Modifying the network-based stochastic SEIR model to account for quarantine: an application to COVID-19

Abstract

Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

Fractional-Order SEIRD Model for Global COVID-19 Outbreak

“…In these studies, the use of mathematical models as a tool proved useful for many researchers and various subsequent mathematical models were written. According to the objectives of the research and how to transfer COVID-19, various mathematical models have been written such as: the modified SI model (Kosmidis et al [8]), the SIR model (Cooper et al [9]), the SIRD model (Martinez [10]), the classical SEIR model (Yousef et al [11]), the modified SEIR model (Lopez et al [12]), the network-based stochastic SEIR model (Groendyke et al [13], the multi-stage SEIR model (Khedher et al [14]), etc. In these modelings, the ordinary-order derivative was used; however, due to the expansion of the fractional-order derivative in recent decades and the good results of fractional-order derivative modeling, many mathematicians have used the fractional-order derivative in their works, we can refer to the approaches of Almeida et al [15], Koca [16], Khan et al [17], Singh [18], Ullah et al [19], Wang et al [20], Pakhira et al [21], Sun et al [22], Edelstein-Keshet [23], Baleanu et al [24], Dokuyucu et al [25], Kumar et al [26], Ozturk et al [27], Alkahtani et al [28], and Pan et al [29].…”

A Generalized Mechanistic Model for Assessing and Forecasting the Spread of the COVID-19 Pandemic

“…Since our model is based on a constant infection rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\beta $ \end{document} , considering that an infected person will be placed on quarantine before its final recovery will allow our model to learn that an infected case in state \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$I$ \end{document} will not affect people daily, i.e., this assumption will make our model closer to reality by allowing it to automatically learn that an infected person may or may not infect people daily and will help, when needed, determine accurate basic reproduction number values regardless the constant parameters. Other studies are considering similar scenario where recovery is only possible through quarantine can be found in [37] , [47] .…”

Capturing the Effects of Transportation on the Spread of COVID-19 With a Multi-Networked SEIR Model

“…A similar model to the SEIR model, the SEIV model has been studied in previous work where the vigilant state V corresponds to a state that is not infected nor immediately susceptible, i.e., similar to the recovered state R [5] . The model has also been extended to account for quarantine [6] and asymptomatic transmission [7] . When considering how transportation can propagate a viral outbreak, the SIS model has been extended to include transportation flows between nodes [8] .…”