SEIRD Model Research Articles

Will there be a third COVID-19wave? A SVEIRD model-based study of India's situation.

Since the first patient was detected in India in late February 2020, the SARS-CoV-II virus is playing havoc on India. After the first wave, India is now riding the second wave. As was in the case of European countries like Italy and the UK, the second wave is more contagious and at the time of writing this paper, the per day infection is as high as 400,000. The alarming thing is it is not uncommon that people are getting infected multiple times. On the other hand, mass vaccination has started step by step. There is also a growing danger of potential third wave is unavoidable, which can even infect kids and minors. In this situation, an estimation of the dynamics of SARS-CoV-II is necessary to combat the pandemic. We have used a modified SEIRD model that includes vaccination and repeat infection as well. We have studied India and 8 Indian states with varying SARS-CoV-II infections. We have shown that the COVID-19 wave will be repeated from time to time, but the intensity will slow down with time. In the most possible situation, our calculation shows COVID-19 will remain endemic for the foreseeable future unless we can increase our vaccination rate manifold.

Explaining COVID-19 outbreaks with reactive SEIRD models

COVID-19 epidemics have varied dramatically in nature across the United States, where some counties have clear peaks in infections, and others have had a multitude of unpredictable and non-distinct peaks. Our lack of understanding of how the pandemic has evolved leads to increasing errors in our ability to predict the spread of the disease. This work seeks to explain this diversity in epidemic progressions by considering an extension to the compartmental SEIRD model. The model we propose uses a neural network to predict the infection rate as a function of both time and the disease’s prevalence. We provide a methodology for fitting this model to available county-level data describing aggregate cases and deaths. Our method uses Expectation-Maximization to overcome the challenge of partial observability, due to the fact that the system’s state is only partially reflected in available data. We fit a single model to data from multiple counties in the United States exhibiting different behavior. By simulating the model, we show that it can exhibit both single peak and multi-peak behavior, reproducing behavior observed in counties both in and out of the training set. We then compare the error of simulations from our model with a standard SEIRD model, and show that ours substantially reduces errors. We also use simulated data to compare our methodology for handling partial observability with a standard approach, showing that ours is significantly better at estimating the values of unobserved quantities.

A study of the COVID‐19 epidemic in India using the SEIRD model

BackgroundThe coronavirus pandemic (COVID‐19) is causing a havoc globally, exacerbated by the newly discovered SARS‐CoV‐2 virus. Due to its high population density, India is one of the most badly effected countries from the first wave of COVID‐19. Therefore, it is extremely necessary to accurately predict the state‐wise and overall dynamics of COVID‐19 to get the effective and efficient organization of resources across India.MethodsIn this study, the dynamics of COVID‐19 in India and several of its selected states with different demographic structures were analyzed using the SEIRD epidemiological model. The basic reproductive ratio R0 was systemically estimated to predict the dynamics of the temporal progression of COVID‐19 in India and eight of its states, Andhra Pradesh, Chhattisgarh, Delhi, Gujarat, Madhya Pradesh, Maharashtra, Tamil Nadu, and Uttar Pradesh.ResultsFor India, the SEIRD model calculations show that the peak of infection is expected to appear around the middle of October, 2020. Furthermore, we compared the model scenario to a Gauss ian fit of the daily infected cases and obtained similar results. The early imposition of a nation‐wide lockdown has reduced the number of infected cases but delayed the appearance of the infection peak significantly.ConclusionAfter comparing our calculations using India’s data to the real life dynamics observed in Italy and Russia, we can conclude that the SEIRD model can predict the dynamics of COVID‐19 with sufficient accuracy.

Data driven high resolution modeling and spatial analyses of the COVID-19 pandemic in Germany.

The SARS-CoV-2 virus has spread around the world with over 100 million infections to date, and currently many countries are fighting the second wave of infections. With neither sufficient vaccination capacity nor effective medication, non-pharmaceutical interventions (NPIs) remain the measure of choice. However, NPIs place a great burden on society, the mental health of individuals, and economics. Therefore the cost/benefit ratio must be carefully balanced and a target-oriented small-scale implementation of these NPIs could help achieve this balance. To this end, we introduce a modified SEIRD-class compartment model and parametrize it locally for all 412 districts of Germany. The NPIs are modeled at district level by time varying contact rates. This high spatial resolution makes it possible to apply geostatistical methods to analyse the spatial patterns of the pandemic in Germany and to compare the results of different spatial resolutions. We find that the modified SEIRD model can successfully be fitted to the COVID-19 cases in German districts, states, and also nationwide. We propose the correlation length as a further measure, besides the weekly incidence rates, to describe the current situation of the epidemic.

Mitigation strategies and compliance in the COVID-19 fight; how much compliance is enough?

The U.S. with only 4% of the world’s population, bears a disproportionate share of infections in the COVID-19 pandemic. To understand this puzzle, we investigate how mitigation strategies and compliance can work together (or in opposition) to reduce (or increase) the spread of COVID-19 infection. Building on the Oxford index, we create state-specific stringency indices tailored to U.S. conditions, to measure the degree of strictness of public mitigation measures. A modified time-varying SEIRD model, incorporating this Stringency Index as well as a Compliance Indicator is then estimated with daily data for a sample of 6 U.S. states: New York, New Hampshire, New Mexico, Colorado, Texas, and Arizona. We provide a simple visual policy tool to evaluate the various combinations of mitigation policies and compliance that can reduce the basic reproduction number to less than one, the acknowledged threshold in the epidemiological literature to control the pandemic. Understanding of this relationship by both the public and policy makers is key to controlling the pandemic. This tool has the potential to be used in a real-time, dynamic fashion for flexible policy options. Our methodology can be applied to other countries and has the potential to be extended to other epidemiological models as well. With this first step in attempting to quantify the factors that go into the “black box” of the transmission factor β, we hope that our work will stimulate further research in the dual role of mitigation policies and compliance.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion–reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD’s ability to extrapolate in time (short-time future estimates).

A novel compartmental model to capture the nonlinear trend of COVID-19

The COVID-19 pandemic took the world by surprise and surpassed the expectations of epidemiologists, governments, medical experts, and the scientific community as a whole. The majority of epidemiological models failed to capture the non-linear trend of the susceptible compartment and were unable to model this pandemic accurately. This study presents a variant of the well-known SEIRD model to account for social awareness measures, variable death rate, and the presence of asymptomatic infected individuals. The proposed SEAIRDQ model accounts for the transition of individuals between the susceptible and social awareness compartments. We tested our model against the reported cumulative infection and death data for different states in the US and observed over 98.8% accuracy. Results of this study give new insights into the prevailing reproduction number and herd immunity across the US.

Modeling the impact of public response on the COVID-19 pandemic in Ontario.

The outbreak of SARS-CoV-2 is thought to have originated in Wuhan, China in late 2019 and has since spread quickly around the world. To date, the virus has infected tens of millions of people worldwide, compelling governments to implement strict policies to counteract community spread. Federal, provincial, and municipal governments have employed various public health policies, including social distancing, mandatory mask wearing, and the closure of schools and businesses. However, the implementation of these policies can be difficult and costly, making it imperative that both policy makers and the citizenry understand their potential benefits and the risks of non-compliance. In this work, a mathematical model is developed to study the impact of social behaviour on the course of the pandemic in the province of Ontario. The approach is based upon a standard SEIRD model with a variable transmission rate that depends on the behaviour of the population. The model parameters, which characterize the disease dynamics, are estimated from Ontario COVID-19 epidemiological data using machine learning techniques. A key result of the model, following from the variable transmission rate, is the prediction of the occurrence of a second wave using the most current infection data and disease-specific traits. The qualitative behaviour of different future transmission-reduction strategies is examined, and the time-varying reproduction number is analyzed using existing epidemiological data and future projections. Importantly, the effective reproduction number, and thus the course of the pandemic, is found to be sensitive to the adherence to public health policies, illustrating the need for vigilance as the economy continues to reopen.

A SEIRD Model for Analysing the Dynamics of Coronavirus (COVID-19) Pandemic in Nigeria

The first case of the novel coronavirus (COVID–19) in sub–Saharan Africa was confirmed by Nigeria and the figure has since then been on the rise. Current global efforts are geared towards getting effective vaccine for the cure of the disease. The hope of accessing the relieve offered by the arrival of such vaccine will obviously take significant amount of time. In the face of the resurgence of the disease, the need to slow the spread and flatten the curves is currently a priority of both governmental and non–governmental organisations in Nigeria. If the dynamics of the disease can be determined, then it becomes easier to strategize and make suitable preventive policies that will slow the spread and ultimately flatten the curves. Here, the goal is to develop a compartmental–based model for analysing the dynamics of the pandemic in Nigeria. Considering the control policies currently in place - social distancing, mask usage, personal hygiene and quarantine, and using data provided by Nigeria Centre for Disease Control (NCDC), World Health Organization (WHO) and Wolfram Data Repository on COVID–19, the proposed model is fitted to the available data using the Quasi-Newton algorithm. The infection rate, average latent time, average infective time and average mortality rate are estimated. Also, the overall effectiveness of the current control policies is measured. Predictions on the turning points and possible vanishing time of the virus in Nigeria are made. Recommendations on how to manage the resurgence of the disease in Nigeria are also suggested.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models.

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion–reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model’s new capabilities.

COVID-19: A Multipeak SIR Based Model for Learning Waves and Optimizing Testing

One of the greatest challenges of the COVID-19 pandemic has been the way evolving regulation, information and sentiment has driven waves of the disease. Traditional epidemiology models, such as the SIR model, are not equipped to handle these behavioral based changes. We propose a novel multipeak SIR model, which can detect and model the waves of the disease. We bring together the SIR model’s compartmental structure with a change-point detection martingale process to identify new waves. We create a dynamic process where new waves can be flagged and learned in real time. We use this approach to extend the traditional SEIRD model into a multipeak SEIRD model and test it on forecasting COVID-19 cases from the John Hopkins University dataset for states in the United States. We found that compared to the traditional SEIRD model, the multipeak SEIRD model improves MAPE by 10%-15% for the United States, and by 25%-40% in the specific regions that were hit by the multiple waves. We then pair this model with an optimization model for testing, which is critical in managing the epidemic and which significantly outperforms alternative testing strategies (more than 57% in detection rate). We show how to prioritize symptomatic, asymptomatic and contact tracing populations, most interestingly when balancing testing early to reach contact tracers and saving tests for later when the epidemic is worse.

Optimal Time-Varying Vaccine Allocation Amid Pandemics With Uncertain Immunity Ratios

There is a concerted effort to develop vaccines to combat the public health crisis caused by COVID-19. Health experts are raising questions concerning the clinical trials, price and distribution of the vaccines among the public. Policymakers must design regulations to allocate vaccines equitably based on epidemiological as well as economic considerations. Allocation strategies must factor in the extent and duration of immunity the vaccines yield from future infections. We present a time-varying linear optimization-based approach, which incorporates epidemiological factors, such as population density, susceptible count and infected ratio as well as transportation costs, to disseminate vaccines among zones. Our approach also employs an update rule on the epidemiological statistics spawning from the SEIRD model to learn the extent of immunity provided by the vaccines. Our experiments are performed on the map of New York State with realistic mobility using spatial and ordinary differential equation-based SEIRD models. We show that the proposed approach allocates vaccines optimally while preventing zones from resource starvation. It adapts its vaccine recommendation to meet the prespecified epidemiological and economic policy requirements of zones, and is highly amenable to accommodate multiple immunity ratios, vaccine types and the time-span of acquired vaccine immunity. Moreover, we demonstrate that one can learn the latent immunity ratios of the vaccines to make more informed recommendations with time. Our ordinary differential equation-based analysis on the real demographic and infection data of New York State show that a small fraction of zones tends to exhibit a high resource demand due to their vulnerability to the pandemic spread. Our vaccine allocation strategy incorporates infection ratio as one of the criteria and is applicable to conceive a drug allocation strategy. The results suggest that incorporating the vulnerability score of zones to the epidemic spread into vaccine allocation may enhance recommendations and aid policy making.

Research on the spread of infectious diseases in closed systems based on SIR and SEIRD models

Aiming at the problem of the spread of infectious diseases in a closed system, this paper uses the Runge-Kutta method to construct a prediction model based on improved SIR infectious disease infection and a SEIRD model based on causality, and comprehensively use MATLAB and other software programming to solve the problem. The number of people infected with infectious diseases increased first and then decreased and eventually tended to zero, and the number of people infected with infectious diseases was related to the daily contact rate between the latent and the population. After the staff took preventive and control measures, the rate of transmission of infectious diseases decreased and the number of people transmitted decreased.

NUMERICAL MODELING OF THE IMPACT OF QUARANTINE MEASURES ON THE DYNAMICS OF THE EPIDEMIOLOGICAL PROCESS BASED ON THE SEIRD MODEL

The COVID-19 epidemic has once again demonstrated the importance of predicting the development of various processes and calculating the consequences. “How effective is the introduction of strict quarantine measures?” and “Will the quarantine be able to stop the epide­mic?” — these questions still have no clear answer. This article aims to answer these questions using mathematical modeling tools using the SEIRD model, modified to account for the peculiarities of the spread of COVID-19. The SEIRD model belongs to the class of differential dynamic models, which allows quick experimentation to predict the spread of the disease and calculate its influence on the development of certain processes. Based on numerical modeling, the author demonstrates that insufficient quarantine measures provide only a temporary effect. After they end, with an insufficient level of “population immunity”, the epidemic starts growing again, leading to a second morbidity peak. This paper presents numerical calculations to track the duration impact and quarantine measures’ severity on the dynamics of the epidemiological process. The results show that strict restrictive measures are not always effective, and strict short-term measures have less effect than softer, but long-term measures. In addition, the author provides an example of finding the parameters of quarantine measures that ensure fixed limits on the morbidity level during the epidemic.

A SEIRD Model for Control of COVID-19: Case of Azerbaijan

Research background:The study uses the key parameters of the spread of the epidemic, dividing the population into several groupsS- susceptible,E- exposed,I- infectious,R- recovered,D- dead. It is found that the model behaves differently depending on theR₀indicator - the average number of people that one infected manages to infect. Measures to suppress the epidemic undertaken by Azerbaijan and their effectiveness have been considered.Purpose of the article:The aim of the article is to model the current dynamics of the disease for future forecasting. The model takes into account all the main parameters of the epidemic: the proportion of severe patients and the mortality rate depending on the age of the patients, the duration of the incubation period and the infectious phase of the disease; incomplete registration of infected people due to the high prevalence of asymptomatic disease and insufficient testing; possible measures to contain and suppress the epidemic and their impact onR₀.Methods:The article uses the linear regression method, which consists in finding estimates of unknown parameters and the formation of a functional relationship between the sickness rate and the factors determining it.Findings & Value added:The constructed model analyzes the growth of patients in the country after removing the restrictive measures taken in early May on the basis of real statistics.

Predicting the spread of COVID-19 in Ireland using an age-cohort SEIRD model

Predicting the spread of COVID-19 in Ireland using an age-cohort SEIRD model

Построение модификации SEIRD-модели распространения эпидемии, учитывающей особенности COVID-19

Статья посвящена построению математической модели SEIIRDm, учитывающей некоторые особенности распространения COVID-19. Представляемая модель построена на основе классической SEIRD-модели распространения эпидемий. В созданной модели, в отличие от базовой, учитывается то, что латентные носители COVID-19 являются в некоторой степени заразными, и что у существенного количества инфицированных болезнь протекает бессимптомно. В SEIIRDm-модели отражен тот факт, что выявленные больные изолируются (госпитализируются) и вероятность заражения от них резко уменьшается, а также, что карантинные меры имеют массовый характер, причем важна как степень их жесткости, так и момент введения. Кроме того, в статье обращается внимание на то, что зависимость между скоростью изменения относительного числа заболевших и относительным количеством заразных и восприимчивых может быть нелинейной, и этот факт отражен в построенной модели. Статья содержит примеры численного прогнозирования развития эпидемиологического процесса, а также моделирования влияния массовых карантинных мер, рассчитанные на основе созданной математической модели. The article is devoted to the construction of a mathematical model that takes into account some features of COVID-19 propagation. The presented model is based on the classic SEIRD epidemic distribution model. The created model, in contrast to the basic one, takes into account the fact that latent COVIND-19 carriers are somewhat contagious and that in a significant number of infected people, the disease is asymptomatic. The SEIIRDm model reflects the fact that identified patients are isolating (hospitalizing) and the probability of infection from them decreases sharply and also that the measures taken over the quarantine are massive moreover, both the degree of their rigidity and the moment of introduction are important. Besides, the article draws attention to the fact that the relationship between the rate of change in the relative number of cases and susceptible and the relative number of infected may be nonlinear, and this fact is reflected in the built model. The article provides examples of numerical forecasting of the development of the epidemiological process as well as modeling the impact of mass quarantine measures, calculated on the basis of the created mathematical model.

Modeling and forecasting of COVID-19 using a hybrid dynamic model based on SEIRD with ARIMA corrections.

The outbreak of novel coronavirus (COVID-19) attracted worldwide attention. It has posed a significant challenge for the global economies, especially the healthcare sector. Even with a robust healthcare system, countries were not prepared for the ramifications of COVID-19. Several statistical, dynamic, and mathematical models of the COVID-19 outbreak including the SEIR model have been developed to analyze the infection its transmission dynamics. The objective of this research is to use public data to study the properties associated with the COVID-19 pandemic to develop a dynamic hybrid model based on SEIRD and ascertainment rate with automatically selected parameters. The proposed model consists of two parts: the modified SEIRD dynamic model and ARIMA models. We fit SEIRD model parameters against historical values of infected, recovered and deceased population divided by ascertainment rate, which, in turn, is also a parameter of the model. Residuals of the first model for infected, recovered, and deceased populations are then corrected using ARIMA models. The model can analyze the input data in real-time and provide long- and short-term forecasts with confidence intervals. The model was tested and validated on the US COVID statistics dataset from the COVID Tracking Project. For validation, we use unseen recent statistical data. We use five common measures to estimate model prediction ability: MAE, MSE, MLSE, Normalized MAE, and Normalized MSE. We proved a great model ability to make accurate predictions of infected, recovered, and deceased patients. The output of the model can be used by the government, private sectors, and policymakers to reduce health and economic risks significantly improved consumer credit scoring.

Optimal control strategy of COVID-19 spread in Morocco using SEIRD model

Abstract This paper aims to predict the development of the COVID-19 pandemic in Morocco from a mathematical approach. Based on the reliability of the data and the nature of confirmed cases, the SEIRD model is employed to provide a theoretical framework to forecast COVID-19 ongoing epidemic. Findings suggest that the structure and parameters of the proposed model give insights into the dynamics of the virus. Hence, this study contributes to the conceptual areas of knowledge on COVID-19 in proposing an optimal control plan to help decrease the number of confirmed cases by applying preventive measures such as social distancing, wearing facial masks. Matlab/Simulink TM simulations are used to illustrate the findings.

SEIRD model to study the asymptomatic growth during COVID-19 pandemic in India.

According to the current perception, symptomatic, presymptomatic and asymptomatic infectious persons can infect the healthy population susceptible to the SARS-CoV-2. More importantly, various reports indicate that the number of asymptomatic cases can be several-fold higher than the reported symptomatic cases. In this article, we take the reported cases in India and various states within the country till September 1, as the specimen to understand the progression of the COVID-19. Employing a modified SEIRD model, we predict the spread of COVID-19 by the symptomatic as well as asymptomatic infectious population. Considering reported infection primarily due to symptomatic, we compare the model predicted results with the available data to estimate the dynamics of the asymptomatically infected population. Our data indicate that in the absence of the asymptomatic infectious population, the number of symptomatic cases would have been much less. Therefore, the current progress of the symptomatic infection can be reduced by quarantining the asymptomatically infectious population via extensive or random testing. This study is motivated strictly toward academic pursuit; this theoretical investigation is not meant for influencing policy decisions or public health practices.