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COVID-19 emerged in Wuhan, China with the first cases of a mysterious pneumonia reported in late December 2019 [1]. Sequencing of the causative agent revealed it was a novel coronavirus, in the same family as SARS and MERS, that had likely spilled over from another species such as bats. Scientists named the virus SARS-CoV-2 and the disease it causes COVID-19. Despite China's lockdown measures in mid-January [1], the first case in the United States was reported on January 20, 2020 in Snonomish County, Washington [2]. When we began this project, a limited number of COVID-19 cases had been recorded in the United States, but since then the virus has spread rapidly throughout the country. Mathematical models serve as important tools in allowing scientists and public health officials to predict the timing, scale, and location of disease outbreaks so that resources and intervention measures can be deployed efficiently and effectively. In this study, we use county-level population data as well as US air traffic information to construct a probabilistic model of COVID-19's spread across five major metropolitan areas in the US beginning in Seattle, WA.
To model the spread of the virus through human hosts, we use an SEIR model, in the family of SIR models. This is a compartmental model where individuals move through four states:
Susceptible: when an individual is able to contract the virus
Exposed: when the virus is replicating in an individual's body but they are not yet infectious
Infectious: when the virus has reached high enough levels that the individual can now transmit it to others
Removed: when the individual is no longer suffering from the disease due to recovery or death, and is therefore no longer able to pass the virus on, and in this case, also unable to be reinfected
Figure 1: SEIR compartmental model.
Deterministic differential equations can be used to represent the rate at which individuals progress from one compartment to another, as well as stochastic processes representing the probability of an individual moving to a new state. In this project, we use a combination of the two approaches, developing an agent-based model where individuals are simulated to come in contact with others and become infected with certain probabilities.
Using this model, we predict the arrival time of the disease in Los Angeles, Chicago, New York, and Atlanta, in addition to the effects of a travel restriction reducing transportation between and within these metropolitan areas. Finally, we highlight two social impacts of this pandemic, including what it means for the American prison system and the mental health implications for college students.
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