A model based study on the dynamics of COVID-19: Prediction and control

Optimal vaccination strategies on networks and in metropolitan areas

This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control function. The commuting patterns are incorporated through a weighted adjacency matrix and a parameter that selects day and night periods. The optimal control problem is formulated to minimize a functional cost that balances the number of hospitalizations and vaccines, including restrictions of a weekly availability cap and an application capacity of vaccines per unit of time. The key findings of this work are bounds for the basic reproduction number, particularly in the case of a metropolitan area, and the study of the optimal control problem. Theoretical analysis and numerical simulations provide insights into disease dynamics and the effectiveness of control measures. The research highlights the importance of prioritizing vaccination in the capital to better control the disease spread, as we depicted in our numerical simulations. This model serves as a tool to improve resource allocation in epidemic control across metropolitan regions.

Designing a model to estimate the burden of COVID-19 in Iran

The novel coronavirus disease 2019 (COVID-19) is the latest evidence of an epidemic disease resulting in an extraordinary number of infections and claimed several lives, along with extensive economic and social consequences. In response to the emergency situation, countries introduced different policies to address the situation, with different levels of efficacy. This paper outlines the protocol for developing a model to analyze the burden of COVID-19 in Iran and the effect of policies on the incidence and cumulative death of the disease. The importance of the model lies in the fact that no study, according to the authors' best knowledge, tried to quantify the impact of the disease on Iran society and the impact of various implemented interventions on disease control. Based on a systematic review of COVID-19 prediction models and expert interviews, we developed a system dynamics model that not only includes an epidemic part but also considers the impact of various policies implemented by the Ministry of Health. The epidemic model estimates the incidence and mortality of COVID-19 in Iran. The model also intends to evaluate the effect of implemented policies on these outcomes. The model reflects the continuum of COVID-19 infection and care in Iran (of which some of its elements are unique) and key activities and decisions in delivering care. The model is calibrated and validated using data published by the Ministry of Health of Iran. Finally, the study aims to provide evidence of the impact of interventions intended to curb COVID-19 in Iran. Insights provided by the model will be necessary for controlling either future waves of the disease or similar future pandemics.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Enhancing COVID-19 forecasting precision through the integration of compartmental models, machine learning and variants

Predicting epidemic evolution is essential for making informed decisions and guiding the implementation of necessary countermeasures. Computational models are vital tools that provide insights into illness progression and enable early detection, proactive intervention, and targeted preventive measures. This paper introduces Sybil, a framework that integrates machine learning and variant-aware compartmental models, leveraging a fusion of data-centric and analytic methodologies. To validate and evaluate Sybil's forecasts, we employed COVID-19 data from several European and U.S. states. The dataset included the number of new and recovered cases, fatalities, and variant presence over time. We evaluate the forecasting precision of Sybil in periods in which there is a change in the trend of the pandemic evolution or a new variant appears. Results demonstrate that Sybil outperforms conventional data-centric approaches, being able to forecast accurately the changes in the trend, the magnitude of these changes, and the future prevalence of new variants.

Assessing the impact of vaccination and medical resource allocation on infectious disease outbreak management: a case study of COVID-19 in Taiyuan City

Introduction

Amidst an emerging infectious disease outbreak, the rational allocation of vaccines and medical resources is crucial for controlling the epidemic's progression.

Method

Analysing COVID-19 data in Taiyuan City from December 2022 to January 2023, this study constructed a S V 1 V 2 V 3 E I Q H R dynamics model to assess the impact of COVID-19 vaccination and resource allocation on epidemic trends.

Results

Vaccination significantly reduces infection rates, hospitalisations, and severe cases, while also curtailing strain on medical resources by reducing congestion periods. An early and sufficient reserve of medical resources can delay the onset of medical congestion, and with increased maximum capacity of medical resources, the congestion's end can be accelerated. Stronger resource allocation capabilities lead to earlier congestion resolution within a fixed total resource pool.

Discussion

Integrating vaccination and medical resource allocation can effectively reduce medical congestion duration and alleviate the epidemic's strain on medical resource capacity (CCMR).

A stochastic approach for co-evolution process of virus and human immune system

Infectious diseases have long been a shaping force in human history, necessitating a comprehensive understanding of their dynamics. This study introduces a co-evolution model that integrates both epidemiological and evolutionary dynamics. Utilizing a system of differential equations, the model represents the interactions among susceptible, infected, and recovered populations for both ancestral and evolved viral strains. Methodologically rigorous, the model's existence and uniqueness have been verified, and it accommodates both deterministic and stochastic cases. A myriad of graphical techniques have been employed to elucidate the model's dynamics. Beyond its theoretical contributions, this model serves as a critical instrument for public health strategy, particularly predicting future outbreaks in scenarios where viral mutations compromise existing interventions.

An Epidemic Model with Infection Age and Vaccination Age Structure

A model of epidemic dynamics is developed that incorporates continuous variables for infection age and vaccination age. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. This property is shown to be of major importance in the severity of the epidemic, when the infectious period of an infected individual precedes the symptomatic period. The model also analyzes the efficacy of vaccination in terms of vaccination age. The immunity to infection of vaccinated individuals varies with vaccination age and is also of major significance in the severity of the epidemic. Application of the model to the 2003 SARS epidemic in Taiwan and the COVID-19 epidemic in New York provides insights into the dynamics of these diseases. It is shown that the SARS outbreak was effectively contained due to the complete overlap of infectious and symptomatic periods, allowing for the timely isolation of affected individuals. In contrast, the pre-symptomatic spread of COVID-19 in New York led to a rapid, uncontrolled epidemic. These findings underscore the critical importance of the pre-symptomatic infectious period and the vaccination strategies in influencing the dynamics of an epidemic.

Paving initial forecasting COVID-19 spread capabilities by nonexperts: A case study

Objective

The COVID-19 outbreak compelled countries to take swift actions across various domains amidst substantial uncertainties. In Israel, significant COVID-19-related efforts were assigned to the Israeli Home Front Command (HFC). HFC faced the challenge of anticipating adequate resources to efficiently and timely manage its numerous assignments despite the absence of a COVID-19 spread forecast. This paper describes the initiative of a group of motivated, though nonexpert, people to provide the needed COVID-19 rate of spread of the epidemic forecasts.

Methods

To address this challenge, the Planning Chamber, reporting to the HFC Medical Commander, undertook the task of mapping HFC healthcare challenges and resource requirements. The nonexpert team continuously collected public COVID-19-related data published by the Israeli Ministry of Health (MoH) of verified cases, light cases, mild cases, serious condition cases, life-support cases, and deaths, and despite lacking expertise in statistics and healthcare and having no sophisticated statistical packages, generated forecasts using Microsoft® Excel.

Results

The analysis methods and applications successfully demonstrated the desired outcome of the lockdown by showing a transition from exponential to polynomial growth in the spread of the virus. These forecasting activities enabled decision-makers to manage resources effectively, supporting the HFC's operations during the pandemic.

Conclusions

Nonexpert forecasting may become a necessity and be beneficial, and similar analysis efforts can be easily replicated in future events. However, they are inherently short-lived and should persist only until knowledge centers can bridge the expertise gap. It is crucial to identify major events, such as lockdowns, during forecasting due to their potential impact on spread rates. Despite the expertise gap, the Planning Chamber's approach provided valuable resource management insights for HFC's COVID-19 response.

Threshold behavior and exponential ergodicity of an sir epidemic model: the impact of random jamming and hospital capacity

This article uses hospital capacity to determine the treatment rate for an infectious disease. To examine the impact of random jamming and hospital capacity on the spread of the disease, we propose a stochastic SIR model with nonlinear treatment rate and degenerate diffusion. Our findings demonstrate that the disease's persistence or eradication depends on the basic reproduction number [Formula: see text]. If [Formula: see text], the disease is eradicated with a probability of 1, while [Formula: see text] results in the disease being almost surely strongly stochastically permanent. We also demonstrate that if [Formula: see text], the Markov process has a unique stationary distribution and is exponentially ergodic. Additionally, we identify a critical capacity which determines the minimum hospital capacity required.

Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity

This paper aims to explore the complex dynamics and impact of vaccinations on controlling epidemic outbreaks. An epidemic transmission model which considers vaccinations and two different infection statuses with different infectivity is developed. In terms of a dynamic analysis, we calculate the basic reproduction number and control reproduction number and discuss the stability of the disease-free equilibrium. Additionally, a numerical simulation is performed to explore the effects of vaccination rate, immune waning rate and vaccine ineffective rate on the epidemic transmission. Finally, a sensitivity analysis revealed three factors that can influence the threshold: transmission rate, vaccination rate, and the hospitalized rate. In terms of optimal control, the following three time-related control variables are introduced to reconstruct the corresponding control problem: reducing social distance, enhancing vaccination rates, and enhancing the hospitalized rates. Moreover, the characteristic expression of optimal control problem. Four different control combinations are designed, and comparative studies on control effectiveness and cost effectiveness are conducted by numerical simulations. The results showed that Strategy C (including all the three controls) is the most effective strategy to reduce the number of symptomatic infections and Strategy A (including reducing social distance and enhancing vaccination rate) is the most cost-effective among the three strategies.

A novel queue-based stochastic epidemic model with adaptive stabilising control

The main objective of this paper is to propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a setup under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate comprise the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly more straightforward and tractable than semi-Markov models with a similar level of generality. Based on stochastic stability, we derive a sufficient condition for a shrinking epidemic regarding the queuing system's occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil, and assess the effect of different stabilising strategies in the latter setting. Results suggest that the proposed approach can curb the epidemic with various occupation rate levels if the mitigation is timely.

Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states

Understanding and forecasting the progression of disease epidemics is possible through the study of nonlinear epidemic biochemical models that describe the relationship among susceptible, infected, and immune individuals in a population. In this paper, by determining the algebraic invariant planes and studying the Hopf bifurcation on these invariant planes, we study the stability of the Hopf bifurcation in the infection-free and endemic states of the SIR and SIRS epidemic models with bilinear incidence rate. We analyze the stability of the limit cycles of the bilinear incidence SIR and SIRS models at the steady state point where infection vanishes and at the endemic steady state point where the system behaves in an oscillatory manner. We demonstrate the algebraic results by numerical simulations for parameter values that satisfy the conditions for both free and endemic states.

Leveraging an epidemic-economic mathematical model to assess human responses to COVID-19 policies and disease progression

It is imperative that resources are channelled towards programs that are efficient and cost effective in combating the spread of COVID-19, the disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). This study proposed and analyzed control strategies for that purpose. We developed a mathematical disease model within an optimal control framework that allows us to investigate the best approach for curbing COVID-19 epidemic. We address the following research question: what is the role of community compliance as a measure for COVID-19 control? Analyzing the impact of community compliance of recommended guidelines by health authorities-examples, social distancing, face mask use, and sanitizing-coupled with efforts by health authorities in areas of vaccine provision and effective quarantine-showed that the best intervention in addition to implementing vaccination programs and effective quarantine measures, is the active incorporation of individuals' collective behaviours, and that resources should also be directed towards community campaigns on the importance of face mask use, social distancing, and frequent sanitizing, and any other collective activities. We also demonstrated that collective behavioral response of individuals influences the disease dynamics; implying that recommended health policy should be contextualized.

Dynamics of an SEIR model with media coverage mediated nonlinear infectious force

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

Stability analysis and optimal control of a fractional-order generalized SEIR model for the COVID-19 pandemic

In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R 0 , the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann-Liouville (R-L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed.

Evaluation of the EsteR Toolkit for COVID-19 Decision Support: Sensitivity Analysis and Usability Study

BACKGROUND

During the COVID-19 pandemic, local health authorities were responsible for managing and reporting current cases in Germany. Since March 2020, employees had to contain the spread of COVID-19 by monitoring and contacting infected persons as well as tracing their contacts. In the EsteR project, we implemented existing and newly developed statistical models as decision support tools to assist in the work of the local health authorities.

OBJECTIVE

The main goal of this study was to validate the EsteR toolkit in two complementary ways: first, investigating the stability of the answers provided by our statistical tools regarding model parameters in the back end and, second, evaluating the usability and applicability of our web application in the front end by test users.

METHODS

For model stability assessment, a sensitivity analysis was carried out for all 5 developed statistical models. The default parameters of our models as well as the test ranges of the model parameters were based on a previous literature review on COVID-19 properties. The obtained answers resulting from different parameters were compared using dissimilarity metrics and visualized using contour plots. In addition, the parameter ranges of general model stability were identified. For the usability evaluation of the web application, cognitive walk-throughs and focus group interviews were conducted with 6 containment scouts located at 2 different local health authorities. They were first asked to complete small tasks with the tools and then express their general impressions of the web application.

RESULTS

The simulation results showed that some statistical models were more sensitive to changes in their parameters than others. For each of the single-person use cases, we determined an area where the respective model could be rated as stable. In contrast, the results of the group use cases highly depended on the user inputs, and thus, no area of parameters with general model stability could be identified. We have also provided a detailed simulation report of the sensitivity analysis. In the user evaluation, the cognitive walk-throughs and focus group interviews revealed that the user interface needed to be simplified and more information was necessary as guidance. In general, the testers rated the web application as helpful, especially for new employees.

CONCLUSIONS

This evaluation study allowed us to refine the EsteR toolkit. Using the sensitivity analysis, we identified suitable model parameters and analyzed how stable the statistical models were in terms of changes in their parameters. Furthermore, the front end of the web application was improved with the results of the conducted cognitive walk-throughs and focus group interviews regarding its user-friendliness.

Modeling and multi-objective optimal control of reaction-diffusion COVID-19 system due to vaccination and patient isolation

In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system's asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R 0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C ( m , σ ) , social benefit B ( m , σ ) , threshold R 0 ( m , σ ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost ( M S C ) and maximum social benefit ( M S B ) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β 1 ( t ) , β 2 ( t ) , and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R 0 ( 1 : 8 ) = 0.4678 , R 0 ( 9 : 20 ) = 2.7655 , R 0 ( 21 : 30 ) = 0.3810 and R 0 ( 31 : 100 ) = 0.7819 ; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control.

Studying of COVID-19 fractional model: Stability analysis

This article focuses on the recent epidemic caused by COVID-19 and takes into account several measures that have been taken by governments, including complete closure, media coverage, and attention to public hygiene. It is well known that mathematical models in epidemiology have helped determine the best strategies for disease control. This motivates us to construct a fractional mathematical model that includes quarantine categories as well as government sanctions. In this article, we prove the existence and uniqueness of positive bounded solutions for the suggested model. Also, we investigate the stability of the disease-free and endemic equilibriums by using the basic reproduction number (BRN). Moreover, we investigate the stability of the considering model in the sense of Ulam-Hyers criteria. To underpin and demonstrate this study, we provide a numerical simulation, whose results are consistent with the analysis presented in this article.

Transfer-recursive-ensemble learning for multi-day COVID-19 prediction in India using recurrent neural networks

The COVID-19 pandemic has put a huge challenge on the Indian health infrastructure. With a larger number of people getting affected during the second wave, hospitals were overburdened, running out of supplies and oxygen. Hence, predicting new COVID-19 cases, new deaths, and total active cases multiple days in advance can aid better utilization of scarce medical resources and prudent pandemic-related decision-making. The proposed method uses gated recurrent unit networks as the main predicting model. A study is conducted by building four models pre-trained on COVID-19 data from four different countries (United States of America, Brazil, Spain, and Bangladesh) and fine-tuned on India's data. Since the four countries chosen have experienced different types of infection curves, the pre-training provides a transfer learning to the models incorporating diverse situations into account. Each of the four models then gives 7-day ahead predictions using the recursive learning method for the Indian test data. The final prediction comes from an ensemble of the predictions of the different models. This method with two countries, Spain and Bangladesh, is seen to achieve the best performance amongst all the combinations as well as compared to other traditional regression models.

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France.

Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: a case study of Pakistan

In this paper, a five-compartment model is used to explore the dynamics of the COVID-19 pandemic, taking the vaccination campaign into account. The present model consists of five components that lead to a system of five ordinary differential equations. In this paper, we examined the disease from the perspective of a fractal fractional derivative in the Caputo sense with a power law type kernal. The model is also fitted with real data for Pakistan between June 1, 2020, and March 8, 2021. The fundamental mathematical characteristics of the model have been investigated thoroughly. We have calculated the equilibrium points and the reproduction number for the model and obtained the feasible region for the system. The existence and stability criteria of the model have been validated using the Banach fixed point theory and the Picard successive approximation technique. Furthermore, we have conducted stability analysis for both the disease-free and endemic equilibrium states. On the basis of sensitivity analysis and the dynamics of the threshold parameter, we have estimated the effectiveness of vaccination and identified potential control strategies for the disease using the proposed model outbreaks. The stability of the concerned solution in Ulam-Hyers and Ulam-Hyers-Rassias sense is also investigated. For the proposed problem, some results regarding basic reproduction numbers and stability analysis for various parameters are represented graphically. Matlab software is used for numerical illustrations. Graphical representations are given for different fractional orders and for various parametric values.

Analysis and dynamical transmission of Covid-19 model by using Caputo-Fabrizio derivative

The SARS-CoV-2 pandemic is an urgent problem with unpredictable properties and is widespread worldwide through human interactions. This work aims to use Caputo-Fabrizio fractional operators to explore the complex action of the Covid-19 Omicron variant. A fixed-point theorem and an iterative approach are used to prove the existence and singularity of the model’s system of solutions. Laplace transform is used to generalize the fractional order model for stability and unique solution of the iterative scheme. A numerical scheme is also constructed by using an exponential law kernel for the computational and simulation of the Covid-19 Model. The graphs demonstrate that the fractional model of Covid-19 is accurate. In the sense of Caputo-Fabrizio, one can obtain trustworthy information about the model in either an integer or non-integer scenario. This sense also provides useful information about the model’s complexity.

Modeling Consequences of COVID-19 and Assessing Its Epidemiological Parameters: A System Dynamics Approach

In 2020, coronavirus (COVID-19) was declared a global pandemic and it remains prevalent today. A necessity to model the transmission of the virus has emerged as a result of COVID-19's exceedingly contagious characteristics and its rapid propagation throughout the world. Assessing the incidence of infection could enable policymakers to identify measures to halt the pandemic and gauge the required capacity of healthcare centers. Therefore, modeling the susceptibility, exposure, infection, and recovery in relation to the COVID-19 pandemic is crucial for the adoption of interventions by regulatory authorities. Fundamental factors, such as the infection rate, mortality rate, and recovery rate, must be considered in order to accurately represent the behavior of the pandemic using mathematical models. The difficulty in creating a mathematical model is in identifying the real model variables. Parameters might vary significantly across models, which can result in variations in the simulation results because projections primarily rely on a particular dataset. The purpose of this work was to establish a susceptible-exposed-infected-recovered (SEIR) model describing the propagation of the COVID-19 outbreak throughout the Kingdom of Saudi Arabia (KSA). The goal of this study was to derive the essential COVID-19 epidemiological factors from actual data. System dynamics modeling and design of experiment approaches were used to determine the most appropriate combination of epidemiological parameters and the influence of COVID-19. This study investigates how epidemiological variables such as seasonal amplitude, social awareness impact, and waning time can be adapted to correctly estimate COVID-19 scenarios such as the number of infected persons on a daily basis in KSA. This model can also be utilized to ascertain how stress (or hospital capacity) affects the percentage of hospitalizations and the number of deaths. Additionally, the results of this study can be used to establish policies or strategies for monitoring or restricting COVID-19 in Saudi Arabia.

Forecasting the COVID-19 with Interval Type-3 Fuzzy Logic and the Fractal Dimension

In this article, the prediction of COVID-19 based on a combination of fractal theory and interval type-3 fuzzy logic is put forward. The fractal dimension is utilized to estimate the time series geometrical complexity level, which in this case is applied to the COVID-19 problem. The main aim of utilizing interval type-3 fuzzy logic is for handling uncertainty in the decision-making occurring in forecasting. The hybrid approach is formed by an interval type-3 fuzzy model structured by fuzzy if then rules that utilize as inputs the linear and non-linear values of the dimension, and the forecasts of COVID-19 cases are the outputs. The contribution is the new scheme based on the fractal dimension and interval type-3 fuzzy logic, which has not been proposed before, aimed at achieving an accurate forecasting of complex time series, in particular for the COVID-19 case. Publicly available data sets are utilized to construct the interval type-3 fuzzy system for a time series. The hybrid approach can be a helpful tool for decision maker in fighting the pandemic, as they could use the forecasts to decide immediate actions. The proposed method has been compared with previous works to show that interval type-3 fuzzy systems outperform previous methods in prediction.

Prediction of the COVID-19 infectivity and the sustainable impact on public health under deep learning algorithm

The aim is to explore the development trend of COVID-19 (Corona Virus Disease 2019) and predict the infectivity of 2019-nCoV (2019 Novel Coronavirus), as well as its impact on public health. First, the existing data are analyzed through data pre-processing to extract useful feature factors. Then, the LSTM (Long-Short Term Memory) prediction model in the deep learning algorithm is used to predict the epidemic situation in Hubei Province, outside Hubei nationwide, and the whole country, respectively. Meanwhile, the impact of intervention time changes on the epidemic situation is compared. The results show that the prediction results are almost consistent with the actual values. Specifically, Hubei Province abolishes quarantine restrictions after the Spring Festival holiday, and the first COVID-19 peak is reached in late February, while the second COVID-19 peak has been reached in early March. Finally, the cumulative number of diagnoses reaches 85,000 cases, with an increase of 15,000 cases compared with the nationwide cases outside Hubei under the continuous implementation of prevention and control measures. Under the prediction of the proposed LSTM model, if the nationwide implementation of prevention and control interventions is postponed by 5 days, the epidemic will peak in early March, and the cumulative number of diagnoses will be about 200,000; and if the intervention measures are implemented five days earlier, the epidemic will peak in mid-February, with a cumulative number of diagnoses of approximately 40,000. Meanwhile, the proposed LSTM model predicts the RMSE values of the epidemic situation in Hubei Province, outside Hubei nationwide, and the whole country as 34.63, 75.42, and 50.27, respectively. Under model comparison analysis, the prediction error of the proposed LSTM model is small and has better applicability over similar algorithms. The results show that the LSTM model is effective and has high performance in infectious disease prediction, and the research results can provide scientific and effective references for subsequent related research.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the S V E I H R deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number ( R 0 ). Detailed stability analysis of the no-disease equilibrium ( E 0 ) of the proposed model to observe the dynamics of the system was carried out and the results showed that E 0 is stable if R 0 < 1 and unstable when R 0 > 1 . The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R 0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our S V E I H R model, the results showed that R 0 = 0 . 208 , which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R 0 = 1 . 7214 , which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community.

Epidemic dynamics in census-calibrated modular contact network

Network-based models are apt for understanding epidemic dynamics due to their inherent ability to model the heterogeneity of interactions in the contemporary world of intense human connectivity. We propose a framework to create a wire-frame that mimics the social contact network of the population in a geography by lacing it with demographic information. The framework results in a modular network with small-world topology that accommodates density variations and emulates human interactions in family, social, and work spaces. When loaded with suitable economic, social, and urban data shaping patterns of human connectance, the network emerges as a potent decision-making instrument for urban planners, demographers, and social scientists. We employ synthetic networks to experiment in a controlled environment and study the impact of zoning, density variations, and population mobility on the epidemic variables using a variant of the SEIR model. Our results reveal that these demographic factors have a characteristic influence on social contact patterns, manifesting as distinct epidemic dynamics. Subsequently, we present a real-world COVID-19 case study for three Indian states by creating corresponding surrogate social contact networks using available census data. The case study validates that the demography-laced modular contact network reduces errors in the estimates of epidemic variables.

Stochastic dynamical behavior of COVID-19 model based on secondary vaccination

This paper mainly studies the dynamical behavior of a stochastic COVID-19 model. First, the stochastic COVID-19 model is built based on random perturbations, secondary vaccination and bilinear incidence. Second, in the proposed model, we prove the existence and uniqueness of the global positive solution using random Lyapunov function theory, and the sufficient conditions for disease extinction are obtained. It is analyzed that secondary vaccination can effectively control the spread of COVID-19 and the intensity of the random disturbance can promote the extinction of the infected population. Finally, the theoretical results are verified by numerical simulations.

Multicriteria group decision making via generalized trapezoidal intuitionistic fuzzy number-based novel similarity measure and its application to diverse COVID-19 scenarios

Havoc, brutality, economic breakdown, and vulnerability are the terms that can be rightly associated with COVID-19, for the kind of impact it is having on the whole world for the last two years. COVID-19 came as a nightmare and it is still not over yet, changing its form factor with each mutation. Moreover, each unpredictable mutation causes more severeness. In the present article, we outline a decision support algorithm using Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs) to deal with various facets of COVID-19 problems. Intuitionistic fuzzy sets (IFSs) and their continuous counterparts, viz., the intuitionistic fuzzy numbers (IFNs), have the flexibility and effectiveness to handle the uncertainty and fuzziness associated with real-world problems. Although a meticulous amount of research works can be found in the literature, a wide majority of them are based mainly on normalized IFNs rather than the more generalized approach, and most of them had several limitations. Therefore, we have made a sincere attempt to devise a novel Similarity Measure (SM) which considers the evaluation of two prominent features of GTrIFNs, which are their expected values and variances. Then, to establish the superiority of our approach we present a comparative analysis of our method with several other established similarity methods considering ten different profiles of GTrIFNs. The proposed SM is then validated for feasibility and applicability, by elaborating a Fuzzy Multicriteria Group Decision Making (FMCGDM) algorithm and it is supportedby a suitable illustrative example. Finally, the proposed SM approach is applied to tackle some significant concerns due to COVID-19. For instance, problems like the selection of best medicine for COVID-19 infected patients; proper healthcare waste disposal technique; and topmost government intervention measures to prevent the COVID-19 spread, are some of the burning issues which are handled with our newly proposed SM approach.

Graphical abstract

A topic-based hierarchical publish/subscribe messaging middleware for COVID-19 detection in X-ray image and its metadata

Putting real-time medical data processing applications into practice comes with some challenges such as scalability and performance. Processing medical images from different collaborators is an example of such applications, in which chest X-ray data are processed to extract knowledge. It is not easy to process data and get the required information in real time using central processing techniques when data get very large in size. In this paper, real-time data are filtered and forwarded to the right processing node by using the proposed topic-based hierarchical publish/subscribe messaging middleware in the distributed scalable network of collaborating computation nodes instead of classical approaches of centralized computation. This enables processing streaming medical data in near real time and makes a warning system possible. End users have the capability of filtering/searching. The returned search results can be images (COVID-19 or non-COVID-19) and their meta-data are gender and age. Here, COVID-19 is detected using a novel capsule network-based model from chest X-ray images. This middleware allows for a smaller search space as well as shorter times for obtaining search results.

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

The coronavirus disease 2019, started spreading around December 2019, still persists in the population all across the globe. Though different countries have been able to cope with the disease to some extent and vaccination for the same has been developed, it cannot be ignored that the disease is still not on the verge of completely eradicating, which in turn creates a need for having deeper insights of the disease in order to understand it well and hence be able to work towards its eradication. Meanwhile, using mitigation strategies like non-pharmaceutical interventions can help in controlling the disease. In this work, our aim is to study the dynamics of COVID-19 using compartmental approach by applying various analytical methods. We obtain formula for important tools like R0 and establish the stability of disease-free equilibrium point for R0<1. Further, based on R0, we discuss the stability and existence of the endemic equilibrium point. We incorporate various control strategies possible and using optimal control theory, study their expected positive impacts on the spread of the disease. Later, using a biologically feasible set of parameters, we numerically analyse the model. We even study the trend of the outbreak in China, for over 120 days, where the active cases rise up to a peak and then the curve flattens.

Future forecasting prediction of Covid-19 using hybrid deep learning algorithm

Due the quick spread of coronavirus disease 2019 (COVID-19), identification of that disease, prediction of mortality rate and recovery rate are considered as one of the critical challenges in the whole world. The occurrence of COVID-19 dissemination beyond the world is analyzed in this research and an artificial-intelligence (AI) based deep learning algorithm is suggested to detect positive cases of COVID19 patients, mortality rate and recovery rate using real-world datasets. Initially, the unwanted data like prepositions, links, hashtags etc., are removed using some pre-processing techniques. After that, term frequency inverse-term frequency (TF-IDF) andBag of Words (BoW) techniques are utilized to extract the features from pre-processed dataset. Then, Mayfly Optimization (MO) algorithm is performed to pick the relevant features from the set of features. Finally, two deep learning procedures, ResNet model and GoogleNet model, are hybridized to achieve the prediction process. Our system examines two different kinds of publicly available text datasets to identify COVID-19 disease as well as to predict mortality rate and recovery rate using those datasets. There are four different datasets are taken to analyse the performance, in which the proposed method achieves 97.56% accuracy which is 1.40% greater than Linear Regression (LR) and Multinomial Naive Bayesian (MNB), 3.39% higher than Random Forest (RF) and Stochastic gradient boosting (SGB) as well as 5.32% higher than Decision tree (DT) and Bagging techniques if first dataset. When compared to existing machine learning models, the simulation result indicates that a proposed hybrid deep learning method is valuable in corona virus identification and future mortality forecast study.

Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain

Omicron, a mutant strain of COVID-19, has been sweeping the world since November 2021. A major characteristic of Omicron transmission is that it is less harmful to healthy adults, but more dangerous for people with underlying disease, the elderly, or children. To simulate the spread of Omicron in the population, we developed a new 9-dimensional mathematical model with high-risk and low-risk exposures. Then we analyzed its dynamic properties and obtain the basic reproduction numberR 0 . With the data of confirmed cases from March 1, 2022 published on the official website of Shanghai, China, we used the weighted nonlinear least square estimation method to estimate the parameters, and get the basic reproduction numberR 0 ≈ 1 . 5118 . Finally, we considered three control measures (isolation, detection and treatment), and studied the optimal control strategy and cost-effectiveness analysis of the model. The control strategy G is determined to be the optimal control strategy from the purpose of making fewer people infected. In strategy G, the three human control measures contain six control variables, and the control strength of these variables needs to be varied according to the pattern shown in Figure 11, so that the number of infections can be minimized and the percentage of reduction of infections can reach more than 95%.

Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods

In this paper, a mathematical epidemiological model in the form of reaction diffusion is proposed for the transmission of the novel coronavirus (COVID-19). The next-generation method is utilized for calculating the threshold number R0 while the least square curve fitting approach is used for estimating the parameter values. The mathematical epidemiological model without and with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Further, for the graphical solution of the non-linear model, we have applied a one-step explicit meshless procedure. We study the numerical simulation of the proposed model under the effects of diffusion. The stability analysis of the endemic equilibrium point is investigated. The obtained numerical results are compared mutually since the exact solutions are not available.

How to enhance psychological security of enterprise employees during the COVID-19 pandemic: Based on MRA and fsQCA

The economic impact caused by the outbreak and dynamic evolution of COVID-19 has reduced employees' psychological security (PS), which not only threatens the physical and mental health of employees but also seriously affects the stable operation and sustainable development of enterprises. PS has been determined to be closely related to daily life experiences. Therefore, the purpose of this article is to examine the types and combinations of life events that improve employees' PS during the pandemic. Cross-sectional data came from 764 enterprise employees in 8 provinces and cities in China during the pandemic period. The participants completed the PS scale to evaluate their PS, and the PS events scale to evaluate the different types of daily life events they experienced. Multiple regression analysis (MRA) and fuzzy-set qualitative comparative analysis (fsQCA) methods were used to test the research hypothesis. The results of MRA suggest that rich leisure activities (RLA), harmonious family relationship (HFR), stable economic order (SEO) and recognition and support from others (RSO) are important life events that enhance employees' PS. The results of fsQCA suggest that the independent role of SEO, the combined role of sound social security system (SSSS), peace and health events (PHE) and HFR, the combined role of PHE, fulfilling work/life status (FWLS), SEO and RSO can substitute for each other to promote employees' high PS. This article reveals the contribution of daily life events to the PS of enterprise employees, and provides an empirical basis for formulating corresponding intervention measures to promote the physical and mental health of enterprise employees and effective enterprise management.

Dynamical analysis of a discrete-time COVID-19 epidemic model

In this paper, we explore local dynamics with topological classifications, bifurcation analysis, and chaos control in a discrete-time COVID-19 epidemic model in the interior ofℝ + 4 . It is explored that for all involved parametric values, discrete-time COVID-19 epidemic model has boundary equilibrium solution and also it has an interior equilibrium solution under definite parametric condition. We have explored the local dynamics with topological classifications about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model by linear stability theory. Further, for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also studied the existence of possible bifurcations about boundary and interior equilibrium solutions and proved that there exists no flip bifurcation about boundary equilibrium solution. Moreover, it is proved that about interior equilibrium solution, there exist Hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Moreover, by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally, theoretical results are verified numerically.

MODELING THE DYNAMICS OF COVID-19 TRANSMISSION IN INDIA: SOCIAL DISTANCING, REGIONAL SPREAD AND HEALTHCARE CAPACITY

In the new paradigm of health-centric governance, policymakers are in constant need of appropriate metrics to determine suitable policies in a non-arbitrary fashion. To this end, in this paper, a compartmentalized model for the transmission of COVID-19 is developed, with a socially distanced compartment added to the model. The modification allows for administrators to quantify the extent to which voluntary social distancing norms are followed, and address restrictions accordingly. Modifications are also made to incorporate inter-region migration, and suitable metrics are proposed to quantify the impact of migration on the rise of cases. The healthcare capacity is modeled and a method is developed to study the consequences of the saturation of the healthcare system. The model and related measures are used to study the nature of the transmission and spread of COVID-19 in India, and appropriate insights are drawn.

Multi-scale causality analysis between COVID-19 cases and mobility level using ensemble empirical mode decomposition and causal decomposition

The global spread of the coronavirus disease 2019 (COVID-19) pandemic has affected the world in many ways. Due to the communicable nature of the disease, it is difficult to investigate the causal reason for the epidemic's spread sufficiently. This study comprehensively investigates the causal relationship between the spread of COVID-19 and mobility level on a multi time-scale and its influencing factors, by using ensemble empirical mode decomposition (EEMD) and the causal decomposition approach. Linear regression analysis investigates the significance and importance of the influential factors on the intrastate and interstate causal strength. The results of an EEMD analysis indicate that the mid-term and long-term domain portrays the macroscopic component of the states' mobility level and COVID-19 cases, which represents overall intrinsic characteristics. In particular, the mobility level is highly associated with the long-term variations of COVID-19 cases rather than short-term variations. Intrastate causality analysis identifies the significant effects of median age and political orientation on the causal strength at a specific time-scale, and some of them cannot be identified from the existing method. Interstate causality results show a negative association with the interstate distance and the positive one with the airline traffic in the long-term domain. Clustering analysis confirms that the states with the higher the gross domestic product and the more politically democratic tend to more adhere to social distancing. The findings of this study can provide practical implications to the policymakers that whether the social distancing policies are effectively working or not should be monitored by long-term trends of COVID-19 cases rather than short-term.

Comparison of prediction accuracies between two mathematical models for the assessment of COVID-19 damage at the early stage and throughout 2020

BACKGROUND

The negative impacts of COVID-19 (ImpactCOVID) on public health are commonly assessed using the cumulative numbers of confirmed cases (CNCCs). However, whether different mathematical models yield disparate results based on varying time frames remains unclear. This study aimed to compare the differences in prediction accuracy between 2 proposed COVID-19 models, develop an angle index that can be objectively used to evaluate ImpactCOVID, compare the differences in angle indexes across countries/regions worldwide, and examine the difference in determining the inflection point (IP) on the CNCCs between the 2 models.

METHODS

Data were downloaded from the GitHub website. Two mathematical models were examined in 2 time-frame scenarios during the COVID-19 pandemic (the early 20-day stage and the entire year of 2020). Angle index was determined by the ratio (=CNCCs at IP÷IP days). The R2 model and mean absolute percentage error (MAPE) were used to evaluate the model's prediction accuracy in the 2 time-frame scenarios. Comparisons were made using 3 visualizations: line-chart plots, choropleth maps, and forest plots.

RESULTS

Exponential growth (EXPO) and item response theory (IRT) models had identical prediction power at the earlier outbreak stage. The IRT model had a higher model R2 and smaller MAPE than the EXPO model in 2020. Hubei Province in China had the highest angle index at the early stage, and India, California (US), and the United Kingdom had the highest angle indexes in 2020. The IRT model was superior to the EXPO model in determining the IP on an Ogive curve.

CONCLUSION

Both proposed models can be used to measure ImpactCOVID. However, the IRT model (superior to EXPO in the long-term and Ogive-type data) is recommended for epidemiologists and policymakers to measure ImpactCOVID in the future.

EKF-SIRD model algorithm for predicting the coronavirus (COVID-19) spreading dynamics

In this paper, we study the Covid 19 disease profile in the Algerian territory since February 25, 2020 to February 13, 2021. The idea is to develop a decision support system allowing public health decision and policy-makers to have future statistics (the daily prediction of parameters) of the pandemic; and also encourage citizens for conducting health protocols. Many studies applied traditional epidemic models or machine learning models to forecast the evolution of coronavirus epidemic, but the use of such models alone to make the prediction will be less precise. For this purpose, we assume that the spread of the coronavirus is a moving target described by an epidemic model. On the basis of a SIRD model (Susceptible-Infection-Recovery- Death), we applied the EKF algorithm to predict daily all parameters. These predicted parameters will be much beneficial to hospital managers for updating the available means of hospitalization (beds, oxygen concentrator, etc.) in order to reduce the mortality rate and the infected. Simulations carried out reveal that the EKF seems to be more efficient according to the obtained results.

The Relative Contribution of Climatic, Demographic Factors, Disease Control Measures and Spatiotemporal Heterogeneity to Variation of Global COVID-19 Transmission

Despite a substantial number of COVID-19 related research papers published, it remains unclear as to which factors are associated with the observed variation in global transmission and what are their relative levels of importance. This study applies a rigorous statistical framework to provide robust estimations of the factor effects for a global and integrated perspective on this issue. We developed a mixed effect model exploring the relative importance of potential factors driving COVID-19 transmission while incorporating spatial and temporal heterogeneity of spread. We use an integrated data set for 87 countries across six continents for model specification and fitting. The best model accounts for 70.4% of the variance in the data analyzed: 10 fixed effect factors explain 20.5% of the variance, random temporal and spatial effects account for 50% of the variance. The fixed effect factors are classified into climatic, demographic and disease control groups. The explained variance in global transmission by the three groups are 0.6%, 1.1%, and 4.4% respectively. The high proportion of variance accounted for by random effects indicated striking differences in temporal transmission trajectories and effects of population mobility among the countries. In particular, the country-specific mobility-transmission relationship turns out to be the most important factor in explaining the observed global variation of transmission in the early phase of COVID-19 pandemic.

Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling

The fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.

Coronavirus (COVID-19): ARIMA-based Time-series Analysis to Forecast near Future and the Effect of School Reopening in India

COVID-19, a novel coronavirus, is currently a major worldwide threat. It has infected more than a million people globally leading to hundred-thousands of deaths. In such grave circumstances, it is very important to predict future scenario to support prevention and recurrence of the disease, aid in healthcare service preparation and help in decision making process. Following that notion, a model has been developed for forecasting future COVID-19 cases in India. The time series analysis indicates that the cases will keep on increasing in India in the coming month as the peak has not been attained until now. A statistical analysis based on the effect of reopening of schools has also been performed. It is revealed that there will be a minor increase in the active cases when pre-/primary schools are opened. The present prediction models will assist the government and medical personnel in gaining insight and planning for forthcoming conditions.

Mathematical Modeling and Control of COVID-19 Using Super Twisting Sliding Mode and Nonlinear Techniques

Since the outbreak of the COVID-19 epidemic, several control strategies have been proposed. The rapid spread of COVID-19 globally, allied with the fact that COVID-19 is a serious threat to people's health and life, motivated many researchers around the world to investigate new methods and techniques to control its spread and offer treatment. Currently, the most effective approach to containing SARS-CoV-2 (COVID-19) and minimizing its impact on education and the economy remains a vaccination control strategy, however. In this paper, a modified version of the susceptible, exposed, infectious, and recovered (SEIR) model using vaccination control with a novel construct of active disturbance rejection control (ADRC) is thus used to generate a proper vaccination control scheme by rejecting those disturbances that might possibly affect the system. For the COVID-19 system, which has a unit relative degree, a new structure for the ADRC has been introduced by embedding the tracking differentiator (TD) in the control unit to obtain an error signal and its derivative. Two further novel nonlinear controllers, the nonlinear PID and a super twisting sliding mode (STC-SM) were also used with the TD to develop a new version of the nonlinear state error feedback (NLSEF), while a new nonlinear extended state observer (NLESO) was introduced to estimate the system state and total disturbance. The final simulation results show that the proposed methods achieve excellent performance compared to conventional active disturbance rejection controls.

A multicompartment mathematical model to study the dynamic behaviour of COVID-19 using vaccination as control parameter

To analyse novel coronavirus disease (COVID-19) transmission in India, this article provides an extended SEIR multicompartment model using vaccination as a control parameter. The model considers eight classes of infection: susceptible ( S ), vaccinated ( V ), exposed ( E ), asymptomatic infected ( A ), symptomatic infected ( I ), isolated ( J ), hospitalised ( H ), recovered ( R ). To begin, a mathematical study is performed to demonstrate the suggested model's uniform boundedness, epidemic equilibrium, and basic reproduction number. The findings indicate that if,R 0 < 1 , the disease-free equilibrium is locally asymptotically stable; but, if,R 0 > 1 the equilibrium is unstable. Secondly, we examine the effect on those who have received vaccinations with what are deemed optimal values. The suggested model is numerically simulated using MATLAB 14.0, and the results confirm the capacity of the proposed model to provide an accurate forecast of the progress of the epidemic in India. Finally, we examine the impact of immunisation on COVID-19 dissemination.

Mathematical Modeling and Numerical Simulation for the Outbreak of COVID-19 Involving Loss of Immunity and Quarantined Class

For the analysis of the recent deadly pandemic Sars-Cov-2, we constructed the mathematical model containing the whole population, partitioned into five different compartments, represented by SEIQR model. This current model especially contains the quarantined class and the factor of loss of immunity. Further, we discussed the stability of the SEIQR model (constructed on the basis of system of coupled differential equations). The basic reproduction that indicates the behavior of the disease is also estimated by the use of next-generation matrix method. Numerical simulation of this model is provided, the results are analyzed by theoretically strong numerical methods, and computationally known tool MATLAB Simulink is also used for visualization of the results. Validation of results by Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions on COVID-19. Our results suggest that the isolation of the active cases and strong immunization of patients or individuals play a major role to fight against the deadly Sars-Cov-2.

Development of Mathematical Models Taking into Account the Effect of Isolating Individuals in a Population

The effect of the isolation of individuals in the population on the dynamics of the epidemic is analyzed. Based on the SIR model, a SIRDi model is built that takes into account the isolation of individuals, as well as the presence of deceased patients, which is appropriate to use in cases of widespread infection, when the number of infected is comparable to the number of susceptible individuals. Simplified IRD and IRDi models are proposed for studying the spread of an infectious disease at the initial stage of an epidemic (or for the case when the rate of infection is not high). It is found that there is a threshold value of the coefficient (fraction) of isolation, which delimits the qualitatively different behavior of the epidemic indicators of the population system. A comparison is made between different models. It is shown that the simplified (IRDi) and more complex (SIRDi) models at the initial stage of the epidemic give approximately the same results.

Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

In this article, we investigate a diffusive two-strain epidemic model with non-monotone incidence rate and virus mutation. The positivity, existence and uniform boundedness of the solutions of the model system are studied. It is found that the system has three equilibrium points, namely the infection-free equilibrium point, the strain-2 endemic equilibrium point and both the strain-1 and strain-2 endemic equilibrium points. The global asymptotic stability analysis of the diffusive model system near all the equilibrium points is carried out by constructing appropriate Lyapunov functional. It is found that the system has no strain-1 endemic equilibrium point possibly due to the virus mutation. So, in this type of diseases, the infection due to strain-1 cannot be persistent in the community.

Simulating COVID-19 classroom transmission on a university campus

We study the airborne transmission risk associated with holding in-person classes on university campuses for the original strain and a more contagious variant of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We adopt a model for airborne transmission risk in an enclosed room that considers room properties, mask efficiency, and initial infection probability of the occupants. Additionally, we study the effect of vaccination on the spread of the virus. The presented model has been evaluated in simulations using fall 2019 (prepandemic) and fall 2020 (hybrid instruction) course registration data of a large US university, allowing for assessing the difference in transmission risk between in-person and hybrid programs and the impact of occupancy reduction, mask-wearing, and vaccination. The simulations indicate that without vaccination, moving 90% of the classes online leads to a 17 to 18× reduction in new cases, and universal mask usage results in an ∼2.7 to 3.6× reduction in new infections through classroom interactions. Furthermore, the results indicate that for the original variant and using vaccines with efficacy greater than 90%, at least 23% (64%) of students need to be vaccinated with (without) mask usage in order to operate the university at full occupancy while preventing an increase in cases due to classroom interactions. For the more contagious variant, even with universal mask usage, at least 93% of the students need to be vaccinated to ensure the same conditions. We show that the model is able to predict trends observed in weekly infection rates for fall 2021.

A Comprehensive Review of Artificial Intelligence in Prevention and Treatment of COVID-19 Pandemic

The unprecedented outbreak of the Corona Virus Disease 2019 (COVID-19) pandemic has seriously affected numerous countries in the world from various aspects such as education, economy, social security, public health, etc. Most governments have made great efforts to control the spread of COVID-19, e.g., locking down hard-hit cities and advocating masks for the population. However, some countries and regions have relatively poor medical conditions in terms of insufficient medical equipment, hospital capacity overload, personnel shortage, and other problems, resulting in the large-scale spread of the epidemic. With the unique advantages of Artificial Intelligence (AI), it plays an extremely important role in medical imaging, clinical data, drug development, epidemic prediction, and telemedicine. Therefore, AI is a powerful tool that can help humans solve complex problems, especially in the fight against COVID-19. This study aims to analyze past research results and interpret the role of Artificial Intelligence in the prevention and treatment of COVID-19 from five aspects. In this paper, we also discuss the future development directions in different fields and prove the validity of the models through experiments, which will help researchers develop more efficient models to control the spread of COVID-19.