COVID‐19: A multiwave SIR‐based model for learning waves

One of the greatest challenges of the COVID‐19 pandemic has been the way evolving regulation, information, and sentiment have 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 multiwave susceptible–infected–recovered (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 susceptible–exposed–infected–recovered–dead (SEIRD) model into a multiwave SEIRD model and test it on forecasting COVID‐19 cases from the John Hopkins University data set for states in the United States. We find that compared to the traditional SEIRD model, the multiwave SEIRD model improves mean absolute percentage error (MAPE) by 15%–25% for the United States. We benchmark the multiwave SEIRD model against top performing Center for Disease Control (CDC) models for COVID‐19 and find that the multiwave SERID model is able to outperform the majority of CDC models in long‐term predictions.

Detection of COVID-19 using ResNet50, VGG19, MobileNet, and Forecasting, using Logistic Regression, Prophet, and SEIRD Model

Artificial Intelligence can quickly identify hazardous viral strains in humans. To detect COVID-19 symptoms, AI algorithms can be used to train to examine medical images like X-rays and CT scans. This can help healthcare providers to diagnose the disease more accurately and quickly. AI helps examine data on the spread of COVID-19 andmake predictions about how it will likely spread in the future. Machine learning algorithms known as Convolutional Neural Networks (CNN) are highly effective at evaluating images. As a result, CNN could assist in the early detection of COVID-19 by evaluating medical images like X-rays and CT scans to spot the disease's symptoms. This article's main aim is to provide brief information on some of the CNN models to detect and forecast COVID-19. The models were purely trained with Chest X-ray images of different categorized patients. The COVID-19 prediction models like ResNet50, VGG19, and MobileNet give accuracies of 98.50%, 97.68%, and 93.94%, respectively. On the other hand, forecasting also plays a vital role in reducing the pandemic because it helps us to analyze the risk and plan a solution to avoid it. The model is trained with some forecasting techniques like Prophet, LogisticRegression, and S EIRD model based on a text-based dataset that contains parameters such as the number of people infected per day recovered per day an d many more for visualizing the trends in forecasting, which help in decision-making to analyze risks and plan solutions to prevent the further spread of the disease. © 2023 IEEE.

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.

Human Mobility Driven Modeling of an Infectious Disease

In conventional disease models, disease properties are dominant parameters (e.g., infection rate, incubation pe-riod). As seen in the recent literature on infectious diseases, human behavior - particularly mobility - plays a crucial role in spreading diseases. This paper proposes an epidemiological model named SEIRD+m that considers human mobility instead of modeling disease properties alone. SEIRD+m relies on the core deterministic epidemic model SEIR (Susceptible, Exposed, Infected, and Recovered), adds a new compartment D - Dead, and enhances each SEIRD component by human mobility information (such as time, location, and movements) retrieved from cell-phone data collected by SafeGraph. We demonstrate a way to reduce the number of infections and deaths due to COVID-19 by restricting mobility on specific Census Block Groups (CBGs) detected as COVID-19 hotspots. A case study in this paper depicts that a reduction of mobility by 50 % could help reduce the number of infections and deaths in significant percentages in different population groups based on race, income, and age. © 2022 IEEE.

Bayesian Inference of a Discrete Fractional SEIRD Model

This paper deals with the Bayesian estimation of the parameters of a discrete fractional epidemic model SEIRD as an extension of the classical SEIR model, describing the dynamics of disease propagation in a population. Equilibrium points are computed and the existence stability nature at these points are discussed. The basic reproduction number R0 is calculated using next generation matrix method. The estimation of the parameters is based on Bayesian inference. The numerical simulations were used to illustrate the stability of the discrete fractional order SEIRD epidemic model and to evaluate the performance of the estimation method. The model introduced is applied to real data concerning pandemic COVID-19 in Morocco. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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.

Prediction of the Spread of Covid-19 in Indonesia Using the SEIRD Model and Hybrid Model with ARIMA Correction

Building an SEIRD segmentation model with life dynamics, estimating its parameters, and utilizing the ARIMA model to determine and predict the difference between the SEIRD model solution and the observed and fitted data constitute the machine learning approach used in this study. We use machine learning techniques to accomplish this. A hybrid method is used to process the newly collected data, using the model predictions and the residuals from the data. The historical values of the infected, recovering, and dying populations divided by the confidence intervals serve as the parameters for the SEIRD model, which in turn serve as parameters for the models' applicability. confidence level range. Long-term and short-term estimates with confidence intervals can be provided by the model, which can assess incoming data in real-time. We tested the model's predictions using actual data on COVID-19 cases in Indonesia. All current models are tested with the maximum allowed deviation during validation using MAE, MSE, MLSE, normalized MAE, and normalized MSE. The findings shown that the features of the current model are highly accurate for infected patients, patients who are recuperating, and patients who have passed away. Governments, business, and policy makers can use the findings of our suggested model to forecast controllable health hazards. This methodology can also be applied to additional research to progress science. © 2022 IEEE.

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.

Bayesian Inference of a Discrete Fractional SEIRD Model

This paper deals with the Bayesian estimation of the parameters of a discrete fractional epidemic model SEIRD as an extension of the classical SEIR model, describing the dynamics of disease propagation in a population. Equilibrium points are computed and the existence stability nature at these points are discussed. The basic reproduction number R0 is calculated using next generation matrix method. The estimation of the parameters is based on Bayesian inference. The numerical simulations were used to illustrate the stability of the discrete fractional order SEIRD epidemic model and to evaluate the performance of the estimation method. The model introduced is applied to real data concerning pandemic COVID-19 in Morocco. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

In December 2019, in Wuhan, China, a new disease was detected, and the virus easily spread throughout other nations. March 2, 2020, Morocco announced 1st infection of coronavirus. Morocco verified a total of 653,286 cases, 582,692 recovered, 60,579 active case, and 10,015 as confirmatory fatalities, as of 4 August 2021. The objective of this article is to study the mathematical modeling of undetected cases of the novel coronavirus in Morocco. The model is shown to have disease-free and an endemic equilibrium point. We have discussed the local and global stability of these equilibria. The parameters of the model and undiscovered instances of COVID-19 were assessed by the least squares approach in Morocco and have been eliminated. We utilized a Matlab tool to show developments in undiscovered instances in Morocco and to validate predicted outcomes. Like results, until August 4, 2021, the total number of infected cases of COVID-19 in Morocco is 24,663,240, including 653,286 confirmed cases, against 24,009,954 undetected. Further, our approach gives a good approximation of the actual COVID-19 data from Morocco and will be used to estimate the undetected cases of COVID-19 in other countries of the world and to study other pandemics that have the same nature of spread as COVID-19.

Stability analysis and numerical simulation of dynamic and fractional SEIRD models for spread of nCOVID-19 in Turkey

There are various mathematical models that have been designed for forecasting the future behavior of coronavirus spreading, which helps to rapidly control the process while there is no treatment and vaccines. The main aim of this study is to describe COVID-19 dynamics in Turkey by using a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) model. For this purpose, a new SEIRD model of nCOVID-19 and its fractional-order version are designed. The basic reproduction number is calculated with the generation operator method. All possible equilibria of the dynamic model are investigated in terms of the basic reproduction number. Further, stability conditions are obtained through the Routh-Hurwitz and Lyapunov stability theories. Finally, some numerical simulations of the dynamic system and its fractional version are given based on the data from the number of nCOVID-19 cases in Turkey. These results provide to implicate the theoretical findings corresponding to the model. © 2022 World Scientific Publishing Company.

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.

An Evaluation of Time Series-Based Modeling and Forecasting of Infectious Diseases Progression using Statistical Versus Compartmental Methods

As a case study for our research, COVID-19, that was caused by a unique coronavirus, has substantially affected the globe, not only in terms of healthcare, but also in terms of economics, education, transportation, and politics. Predicting the pandemic's course is critical to combating and tracking its spread. The objective of our study is to evaluate, optimize and fine-Tune state of the art prediction models in order to enhance its performance and to automate its function as possible. Therefore, a comparison between statistical versus compartmental methods for time series-based modeling and forecasting of infectious disease progression was conducted. The comparison included several classical univariate time series statistical models, including Exponential Smoothing, Holt, Holt-Winters, and Seasonal Auto Regressive Integrated Moving Average (SARIMA), as opposed to an optimized version of the compartmental multivariate epidemiological model SEIRD, which is referred to in our study, as, Non-Linear L-BFGS-B Fitted SEIRD. The mentioned methods were implemented and fine-Tuned to model and forecast COVID-19 outbreak situation represented by confirmed cases, recoveries, and fatalities in (Australia, Canada, Egypt, India, United States of America and United Kingdom). Through the implementing and tuning of both types of models, we have observed that while univariate time series forecasting models such as SARIMA produce highly accurate predictions due to their ease of use and procedure, as well as their ability to deal with seasonality and cycles in time series, multivariate epidemiological models are more powerful and extendible. Despite their complexity, epidemiological models have aided extensively in understanding the spread and severity of infectious disease pandemics such as the COVID-19 global pandemic. Using our optimized SEIRD, we have obtained a Mean Squared Log Error of 10-3 order, demonstrating the forecasts' elevated accuracy and reliability. In addition to forecasting the course of the pandemic for a 3 months season in all countries under investigation, we were able to estimate the transmission potential of COVID-19 represented by its effective reproduction number Rt. With Rt=1 is considered as the pandemic control threshold, it is evident that all of the countries under investigation are hovering just above the control threshold. This study might be relieving since it can demonstrate that the world is on the right track in terms of putting an end to the pandemic as soon as possible. The whole study shows how powerful is compartmental methods compared to classical statistical methods when used to model and forecast an infectious disease outbreak which encourages our further related research concerning the study of implementing advanced compartmental models considering additional parameters and controls. © 2022 IEEE.