Juliacon 2024

The global spread of the COVID-19 pandemic has highlighted the importance of monitoring the real-time spread and predicting future disease dynamics to inform intervention policies. Mathematical modeling of infectious disease dynamics - including the estimation of relevant parameters - have become a key objective of this effort.
However, basing the inference approach solely on confirmed infections yields several challenges. The foremost is the problem of underascertainment of infections. Individuals who do not experience symptoms after being infected are not likely to seek testing. Additionally, insufficient testing capacities and a lack of public awareness may cause underascertainment.
Therefore, our approach proposes a mathematical model combining case count data with wastewater-based surveillance data, which reports the viral concentration in the wastewater from fecal shedding of the infected individuals. Wastewater-based surveillance is a promising tool for monitoring public health, but still in its infancy. One of its major challenges is the inherently high stochasticity of the observations in the low-cases regime. Furthermore, quantitative links to disease dynamics and reliable predictions are still under development. The combination of these two data sources may help to overcome the numerous challenges inherent to each of them.
The proposed mathematical model consists of a multi-level epidemic model for the dynamics on the population level that jointly models the number of new infections, infection-confirmation lag times and ascertainment probabilities utilizing case count data. This is expanded by an simple advection-dispersion-decay model for the RNA transport in the wastewater. With this, the transmission model can be informed by viral concentration measurements. The resulting multi-hierarchical model is well interpretable due to its mechanistic nature, while taking care of measurement errors and uncertainty in the data using a probabilistic description of the modeled quantities.
Parameters shall then be learned using a Bayesian inference framework based on the likelihood function, which is partly analytically available and partly approximated by sampling schemes.
After parameter estimation, we want to conduct simulation studies to evaluate the performance of the model, including uncertainty quantification and robustness. Furthermore, we then aim to apply the model to publicly available data from Canadian cities.
In summary, we employ the Julia programming language to simulate the dynamics of an infectious disease by incorporating diverse real-world data sources. Julia's modularity allows a neat integration of the different processes included in the model, while its clear syntax makes it easy to resemble the mathematical formulas needed and reduce code complexity. Especially, the simulation intensive inference framework benefits from Julia's speed and possibility for parallelized computation. With our talk we aim to contribute not only insights into integrative modeling of serious infectious disease, but also provide an overview of our considerations and experiences when solving models with hierarchical random variables using the Julia programming language.