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Susceptible–exposed–infectious–recovered (SEIR) models were applied to assess the effectiveness of non-pharmaceutical interventions (NPIs) and to study the dynamic behavior of the COVID-19 pandemic. Recently, SEIR models have evolved to address the change of human mobility by some NPIs for predicting the new confirmed cases. However, the models have serious limitations when applied to Seoul. Seoul has two representative quarantine policies, i.e. social distancing and the ban on gatherings. Effects of the two policies need to be reflected in different functional forms in the model because changes in human mobility do not fully reflect the ban on gatherings. Thus we propose a modified SEIR model to assess the effectiveness of social distancing, ban on gatherings and vaccination strategies. The application of the modified SEIR model was illustrated by comparing the model output with real data. • Seoul has two quarantine policies such as social distancing and ban on gatherings. • Ban on gatherings aims to mitigate the risk of mass infection in various facilities. • We propose a modified SEIR model to assess the effectiveness of the two policies. • Effects of the two policies need to be reflected in different functional forms. [ABSTRACT FROM AUTHOR]

News reporting has the potential to modify a community׳s knowledge of emerging infectious diseases and affect peoples’ attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people׳s behavioral changes, which are critical for limiting the spread of disease. [ABSTRACT FROM AUTHOR]

• An SEIR model on an adaptive network with clustering is proposed. • The impacts of different types of social distancing interventions are considered. • A threshold-based intervention captures rich behavior in the prevalence curve. • The most effective interventions start early and are restrictive. The COVID-19 pandemic has proved to be one of the most disruptive public health emergencies in recent memory. Among non-pharmaceutical interventions, social distancing and lockdown measures are some of the most common tools employed by governments around the world to combat the disease. While mathematical models of COVID-19 are ubiquitous, few have leveraged network theory in a general way to explain the mechanics of social distancing. In this paper, we build on existing network models for heterogeneous, clustered networks with random link activation/deletion dynamics to put forth realistic mechanisms of social distancing using piecewise constant activation/deletion rates. We find our models are capable of rich qualitative behavior, and offer meaningful insight with relatively few intervention parameters. In particular, we find that the severity of social distancing interventions and when they begin have more impact than how long it takes for the interventions to take full effect. [ABSTRACT FROM AUTHOR]

• Insufficient diagnostic testing capacity hampers epidemic response efforts. • COVID-19 has highlighted the need to treat testing as a resource allocation problem. • We introduce a flexible model of testing into an SEIR-based COVID-19 model. • At low testing capacities, all resources should focus on clinical testing. • As testing capacities increase, a mix of clinical and non-clinical testing is optimal. Insufficient testing capacity has been a critical bottleneck in the worldwide fight against COVID-19. Optimizing the deployment of limited testing resources has therefore emerged as a keystone problem in pandemic response planning. Here, we use a modified SEIR model to optimize testing strategies under a constraint of limited testing capacity. We define pre-symptomatic, asymptomatic, and symptomatic infected classes, and assume that positively tested individuals are immediately moved into quarantine. We further define two types of testing. Clinical testing focuses only on the symptomatic class. Non-clinical testing detects pre- and asymptomatic individuals from the general population, and a concentration parameter governs the degree to which such testing can be focused on high infection risk individuals. We then solve for the optimal mix of clinical and non-clinical testing as a function of both testing capacity and the concentration parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. At high but empirically observed testing capacities, a mix of clinical testing and non-clinical testing, even if extremely unfocused, becomes optimal. We further highlight the advantages of early implementation of testing programs, and of combining optimized testing with contact reduction interventions such as lockdowns, social distancing, and masking. [ABSTRACT FROM AUTHOR]

Abstract: The relationship between the basic reproduction number and the exponential growth rate, specific to pair approximation models, is derived for the SIS, SIR and SEIR deterministic models without demography. These models are extended by including a random rewiring of susceptible individuals from infectious (and exposed) neighbours. The derived relationship between the exponential growth rate and appears as formally consistent with those derived from homogeneous mixing models, enabling us to measure the transmission potential using the early growth rate of cases. On the other hand, the algebraic expression of for the SEIR pairwise model shows that its value is affected by the average duration of the latent period, in contrast to what happens for the homogeneous mixing SEIR model. Numerical simulations on complex contact networks are performed to check the analytical assumptions and predictions. [Copyright &y& Elsevier]

• Extend SEIR model with undetected, social interaction, hospitalization, vaccination. • Sweden, Luxembourg and Austria far from herd immunity in December 2020. • Low social interaction levels still required in December 2020 to keep Reff(t) < 1. • Social interactions impact infectious curve more than vaccination in early 2021. • Estimate vaccination rates needed to reach herd immunity by different times in 2021. Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number R eff t below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come. [ABSTRACT FROM AUTHOR]