• DOI:10.48550/arXiv.2203.16345
• Corpus ID: 247793199

An Algebraic Framework for Structured Epidemic Modeling

@article{Libkind2022AnAF,
  title={An Algebraic Framework for Structured Epidemic Modeling},
  author={Sophie Libkind and Andre Baas and Micah Halter and Evan Patterson and James P. Fairbanks},
  journal={ArXiv},
  year={2022},
  volume={abs/2203.16345}
}

• Sophie Libkind, Andre Baas, +2 authors James P. Fairbanks
• Published 28 February 2022
• Computer Science
• ArXiv

Pandemic management requires that scientists rapidly formulate and analyze epidemiological models in order to forecast the spread of disease and the effects of mitigation strategies. Scientists must modify existing models and create novel ones in light of new biological data and policy changes such as social distancing and vaccination. Traditional scientific modeling workflows detach the structure of a model—its submodels and their interactions—from its implementation in software. Consequently, incorporating local changes to model components may require global edits to the code-base through a manual, time-intensive, and error-prone process. We propose a compositional modeling framework that uses high-level algebraic structures to capture domain-specific scientific knowledge and bridge the gap between how scientists think about models and the code that implements them. These algebraic structures, grounded in applied category theory, simplify and expedite modeling tasks such as model specification, stratification, analysis, and calibration. With their structure made explicit, models also become easier to communicate, criticize, and refine in light of stakeholder feedback. The plots demonstrate that the mass action bloodmeal model causes the density of infected hosts and infected vectors to vanish, whereas in the Ross Macdonald models the densities stabilize. These observations suggest that the Ross-Macdonald models are better suited to this modeling problem. On the other hand, the ordinary and delay differential equation Ross-Macdonald models reach the same equilibrium, although they exhibit different transient behavior before settling down. This structured approach to model composition benefits the modeling workflow by providing tools to rapidly explore variations on model strucure in order to evaluate the cost-benefit tradeoffs for different models. In this case, we determined that the assumption of mass action is inconsitent with observed phenomena and that the ordinary and delay differential equation Ross-Macdonald models have equivalent equilibrium behavior. Modelers can thus consider their purpose in studying either transient or equilibrium behavior when deciding if the additional computational requirements of a DDE model are worth the improved fidelity to the transient phenomena. This interactive model exploration environment where changes in a model's behavior can be tied back to changes in the model strucure, enables scientists to spend more time on their domain science and less time building, running, and analyzing software systems. two stratification schemes are spatial stratifications with population dynamics, which were studied in Citron et. al, 2021. In the flux model of spatial dynamics individuals move between patches and only individuals in the same patch can interact.