A SEIR-like model with a time-dependent contagion factor describes the dynamics of the Covid-19 pandemic

Abstract

I consider a simple, deterministic SEIR-like model without spatial or age structure, including a presymptomatic state and distinguishing between reported and nonreported infected individuals. Using a time-dependent contagion factor β(t) (in the form a piecewise constant function) and literature values for other epidemiological parameters, I obtain good fits to observational data for the cumulative number of confirmed cases in over 160 regions (103 countries, 24 Brazilian states and 34 U.S. counties). The evolution of β is useful for characterizing the state of the epidemic. The analysis provides insight into general trends associated with the pandemic, such as the tendency toward reduced contagion, and the fraction of the population exposed to the virus.

Consistent Pattern of Epidemic Slowing Across Many Geographies Led to Longer, Flatter Initial Waves of the COVID-19 Pandemic

“…Whereas the conclusions of our study do not directly contradict any of these previously published results [15][16][17][18][19][20][21][22][23][24][25][26][27][42][43][44][45], our approach of using the dynamics and prevalence of COVID-19 to understand patterns in R(t) is unique in several ways, and particularly through the introduction of "local pandemic time". Changes in the March 31, 2022 10/24 time-dependent transmission are driven by many factors that vary from one location to another.…”

“…We note that a large number of studies have used available databases of interventions [8][9][10], coupled with statistical methods, to estimate the impact of different interventions on the time-varying reproduction number [15][16][17][18][19][20][21][22][23][24][25][26][27][42][43][44][45] . In an extensive study, Liu et al [16] applied statistical methods to 13 categories of NPIs using confirmed cases data from January to June of 2020 from 130 countries.…”

“…The reproduction number was fit using a machine learning (ML) procedure and the authors found a strong correlation between passenger air travel, driving, walking and transit mobility and the effective reproduction number (with a long time delay of about 17 days). In another study Dickman [43] developed a deterministic SEIR model without age or spatial structure but with a time-dependent reproduction number. The model allowed the transmission parameter, β , to have three piecewise constant values and the parameters of the model were obtained by least squares fitting to the reported cumulative confirmed number of cases at a large number (160) of locations, providing insight into the initial decrease in the value of the reproduction number.…”

“…In contrast with many other studies [15][16][17][18][19][20][21][22][23][24][25][26][27][42][43][44][45], we did not explicitly consider individual interventions as explanations for reducing values of R. Rather, we investigated overall trends in R. This, we believe, may help guide higher-level planning for the next pandemic caused by a severe respiratory pathogen. We found a common pattern of a reduction in transmissibility during the initial period, rather than constant transmissibility, of which there were no obvious examples.…”

Serious role of non-quarantined COVID-19 patients for random walk simulations

“…So far, various epidemic models have been presented for analyzing an epidemic spread 34 – 37 . In most cases, the epidemic of influenza and other infectious diseases has been theoretically explained by SIR model 38 – 41 that considers susceptible (S), infected (I), and recovered (R) people.…”