1. A model of COVID-19 propagation based on a gamma subordinated negative binomial branching process
- Author
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Jérôme Levesque, David William Maybury, and Rha David Shaw
- Subjects
0301 basic medicine ,Statistics and Probability ,Subordinator ,Computer science ,Process (engineering) ,Bayesian inference ,Bayesian probability ,Negative binomial distribution ,Models, Biological ,Article ,Infection disease propagation ,General Biochemistry, Genetics and Molecular Biology ,Interpretation (model theory) ,03 medical and health sciences ,0302 clinical medicine ,97K60 ,92D30 ,Econometrics ,Humans ,Limit (mathematics) ,Pandemics ,Branching process ,General Immunology and Microbiology ,SARS-CoV-2 ,Applied Mathematics ,COVID-19 ,Bayes Theorem ,General Medicine ,Branching processes ,030104 developmental biology ,Modeling and Simulation ,General Agricultural and Biological Sciences ,030217 neurology & neurosurgery ,Count data - Abstract
Highlights • Analytical properties of the branching processes describe COVID-19 propagation. • As an outbreak begins, the model allows for comparisons between mitigation scenarios. • The asymptotics of the process permit calibration to COVID-19 case count data., We build a parsimonious Crump-Mode-Jagers continuous time branching process of COVID-19 propagation based on a negative binomial process subordinated by a gamma subordinator. By focusing on the stochastic nature of the process in small populations, our model provides decision making insight into mitigation strategies as an outbreak begins. Our model accommodates contact tracing and isolation, allowing for comparisons between different types of intervention. We emphasize a physical interpretation of the disease propagation throughout which affords analytical results for comparison to simulations. Our model provides a basis for decision makers to understand the likely trade-offs and consequences between alternative outbreak mitigation strategies particularly in office environments and confined work-spaces. Combining the asymptotic limit of our model with Bayesian hierarchical techniques, we provide US county level inferences for the reproduction number from cumulative case count data over July and August of this year.
- Published
- 2021