This paper proposes and analyzes a stochastic Susceptible-Exposed-Infected-Removed (SEIR) spreading model on networks. Imagine a nursing home housing 28 seniors and 7 staff workers, in which one of the staff has tested positive for COVID-19. Unfortunately, the results of this test are 3 days late and the infected person had not been quarantining while waiting for their test results. What is now the individual risk to the different people living in this nursing home? If the home has access to two rapid COVID-19 viral tests, who should they be given to and why? In order to answer questions like this, we need to study stochastic models rather than deterministic ones. Unlike the vast majority of works that analyze various deterministic models, stochastic models are required when analyzing the risk of COVID-19 to individual people rather than tracking aggregate numbers in a given region. More specifically, this paper compares the results provided by analyzing stochastic and deterministic models and investigating when it is suitable to use the different models. In particular, we show why it is not suitable to use deterministic models when analyzing the spread in small communities and how these questions can be better addressed using stochastic ones. Finally, we show the added complications that arise due to the relatively long incubation period of COVID-19, and how it can be addressed. A simulated case study of the spread of COVID-19 in a 35-person nursing home is used to help illustrate our results. © 2021 American Automatic Control Council.
Stochastic vs. Deterministic Modeling for the Spread of COVID-19 in Small Networks