Quarantine and Vaccination in Hierarchical Epidemic Model

The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained. © 2023 by the authors.

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States.

The rapid spread of the numerous outbreaks of the coronavirus disease 2019 (COVID-19) pandemic has fueled interest in mathematical models designed to understand and predict infectious disease spread, with the ultimate goal of contributing to the decision making of public health authorities. Here, we propose a computational pipeline that dynamically parameterizes a modified SEIRD (susceptible-exposed-infected-recovered-deceased) model using standard daily series of COVID-19 cases and deaths, along with isolated estimates of population-level seroprevalence. We test our pipeline in five heavily impacted states of the US (New York, California, Florida, Illinois, and Texas) between March and August 2020, considering two scenarios with different calibration time horizons to assess the update in model performance as new epidemiologic data become available. Our results show a median normalized root mean squared error (NRMSE) of 2.38% and 4.28% in calibrating cumulative cases and deaths in the first scenario, and 2.41% and 2.30% when new data are assimilated in the second scenario, respectively. Then, 2-week (4-week) forecasts of the calibrated model resulted in median NRMSE of cumulative cases and deaths of 5.85% and 4.68% (8.60% and 17.94%) in the first scenario, and 1.86% and 1.93% (2.21% and 1.45%) in the second. Additionally, we show that our method provides significantly more accurate predictions of cases and deaths than a constant parameterization in the second scenario (p < 0.05). Thus, we posit that our methodology is a promising approach to analyze the dynamics of infectious disease outbreaks, and that our forecasts could contribute to designing effective pandemic-arresting public health policies. Supplementary Information: The online version contains supplementary material available at 10.1007/s00366-023-01816-9.

Estimation of Mortality Rate of COVID-19 in India using SEIRD Model

In India, the number of infections is rapidly increased with a mounting death toll during the second wave of Coronavirus disease (COVID-19). To measure the severity of the said disease, the mortality rate plays an important role. In this research work, the mortality rate of COVID-19 is estimated by using the Susceptible-Exposed-Infected-Recovered-Dead (SEIRD) epidemiological model. As the disease contains a significant amount of uncertainty, a fundamental SEIRD model with minimal assumptions is employed. Further, a basic method is proposed to obtain time-dependent estimations of the parameters of the SEIRD model by using historical data. From our proposed model and with the predictive analysis, it is expected that the infection may go rise in the month of May-2021 and the mortality rate could go as high as 1.8%. Such high rates of mortality may be used as a measure to understand the severity of the situation.

Sequential time-window learning with approximate Bayesian computation: an application to epidemic forecasting.

The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more sophisticated mathematical techniques for analyzing epidemic data and generating reliable forecasts. In this work, we propose a framework for analyzing complex dynamical systems by dividing the data in consecutive time-windows to be separately analyzed. We fit parameters for each time-window through an approximate Bayesian computation (ABC) algorithm, and the posterior distribution of parameters obtained for one window is used as the prior distribution for the next window. This Bayesian learning approach is tested with data on COVID-19 cases in multiple countries and is shown to improve ABC performance and to produce good short-term forecasting. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-022-07865-x.

Model Development and Prediction of Covid-19 Pandemic in Bangladesh with Nonlinear Incident

We introduce a SEIRD compartmental model to analyze the dynamics of the pandemic in Bangladesh. The multi-wave patterns of the new infective in Bangladesh from the day of the official confirmation to August 15, 2021, are simulated in the proposed SEIRD model. To solve the model equations numerically, we use the RK-45 method. Primarily, we establish some theorems including local and global stability for the proposed model. The analysis shows that the death curve simulated by the model provides a very good agreement with the officially confirmed death data for the Covid-19 pandemic in Bangladesh. Furthermore, the proposed model estimates the duration and peaks of Covid-19 in Bangladesh which are compared with the real data.

Responses to COVID-19 with probabilistic programming.

The COVID-19 pandemic left its unique mark on the twenty-first century as one of the most significant disasters in history, triggering governments all over the world to respond with a wide range of interventions. However, these restrictions come with a substantial price tag. It is crucial for governments to form anti-virus strategies that balance the trade-off between protecting public health and minimizing the economic cost. This work proposes a probabilistic programming method to quantify the efficiency of major initial non-pharmaceutical interventions. We present a generative simulation model that accounts for the economic and human capital cost of adopting such strategies, and provide an end-to-end pipeline to simulate the virus spread and the incurred loss of various policy combinations. By investigating the national response in 10 countries covering four continents, we found that social distancing coupled with contact tracing is the most successful policy, reducing the virus transmission rate by 96% along with a 98% reduction in economic and human capital loss. Together with experimental results, we open-sourced a framework to test the efficacy of each policy combination.

Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach.

This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model [1,2,3,4] by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ \mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ \mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ \mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.

Artificial intelligence approach toward analysis of COVID-19 development—Personalized and epidemiological model

Although ML has been examined for a variety of epidemiological and clinical concerns, as well as for COVID-19 survival prediction, there is a notable lack of research dealing with ML utilization in predicting disease severity changes during the course of the disease. This chapter encompasses two approaches in predicting COVID-19 spread—personalized model for predicting disease development in infected individual patients and an epidemiological model for predicting disease spread in population. Personalized model uses XGboost for the classification of infected individuals into four different groups based on the values of blood biomarkers analyzed by Gradient boosting regressor and chosen as biomarkers with the highest effect on the classification of COVID-19 patients. The epidemiological model includes two proposed methods—differential equation-based SEIRD model and an LSTM deep learning model. Proposed models can be used as tools useful in the research and control of infectious illnesses and in reducing the burden on the health system. © 2022 Elsevier Inc. All rights reserved.

Simulation of prevention and control of COVID-19 epidemic based on computer modeling

Taking Henan Province as the research object, this paper discusses the temporal and spatial distribution of COVID-19 and its spreading laws and characteristics. Through computer modeling and intelligent fitting, the Moran'I and Moran's I exponential distributions are obtained to describe the global space and local space density. Establish SEIRD model and use simulated annealing algorithm to predict its development trend. At the same time, taking into account the development of the epidemic and the infection rate under different conditions, as well as the local testing capabilities and testing costs, combined with mathematical expectations, design a reasonable virus testing program. © 2021 IEEE.

A fractional-order model for the novel coronavirus (COVID-19) outbreak.

The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide. To understand and predict the transmission dynamics of this disease, mathematical models can be very effective. It has been shown that the fractional order is related to the memory effects, which seems to be more effective for modeling the epidemic diseases. Motivated by this, in this paper, we propose fractional-order susceptible individuals, asymptomatic infected, symptomatic infected, recovered, and deceased (SEIRD) model for the spread of COVID-19. We consider both classical and fractional-order models and estimate the parameters by using the real data of Italy, reported by the World Health Organization. The results show that the fractional-order model has less root-mean-square error than the classical one. Finally, the prediction ability of both of the integer- and fractional-order models is evaluated by using a test data set. The results show that the fractional model provides a closer forecast to the real data.

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

Background: The 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. Methods: In 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 R 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. Results: For 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 Gaussian 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. Conclusion: After 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.

The impact of travelling on the COVID-19 infection cases in Germany.

BACKGROUND: COVID-19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. Looking back at the situation in Germany in 2020, the number of cases increased exponentially in early March. Social restrictions were imposed by closing e.g. schools, shops, cafés and restaurants, as well as borders for travellers. This reaped success as the infection rate descended significantly in early April. In mid July, however, the numbers started to rise again. Of particular reasons was that from mid June onwards, the travel ban has widely been cancelled or at least loosened. We aim to measure the impact of travellers on the overall infection dynamics for the case of (relatively) few infectives and no vaccinations available. We also want to analyse under which conditions political travelling measures are relevant, in particular in comparison to local measures. By travel restrictions in our model we mean all possible measures that equally reduce the possibility of infected returnees to further spread the disease in Germany, e.g. travel bans, lockdown, post-arrival tests and quarantines. METHODS: To analyse the impact of travellers, we present three variants of an susceptible-exposed-infected-recovered-deceased model to describe disease dynamics in Germany. Epidemiological parameters such as transmission rate, lethality, and detection rate of infected individuals are incorporated. We compare a model without inclusion of travellers and two models with a rate measuring the impact of travellers incorporating incidence data from the Johns Hopkins University. Parameter estimation was performed with the aid of the Monte-Carlo-based Metropolis algorithm. All models are compared in terms of validity and simplicity. Further, we perform sensitivity analyses of the model to observe on which of the model parameters show the largest influence the results. In particular, we compare local and international travelling measures and identify regions in which one of these shows larger relevance than the other. RESULTS: In the comparison of the three models, both models with the traveller impact rate yield significantly better results than the model without this rate. The model including a piecewise constant travel impact rate yields the best results in the sense of maximal likelihood and minimal Bayesian Information Criterion. We synthesize from model simulations and analyses that travellers had a strong impact on the overall infection cases in the considered time interval. By a comparison of the reproductive ratios of the models under traveller/no-traveller scenarios, we found that higher traveller numbers likely induce higher transmission rates and infection cases even in the further course, which is one possible explanation to the start of the second wave in Germany as of autumn 2020. The sensitivity analyses show that the travelling parameter, among others, shows a larger impact on the results. We also found that the relevance of travel measures depends on the value of the transmission parameter: In domains with a lower transmission parameter, caused either by the current variant or local measures, it is found that handling the travel parameters is more relevant than those with lower value of the transmission. CONCLUSIONS: We conclude that travellers is an important factor in controlling infection cases during pandemics. Depending on the current situation, travel restrictions can be part of a policy to reduce infection numbers, especially when case numbers and transmission rate are low. The results of the sensitivity analyses also show that travel measures are more effective when the local transmission is already reduced, so a combination of those two appears to be optimal. In any case, supervision of the influence of travellers should always be undertaken, as another pandemic or wave can happen in the upcoming years and vaccinations and basic hygiene rules alone might not be able to prevent further infection waves.

A robust prediction from a minimal model of COVID-19 - Can we avoid the third wave?

COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here, we have modified the susceptible-exposed-infected-recovered-dead model by introducing a vaccination term. One of our main assumptions is that the infection rate (β(t)) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case, we invoke this nature of the infection rate (β(t)) to model the cyclical behavior of the COVID-19 pandemic within a short period. This study focuses on a minimalistic approach where we have logically deduced that the infection rate (β(t)) and the vaccination rate (λ) are the most important parameters while the other parameters can be assumed to be constants throughout the simulation. Finally, we have studied the rich interplay between the infection rate (β(t)) and the vaccination rate (λ) on the infectious cases of COVID-19 and made some robust conclusions regarding the global behavior of this pandemic in near future. © 2022 World Scientific Publishing Company.

A Time-Dependent SEIRD Model for Forecasting the Transmission Dynamics in Infectious Diseases: COVID-19 a Case Study

The spread of a disease caused by a virus can happen through human-to-human contact or from the environment. An estimation is crucial to make policy decisions and plan for the medical emergencies that may arise. Many mathematical models extend the standard SIR model to capture disease spread and estimate the infections, recoveries, and fatalities that may result from the disease. One major factor important in the forecasts using the models is the dynamic nature of the disease spread. Unless we can develop a way to guide this dynamic spread, estimating the parameters may not give accurate forecasts. To capture the transmission dynamics, we implement a time-dependent SEIRD model. In this data-driven model, we try to estimate parameters from the equations derived from the traditional SEIRD model. The main principle is to keep the model generic while making minimal assumptions. In this work, we have derived a data-driven model from SEIRD, where we attempt to forecast infected, recovered, and deceased rates of COVID-19 for the next 21 days. A method for estimating the dynamic change in the parameters of the model is the crucial contribution of this work. The model has been tested for India at the district level and the USA at the state level. The mean absolute percentage error (MAPE) obtained for predicting confirmed/deceased for day 7 is between 4–5%, by day 14 is about 8–10%,and 12–15% for day 21. A dashboard has been developed based on the proposed model showing the predictions for active, recovered, and deaths at the district level in India [1]. We believe that these forecasts can help the governments in planning for emergencies such as ICU requirements, PPEs, and hospitalizations during the spread of infectious diseases. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Epidemiological Predictive Modeling of COVID-19 Infection: Development, Testing, and Implementation on the Population of the Benelux Union.

Since the outbreak of coronavirus disease-2019 (COVID-19), the whole world has taken interest in the mechanisms of its spread and development. Mathematical models have been valuable instruments for the study of the spread and control of infectious diseases. For that purpose, we propose a two-way approach in modeling COVID-19 spread: a susceptible, exposed, infected, recovered, deceased (SEIRD) model based on differential equations and a long short-term memory (LSTM) deep learning model. The SEIRD model is a compartmental epidemiological model with included components: susceptible, exposed, infected, recovered, deceased. In the case of the SEIRD model, official statistical data available online for countries of Belgium, Netherlands, and Luxembourg (Benelux) in the period of March 15 2020 to March 15 2021 were used. Based on them, we have calculated key parameters and forward them to the epidemiological model, which will predict the number of infected, deceased, and recovered people. Results show that the SEIRD model is able to accurately predict several peaks for all the three countries of interest, with very small root mean square error (RMSE), except for the mild cases (maximum RMSE was 240.79 ± 90.556), which can be explained by the fact that no official data were available for mild cases, but this number was derived from other statistics. On the other hand, LSTM represents a special kind of recurrent neural network structure that can comparatively learn long-term temporal dependencies. Results show that LSTM is capable of predicting several peaks based on the position of previous peaks with low values of RMSE. Higher values of RMSE are observed in the number of infected cases in Belgium (RMSE was 535.93) and Netherlands (RMSE was 434.28), and are expected because of thousands of people getting infected per day in those countries. In future studies, we will extend the models to include mobility information, variants of concern, as well as a medical intervention, etc. A prognostic model could help us predict epidemic peaks. In that way, we could react in a timely manner by introducing new or tightening existing measures before the health system is overloaded.

National Holidays and Social Mobility Behaviors: Alternatives for Forecasting COVID-19 Deaths in Brazil.

In this paper, we investigate the influence of holidays and community mobility on the transmission rate and death count of COVID-19 in Brazil. We identify national holidays and hallmark holidays to assess their effect on disease reports of confirmed cases and deaths. First, we use a one-variate model with the number of infected people as input data to forecast the number of deaths. This simple model is compared with a more robust deep learning multi-variate model that uses mobility and transmission rates (R0, Re) from a SEIRD model as input data. A principal components model of community mobility, generated by the principal component analysis (PCA) method, is added to improve the input features for the multi-variate model. The deep learning model architecture is an LSTM stacked layer combined with a dense layer to regress daily deaths caused by COVID-19. The multi-variate model incremented with engineered input features can enhance the forecast performance by up to 18.99% compared to the standard one-variate data-driven model.

A stochastic metapopulation state-space approach to modeling and estimating COVID-19 spread.

Mathematical models are widely recognized as an important tool for analyzing and understanding the dynamics of infectious disease outbreaks, predict their future trends, and evaluate public health intervention measures for disease control and elimination. We propose a novel stochastic metapopulation state-space model for COVID-19 transmission, which is based on a discrete-time spatio-temporal susceptible, exposed, infected, recovered, and deceased (SEIRD) model. The proposed framework allows the hidden SEIRD states and unknown transmission parameters to be estimated from noisy, incomplete time series of reported epidemiological data, by application of unscented Kalman filtering (UKF), maximum-likelihood adaptive filtering, and metaheuristic optimization. Experiments using both synthetic data and real data from the Fall 2020 COVID-19 wave in the state of Texas demonstrate the effectiveness of the proposed model.

The effect of dispatch of national medical teams to Wuhan on its control and prevention of COVID-19.

OBJECTIVES: As a unique prevention and control measure, the dispatch of national medical teams to Wuhan has played a key role in protecting Wuhan against COVID-19. This study aimed to quantitatively evaluate the effect of this key measure in reducing infections and fatalities. STUDY DESIGN: A scenario analysis is used in this study, where the forming of scenarios is on the basis of the stages of medical to Wuhan. We divided the evaluation into 4 scenarios: Scenario Ⅰ-no dispatch, Scenario Ⅱ-dispatch of 4599 medical staff, Scenario Ⅲ-dispatch of 16,000 staff, and Scenario Ⅳ-dispatch of 32,000 staff. METHODS: The extended Susceptible-Exposed-Infectious-Recovered-Death model was adopted to quantify the effect of the dispatch of national medical teams to Wuhan on COVID-19 prevention and control. RESULTS: The dispatch dramatically cuts the channels for the transmission of the virus and succeeds in raising the cure rates while reducing the fatality rates. If there were no dispatch at all, a cumulative total of 158,881 confirmed cases, 18,700 fatalities and a fatality rate of 11.77% would have occurred in Wuhan, which are 3.2 times, 4.8 times and 1.5 times the real figures respectively. The dispatch has avoided 108,541 confirmed cases and 14,831 fatalities in this city. CONCLUSIONS: The proven successful measure provides valuable experience and enlightenment to international cooperation on prevention and control of COVID-19, as well as a similar outbreak of new emerging infectious diseases.

Modelling the spread of covid-19 in the capital of Brazil using numerical solution and cellular automata.

The novel coronavirus disease 2019 (COVID-19) still challenges researchers due to its spread and deaths. Hence, the classical epidemic SIR and SEIRD models inspired by the epidemic's outbreak are widely used to predict the evolution of the disease. In addition to classical approaches, describing complex phenomena through Cellular Automata (CA) is a highly effective way to understand the iterations on a populated system. The present research analyzed the usage of CA to generate an epidemic-computational model from a micro perspective based on parameters obtained through a statistical fit from a macro perspective. After validating SIR and SEIRD models with the government official data for Brasilia, Brazil, the authors applied the obtained parameters to the Cellular Automata model. The CA model simulated the spread of the virus from infected to uninfected people in a restrained environment (i.e., a supermarket) under several varied conditions applying an approach never adopted before. The manner of applying CA in this research proved to represent an essential tool in predicting the spread of the coronavirus in confined spaces with random movements of people. The CA numerical open-source presented has the purpose of clarifying how the spread occurs not only as a mathematical curve but in an organic way. The numerical simulations from the CA model allowed the authors to conclude that markets and stores are relevant places where might be infections. Thus, every local store and the market owner should reason about the aspects that could avoid the spread of the disease, coming up with efficient solutions. Each environment has specific features that only those who know them are the ones capable of managing.

The spreading of Covid-19 in Mexico: A diffusional approach.

In this work, we analyze the spreading of Covid-19 in Mexico using the spatial SEIRD epidemiologic model. We use the information of the 32 regions (States) that conform the country, such as population density, verified infected cases, and deaths in each State. We extend the SEIRD compartmental epidemiologic with diffusion mechanisms in the exposed and susceptible populations. We use the Fickian law with the diffusion coefficient proportional to the population density to encompass the diffusion effects. The numerical results suggest that the epidemiologic model demands time-dependent parameters to incorporate non-monotonous behavior in the actual data in the global dynamic. The diffusional model proposed in this work has great potential in predicting the virus spreading on different scales, i.e., local, national, and between countries, since the complete reduction in people mobility is impossible.