scholarly journals Covid-19: analysis of a modified SEIR model, a comparison of different intervention strategies and projections for India

2020 ◽  
Author(s):  
Arghya Das ◽  
Abhishek Dhar ◽  
Srashti Goyal ◽  
Anupam Kundu
Keyword(s):  
Initial Conditions ◽  
Early Time ◽  
Intervention Strategies ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Post Intervention ◽  
Seir Model ◽  
Asymptomatic Carriers ◽  
Analytic Expressions ◽  
Model Equations

To understand the spread of Covid-19, we analyse an extended Susceptible-Exposed-Infected-Recovered (SEIR) model that accounts for asymptomatic carriers, and explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, R0, to a target value , but in distinct ways, which we implement in our model equations. We find that for the same , TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post-intervention, and explains observed data for many countries. We propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Weak intervention strategies (that reduce R0 but not sufficiently) reduce the peak values of infections and the asymptotic affected population and we provide analytic expressions for these in terms of the disease parameters. We apply them in the Indian context to obtain heuristic projections for the course of the pandemic, noting that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

scholarly journals Control of COVID-19 outbreak using an extended SEIR model

2021 ◽  
pp. 1-26
Author(s):  
Sean T. McQuade ◽  
Ryan Weightman ◽  
Nathaniel J. Merrill ◽  
Aayush Yadav ◽  
Emmanuel Trélat ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Optimal Strategies ◽  
Economic Cost ◽  
Contact Tracing ◽  
Economic Activities ◽  
Seir Model ◽  
Proposed Model ◽  
High Death ◽  
Containment Measures ◽  
The Cost

The outbreak of COVID-19 resulted in high death tolls all over the world. The aim of this paper is to show how a simple SEIR model was used to make quick predictions for New Jersey in early March 2020 and call for action based on data from China and Italy. A more refined model, which accounts for social distancing, testing, contact tracing and quarantining, is then proposed to identify containment measures to minimize the economic cost of the pandemic. The latter is obtained taking into account all the involved costs including reduced economic activities due to lockdown and quarantining as well as the cost for hospitalization and deaths. The proposed model allows one to find optimal strategies as combinations of implementing various non-pharmaceutical interventions and study different scenarios and likely initial conditions.

scholarly journals Digital proximity tracing on empirical contact networks for pandemic control

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
G. Cencetti ◽  
G. Santin ◽  
A. Longa ◽  
E. Pigani ◽  
A. Barrat ◽  
...  
Keyword(s):  
Large Scale ◽  
Disease Outbreaks ◽  
Physical Distance ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Modeling Framework ◽  
Infectious Disease Outbreaks ◽  
Contact Patterns ◽  
Contact Data ◽  
The Impact

AbstractDigital contact tracing is a relevant tool to control infectious disease outbreaks, including the COVID-19 epidemic. Early work evaluating digital contact tracing omitted important features and heterogeneities of real-world contact patterns influencing contagion dynamics. We fill this gap with a modeling framework informed by empirical high-resolution contact data to analyze the impact of digital contact tracing in the COVID-19 pandemic. We investigate how well contact tracing apps, coupled with the quarantine of identified contacts, can mitigate the spread in real environments. We find that restrictive policies are more effective in containing the epidemic but come at the cost of unnecessary large-scale quarantines. Policy evaluation through their efficiency and cost results in optimized solutions which only consider contacts longer than 15–20 minutes and closer than 2–3 meters to be at risk. Our results show that isolation and tracing can help control re-emerging outbreaks when some conditions are met: (i) a reduction of the reproductive number through masks and physical distance; (ii) a low-delay isolation of infected individuals; (iii) a high compliance. Finally, we observe the inefficacy of a less privacy-preserving tracing involving second order contacts. Our results may inform digital contact tracing efforts currently being implemented across several countries worldwide.

Waves and turbulence on a beta-plane

1975 ◽  
Vol 69 (3) ◽  
pp. 417-443 ◽  
Author(s):  
Peter B. Rhines
Keyword(s):  
Weak Interaction ◽  
Initial Conditions ◽  
Computer Experiments ◽  
Zonal Flow ◽  
Similarity Solutions ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Homogeneous Fluid ◽  
Restoring Force ◽  
Model Equations

Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber kβ = (β/2U)½ independent of the initial conditions other than U, the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as \[ T = 2\int_0^{\infty} kF(k)dk/U^3\langle k\rangle , \] where F is the nonlinear transfer spectrum and 〈k〉 the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U−1d〈k〉−1/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3·0 × 10−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k [Lt ] kβ.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, $k_{\beta}^{-1} = 70\,{\rm km} $, while for the atmosphere, $k_{\beta}^{-1} = 1000\,{\rm km}$. In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).

scholarly journals Finding Research Topic and Its Effect on Research Learners’ Motivation: An Action Research

2020 ◽  
pp. 36-47
Author(s):  
Jigme Dorji
Keyword(s):  
Action Research ◽  
Undergraduate Students ◽  
Learning Experience ◽  
Intervention Strategies ◽  
Research Topic ◽  
Methods Course ◽  
Future Research ◽  
Post Intervention ◽  
Language And Culture ◽  
Interest And Motivation

This paper reports the findings from an action research on effect of teaching how to find research topic to the undergraduate students’ interest and motivation in learning research. The action research employing mixed methods approach was conducted on 95 first year Bachelor of Bhutan and Himalayan Studies (BHS) students taking research methods course at the College of Language and Culture Studies, Royal University of Bhutan. Baseline data were collected using self-developed questionnaire (N=95), focus group interview (N=6) and four experts’ rating on students’ research topics. Intervention strategies to find research topic were adapted from Bui [1] and Lester and Lester Jr.’s [2] framework and implemented to enable students to speculate, frame and evaluate their research topic. After three weeks of intervention, a post-intervention data were collected employing same procedures and tools as the pre-survey data were collected. Further, to validate the findings, researcher added field notes from the observation during implementing the intervention. Findings showed that intervention strategies have made an impact on students’ ability to find research topic, which in turn indicated that students interest and motivation towards research learning augmented. Recommendations to fortify students’ research learning experience and need for future research are also provided. 

scholarly journals Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model

2020 ◽  
Author(s):  
Victor Alexander Okhuese
Keyword(s):  
Recovery Rate ◽  
Death Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Chain Reaction ◽  
Health Community ◽  
Polymerase Chain ◽  
Model Equations ◽  
Disease Free ◽  
Pcr Test

AbstractWith sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered population. Therefore, in a bid to answer a burning question of reinfection in the recovered class, the model equations which exhibits the disease-free equilibrium (E0) state for COVID-19 coronavirus was developed in this study and was discovered to both exist as well as satisfy the criteria for a locally or globally asymptotic stability with a basic reproductive number R0 = 0 for and endemic situation. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B = 0.Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally and most significant for this study is the rate of reinfection by the recovered population which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

scholarly journals Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications

2020 ◽  
Vol 10 (20) ◽  
pp. 7113 ◽  
Author(s):  
Enrique Hernández-Orallo ◽  
Carlos T. Calafate ◽  
Juan-Carlos Cano ◽  
Pietro Manzoni
Keyword(s):  
Infectious Diseases ◽  
Epidemic Model ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Smartphone Applications ◽  
Social Distancing ◽  
Implementation Model ◽  
Decentralized Model ◽  
Centralized Model

One of the strategies to control the spread of infectious diseases is based on the use of specialized applications for smartphones. These apps offer the possibility, once individuals are detected to be infected, to trace their previous contacts in order to test and detect new possibly-infected individuals. This paper evaluates the effectiveness of recently developed contact tracing smartphone applications for COVID-19 that rely on Bluetooth to detect contacts. We study how these applications work in order to model the main aspects that can affect their performance: precision, utilization, tracing speed and implementation model (centralized vs. decentralized). Then, we propose an epidemic model to evaluate their efficiency in terms of controlling future outbreaks and the effort required (e.g., individuals quarantined). Our results show that smartphone contact tracing can only be effective when combined with other mild measures that can slightly reduce the reproductive number R0 (for example, social distancing). Furthermore, we have found that a centralized model is much more effective, requiring an application utilization percentage of about 50% to control an outbreak. On the contrary, a decentralized model would require a higher utilization to be effective.

scholarly journals Modelling and Simulating the Novel Coronavirus with Implications of Asymptomatic Carriers

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ghassane Benrhmach ◽  
Khalil Namir ◽  
Jamal Bouyaghroumni
Keyword(s):  
Control Strategies ◽  
World Health ◽  
Contact Tracing ◽  
Effective Control ◽  
Public Authorities ◽  
Asymptomatic Carriers ◽  
Social Distancing ◽  
Infected People ◽  
Novel Coronavirus ◽  
Health Organization

The World Health Organization declared that the total number of confirmed cases tested positive for SARS‐CoV‐2, affecting 210 countries, exceeded 3 million on 29 April 2020, with more than 207,973 deaths. In order to end the global COVID‐19 pandemic, public authorities have put in place multiple strategies like testing, contact tracing, and social distancing. Predictive mathematical models for epidemics are fundamental to understand the development of the epidemic and to plan effective control strategies. Some hosts may carry SARS‐CoV‐2 and transmit it to others, yet display no symptoms themselves. We propose applying a model (SELIAHRD) taking in consideration the number of asymptomatic infected people. The SELIAHRD model consists of eight stages: Susceptible, Exposed, Latent, Symptomatic Infected, Asymptomatic Infected, Hospitalized, Recovered, and Dead. The asymptomatic carriers contribute to the spread of disease, but go largely undetected and can therefore undermine efforts to control transmission. The simulation of possible scenarios of the implementation of social distancing shows that if we rigorously follow the social distancing rule then the healthcare system will not be overloaded.

scholarly journals Self-Similar Gravitational Clustering

1983 ◽  
Vol 104 ◽  
pp. 393-400
Author(s):  
G. Efstathiou
Keyword(s):  
Initial Conditions ◽  
Gravitational Instability ◽  
Early Time ◽  
Density Parameter ◽  
Small Perturbations ◽  
Gravitational Clustering ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Similarity Scaling ◽  
Clustering Pattern

The nature of the distribution of galaxies poses a challenging problem for theorists. It seems reasonable, as a start, to suppose that galaxies and clusters arose from small perturbations by gravitational instability. However, one still has the problem of the choice of initial conditions, for example, the shape of the fluctuation spectrum and the cosmological density parameter Ω. A considerable simplification is to assume that the clustering pattern obeys some simple similarity scaling, so that the clustering at some early time, apart from a change in length scale, is statistically indistinguishable from the pattern observed today. The power-law shape of the two-point correlation function and the simple forms of higher order correlation functions (Peebles, 1980) have provided some evidence that such a simplifying assumption may be relevant - just how relevant is the subject of this article.

scholarly journals A Simulation on Potential Secondary Spread of Novel Coronavirus in an Exported Country Using a Stochastic Epidemic SEIR Model

2020 ◽  
Vol 9 (4) ◽  
pp. 944 ◽  
Author(s):  
Kentaro Iwata ◽  
Chisato Miyakoshi
Keyword(s):  
Healthcare Professionals ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asian Countries ◽  
Hospital Visit ◽  
Seir Model ◽  
Stochastic Epidemic ◽  
Novel Coronavirus ◽  
The Impact ◽  
Multiple Scenarios

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection.

scholarly journals Using symbolic computation in the characterization of frictional instabilities involving orthotropic materials

2015 ◽  
Vol 25 (2) ◽  
pp. 259-267 ◽  
Author(s):  
Mohamed A. Agwa ◽  
António Pinto Da Costa
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Initial Conditions ◽  
Orthotropic Materials ◽  
Isotropic Case ◽  
Linear Elastic ◽  
Analytic Expressions ◽  
The Coefficient Of Friction ◽  
Unstable Solutions ◽  
Computer Algebra Software

Abstract The present work addresses the problem of determining under what conditions the impending slip state or the steady sliding of a linear elastic orthotropic layer or half space with respect to a rigid flat obstacle is dynamically unstable. In other words, we search the conditions for the occurrence of smooth exponentially growing dynamic solutions with perturbed initial conditions arbitrarily close to the steady sliding state, taking the system away from the equilibrium state or the steady sliding state. Previously authors have shown that a linear elastic isotropic half space compressed against and sliding with respect to a rigid flat surface may get unstable by flutter when the coefficient of friction μ and Poisson’s ratio ν are sufficiently large. In the isotropic case they have been able to derive closed form analytic expressions for the exponentially growing unstable solutions as well as for the borders of the stability regions in the space of parameters, because in the isotropic case there are only two dimensionless parameters (μ and ν). Already for the simplest version of orthotropy (an orthotropic transversally isotropic material) there are seven governing parameters (μ, five independent material constants and the orientation of the principal directions of orthotropy) and the expressions become very lengthy and literally impossible to manipulate manually. The orthotropic case addressed here is impossible to solve with simple closed form expressions, and therefore the use of computer algebra software is required, the main commands being indicated in the text.

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