spread of a verotoxigenic E. coli prevalent in the Swedish cattle population. The data includes a high-resolution transport network and actual bacterial-swab observations from selected farms. The results show that even if the data is sparse in space and time, it is still possible to recover a posterior that replicates the data and is viable for mitigation evaluations. Paper III studies a form of meta-models, the Ornstein-Uhlenbeck process, and how they approximate epidemiological models and enable broad analysis. We state an analytical limit of what is possible to learn from data subject to binary filters with confirming numerical examples. Finally, Paper IV finds a posterior model of the COVID-19 pandemic in Sweden and the 21 regions using a Kalman filter approximation. The findings result in a probabilistic regional surveillance tool for an epidemic at a national scale with considerable cost-cutting potential independent of large-scale testing of individuals.In conclusion, the thesis examines how reasonably realistic and computationally expensive epidemic models can be adapted to data using a Bayesian framework without compromising model complexity and estimating uncertainties that further support decision-making.