Short-term predictions and prevention strategies for COVID-19: A model-based study

Effectiveness of non-pharmaceutical interventions as implemented in the UK during the COVID-19 pandemic: a rapid review

BACKGROUND

Although non-pharmaceutical inventions (NPIs) were used globally to control the spread of COVID-19, their effectiveness remains uncertain. We aimed to assess the evidence on NPIs as implemented in the UK, to allow public health bodies to prepare for future pandemics.

METHODS

We used rapid systematic methods (search date: January 2024) to identify, critically appraise and synthesize interventional, observational and modelling studies reporting on NPI effectiveness in the UK.

RESULTS

Eighty-five modelling, nine observational and three interventional studies were included. Modelling studies had multiple quality issues; six of the 12 non-modelling studies were high quality. The best available evidence was for test and release strategies for case contacts (moderate certainty), which was suggestive of a protective effect. Although evidence for school-related NPIs and universal lockdown was also suggestive of a protective effect, this evidence was considered low certainty. Evidence certainty for the remaining NPIs was very low or inconclusive.

CONCLUSION

The validity and reliability of evidence on the effectiveness of NPIs as implemented in the UK during the COVID-19 pandemic is weak. To improve evidence generation and support decision-making during future pandemics or other public health emergencies, it is essential to build evaluation into the design of public health interventions.

Dynamic properties of deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences

The classical compartment model is often used to study the spread of an epidemic with one virus. However, there are few types of research on epidemic models with multiple viruses. The article aims to propose two new deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. We obtain asymptotic properties of disease-free and several endemic equilibria for the deterministic model. In the stochastic case, we prove the existence and uniqueness of positive global solutions. The extinction and persistence of diseases are obtained under different threshold conditions. We analyze the existence of stationary distribution through a suitable Lyapunov function. The results indicate that the extinction or persistence of the two viruses is closely related to the intensity of white noise interference. Specifically, considerable white noise is beneficial for the extinction of diseases, while slight one can lead to long-term epidemics of diseases. Finally, numerical simulations illustrate our theoretical results and the effect of essential parameters.

An individual-level probabilistic model and solution for control of infectious diseases

We present an individual-level probabilistic model to evaluate the effectiveness of two traditional control measures for infectious diseases: the isolation of symptomatic individuals and contact tracing (plus subsequent quarantine). The model allows us to calculate the reproduction number and the generation-time distribution under the two control measures. The model is related to the work of Fraser et al. on the same topic [1], which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. In particular, we are able to provide more precise results for a disease that has two classes of infected individuals - the individuals who will remain asymptomatic throughout and the individuals who will eventually become symptomatic. Using the properties of integral operators with positive kernels, we also resolve the important theoretical issue as to why the density function of the steady-state generation time is the eigenfunction associated with the largest eigenvalue of the underlying integral operator. Moreover, the same theoretical result shows why the simple algorithm of repeated integration can find numerical solutions for virtually all initial conditions. We discuss the model's implications, especially how it enhances our understanding about the impact of asymptomatic individuals. For instance, in the special case where the infectiousness of the two classes is proportional to each other, the effects of the asymptomatic individuals can be understood by supposing that all individuals will be symptomatic but with modified infectiousness and modified efficacy of the isolation measure. The numerical results show that, out of the two measures, isolation is the more decisive one, at least for the COVID-19 parameters used in the numerical experiments.

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.

Non-pharmaceutical interventions to reduce COVID-19 transmission in the UK: a rapid mapping review and interactive evidence gap map

BACKGROUND

Non-pharmaceutical interventions (NPIs) were crucial in the response to the COVID-19 pandemic, although uncertainties about their effectiveness remain. This work aimed to better understand the evidence generated during the pandemic on the effectiveness of NPIs implemented in the UK.

METHODS

We conducted a rapid mapping review (search date: 1 March 2023) to identify primary studies reporting on the effectiveness of NPIs to reduce COVID-19 transmission. Included studies were displayed in an interactive evidence gap map.

RESULTS

After removal of duplicates, 11 752 records were screened. Of these, 151 were included, including 100 modelling studies but only 2 randomized controlled trials and 10 longitudinal observational studies.Most studies reported on NPIs to identify and isolate those who are or may become infectious, and on NPIs to reduce the number of contacts. There was an evidence gap for hand and respiratory hygiene, ventilation and cleaning.

CONCLUSIONS

Our findings show that despite the large number of studies published, there is still a lack of robust evaluations of the NPIs implemented in the UK. There is a need to build evaluation into the design and implementation of public health interventions and policies from the start of any future pandemic or other public health emergency.

Country-report pattern corrections of new cases allow accurate 2-week predictions of COVID-19 evolution with the Gompertz model

Accurate short-term predictions of COVID-19 cases with empirical models allow Health Officials to prepare for hospital contingencies in a two-three week window given the delay between case reporting and the admission of patients in a hospital. We investigate the ability of Gompertz-type empiric models to provide accurate prediction up to two and three weeks to give a large window of preparation in case of a surge in virus transmission. We investigate the stability of the prediction and its accuracy using bi-weekly predictions during the last trimester of 2020 and 2021. Using data from 2020, we show that understanding and correcting for the daily reporting structure of cases in the different countries is key to accomplish accurate predictions. Furthermore, we found that filtering out predictions that are highly unstable to changes in the parameters of the model, which are roughly 20%, reduces strongly the number of predictions that are way-off. The method is then tested for robustness with data from 2021. We found that, for this data, only 1-2% of the one-week predictions were off by more than 50%. This increased to 3% for two-week predictions, and only for three-week predictions it reached 10%.

Dynamical vaccination behavior with risk perception and vaccination rewards

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

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.

Predicting COVID-19 positivity and hospitalization with multi-scale graph neural networks

The pandemic of COVID-19 is undoubtedly one of the biggest challenges for modern healthcare. In order to analyze the spatio-temporal aspects of the spread of COVID-19, technology has helped us to track, identify and store information regarding positivity and hospitalization, across different levels of municipal entities. In this work, we present a method for predicting the number of positive and hospitalized cases via a novel multi-scale graph neural network, integrating information from fine-scale geographical zones of a few thousand inhabitants. By leveraging population mobility data and other features, the model utilizes message passing to model interaction between areas. Our proposed model manages to outperform baselines and deep learning models, presenting low errors in both prediction tasks. We specifically point out the importance of our contribution in predicting hospitalization since hospitals became critical infrastructure during the pandemic. To the best of our knowledge, this is the first work to exploit high-resolution spatio-temporal data in a multi-scale manner, incorporating additional knowledge, such as vaccination rates and population mobility data. We believe that our method may improve future estimations of positivity and hospitalization, which is crucial for healthcare planning.

Uncertainty Quantification for Epidemic Risk Management: Case of SARS-CoV-2 in Morocco

In this paper, we propose a new method for epidemic risk modelling and prediction, based on uncertainty quantification (UQ) approaches. In UQ, we consider the state variables as members of a convenient separable Hilbert space, and we look for their representation in finite dimensional subspaces generated by truncations of a suitable Hilbert basis. The coefficients of the finite expansion can be determined by approaches established in the literature, adapted to the determination of the probability distribution of epidemic risk variables. Here, we consider two approaches: collocation (COL) and moment matching (MM). Both are applied to the case of SARS-CoV-2 in Morocco, as an epidemic risk example. For all the epidemic risk indicators computed in this study (number of detections, number of deaths, number of new cases, predictions and human impact probabilities), the proposed models were able to estimate the values of the state variables with precision, i.e., with very low root mean square errors (RMSE) between predicted values and observed ones. Finally, the proposed approaches are used to generate a decision-making tool for future epidemic risk management, or, more generally, a quantitative disaster management approach in the humanitarian supply chain.

Mathematical analysis of a COVID-19 model with different types of quarantine and isolation

A COVID-19 deterministic compartmental mathematical model with different types of quarantine and isolation is proposed to investigate their role in the disease transmission dynamics. The quarantine compartment is subdivided into short and long quarantine classes, and the isolation compartment is subdivided into tested and non-tested home-isolated individuals and institutionally isolated individuals. The proposed model has been fully analyzed. The analysis includes the positivity and boundedness of solutions, calculation of the control reproduction number and its relation to all transmission routes, existence and stability analysis of disease-free and endemic equilibrium points and bifurcation analysis. The model parameters have been estimated using a dataset for Oman. Using the fitted parameters, the estimated values of the control reproduction number and the contribution of all transmission routes to the reproduction number have been calculated. Sensitivity analysis of the control reproduction number to model parameters has also been performed. Finally, numerical simulations to demonstrate the effect of some model parameters related to the different types of quarantine and isolation on the disease transmission dynamics have been carried out, and the results have been demonstrated graphically.

Forecasting COVID-19 cases by assessing control-intervention effects in Republic of Korea: A statistical modeling approach

The Coronavirus disease of 2019 (COVID-19) is an ongoing public health concern worldwide. COVID-19 infections continue to occur and thus, it is important to assess the effects of various public health measures. This study aims to forecast COVID-19 cases by geographical area in Korea, based on the effects of different control-intervention intensities (CII). Methods involved estimating the effective reproduction number (Rt) by Korean geographical area using the SEIHR model, and the instantaneous reproduction number using statistical model, comparing the epidemic curves and high-, intermediate-, and low-intensity control interventions. Here, short-term four-week forecasts by geographical area were conducted. The mean of delayed instantaneous reproduction number was estimated at 1.36, 1.03, and 0.93 for the low-, intermediate-, and high-intensity control interventions, respectively, in the capital area of Korea from July 16, 2020, to March 4, 2021. The COVID-19 cases were forecasted with an accuracy rate of 11.28%, 13.62%, and 20.19% MAPE in Korea, including both the capital and non-capital areas. High-intensity control measures significantly reduced the reproduction number to be less than one. The proposed model forecasted COVID-19 transmission dynamics with good accuracy and interpretability. High-intensity control intervention, active case detection, and isolation efforts should be maintained to control the pandemic.

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.

Socio-economic analysis of short-term trends of COVID-19: modeling and data analytics

BACKGROUND

COVID-19 caused a worldwide outbreak leading the majority of human activities to a rough breakdown. Many stakeholders proposed multiple interventions to slow down the disease and number of papers were devoted to the understanding the pandemic, but to a less extend some were oriented socio-economic analysis. In this paper, a socio-economic analysis is proposed to investigate the early-age effect of socio-economic factors on COVID-19 spread.

METHODS

Fifty-two countries were selected for this study. A cascade algorithm was developed to extract the R0 number and the day J*; these latter should decrease as the pandemic flattens. Subsequently, R0 and J* were modeled according to socio-economic factors using multilinear stepwise-regression.

RESULTS

The findings demonstrated that low values of days before lockdown should flatten the pandemic by reducing J*. Hopefully, DBLD is only parameter to be tuned in the short-term; the other socio-economic parameters cannot easily be handled as they are annually updated. Furthermore, it was highlighted that the elderly is also a major influencing factor especially because it is involved in the interactions terms in R0 model. Simulations proved that the health care system could improve the pandemic damping for low elderly. In contrast, above a given elderly, the reproduction number R0 cannot be reduced even for developed countries (showing high HCI values), meaning that the disease's severity cannot be smoothed regardless the performance of the corresponding health care system; non-pharmaceutical interventions are then expected to be more efficient than corrective measures.

DISCUSSION

The relationship between the socio-economic factors and the pandemic parameters R0 and J* exhibits complex relations compared to the models that are proposed in the literature. The quadratic regression model proposed here has discriminated the most influencing parameters within the following approximated order, DLBL, HCI, Elderly, Tav, CO2, and WC as first order, interaction, and second order terms.

CONCLUSIONS

This modeling allowed the emergence of interaction terms that don't appear in similar studies; this led to emphasize more complex relationship between the infection spread and the socio-economic factors. Future works will focus on enriching the datasets and the optimization of the controlled parameters to short-term slowdown of similar pandemics.

Isolation in the control of epidemic

Among many epidemic prevention measures, isolation is an important method to control the spread of infectious disease. Scholars rarely study the impact of isolation on disease dissemination from a quantitative perspective. In this paper, we introduce an isolation ratio and establish the corresponding model. The basic reproductive number and its biological explanation are given. The stability conditions of the disease-free and endemic equilibria are obtained by analyzing its distribution of characteristic values. It is shown that the isolation ratio has an important influence on the basic reproductive number and the stability conditions. Taking the COVID-19 in Wuhan as an example, isolating more than 68% of the population can control the spread of the epidemic. This method can provide precise epidemic prevention strategies for government departments. Numerical simulations verify the effectiveness of the results.

Researchers' transfer network reveals the evolution of national science and technology capabilities

Science and technology capability refers to the comprehensive capability of all factors that affect the development of science and technology, mainly referring to human and material factors related to science and technology, among which human resources are the foundation and driving force. Therefore, researchers become a unique research perspective for the evaluation of national science and technology capabilities. Taking the integrated circuit field as the analysis case, this article proposed a researchers' transfer network model based on the online open source literature database. From the published literature information, the model obtains the researchers' transfer network that has a core-periphery structure. The core nodes are the European Union, the United States, China, etc., and these nodes are the most closely connected. A country/region role evolution model is also proposed, which reveals the characteristics of the role evolution of the European Union, the United States, China, and other countries from the perspective of researchers' transfer, especially their transfer between countries.

Identifying influential spreaders in complex networks for disease spread and control

Identifying influential spreaders is an important task in controlling the spread of information and epidemic diseases in complex networks. Many recent studies have indicated that the identification of influential spreaders is dependent on the spreading dynamics. Finding a general optimal order of node importance ranking is difficult because of the complexity of network structures and the physical background of dynamics. In this paper, we use four metrics, namely, betweenness, degree, H-index, and coreness, to measure the central attributes of nodes for constructing the disease spreading models and target immunization strategies. Numerical simulations show that spreading processes based on betweenness centrality lead to the widest range of propagation and the smallest epidemic threshold for all six networks (including four real networks and two BA scale-free networks generated according to Barabasi–Albert algorithm). The target immunization strategy based on the betweenness centrality of nodes is the most effective for BA scale-free networks but displays poor immune effect for real networks in identifying the most important spreaders for disease control. The immunization strategy based on node degrees is the most effective for the four real networks. Findings show that the target immune strategy based on the betweenness centrality of nodes works best for standard scale-free networks, whereas that based on node degrees works best for other nonstandard scale-free networks. The results can provide insights into understanding the different metrics of measuring node importance in disease transmission and control.

The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number ℜ 1 of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when ℜ 1 < 1 under certain conditions, which will lead to backward bifurcation. The stability of equilibria are analyzed, and the condition for the backward bifurcation is given. Due to the existence of backward bifurcation, even if ℜ 1 < 1 , COVID-19 may remain prevalent. Sensitivity analysis and simulations show that improving vaccine efficacy can control the spread of COVID-19 faster, while increasing the vaccination rate can reduce and postpone the peak of infection to a greater extent. However, in reality, the improvement of vaccine efficacy cannot be realized in a short time, and relying only on increasing the vaccination rate cannot quickly achieve the control of COVID-19. Therefore, relying only on vaccination may not completely and quickly control COVID-19. Some non-pharmaceutical interventions should continue to be enforced to combat the virus. According to the sensitivity analysis, we improve the model by including some non-pharmaceutical interventions. Combining the sensitivity analysis with the simulation of the improved model, we conclude that together with vaccination, reducing the contact rate of people and increasing the isolation rate of infected individuals will greatly reduce the number of infections and shorten the time of COVID-19 spread. The analysis and simulations in this paper can provide some useful suggestions for the prevention and control of COVID-19.

Global Analysis and Optimal Control Model of COVID-19

COVID-19 remains the concern of the globe as governments struggle to defeat the pandemic. Understanding the dynamics of the epidemic is as important as detecting and treatment of infected individuals. Mathematical models play a crucial role in exploring the dynamics of the outbreak by deducing strategies paramount for curtailing the disease. The research extensively studies the SEQIAHR compartmental model of COVID-19 to provide insight into the dynamics of the disease by underlying tailored strategies designed to minimize the pandemic. We first studied the noncontrol model's dynamic behaviour by calculating the reproduction number and examining the two nonnegative equilibria' existence. The model utilizes the Castillo-Chavez method and Lyapunov function to investigate the global stability of the disease at the disease-free and endemic equilibrium. Sensitivity analysis was carried on to determine the impact of some parameters on R₀. We further examined the COVID model to determine the type of bifurcation that it exhibits. To help contain the spread of the disease, we formulated a new SEQIAHR compartmental optimal control model with time-dependent controls: personal protection and vaccination of the susceptible individuals. We solved it by utilizing Pontryagin's maximum principle after studying the dynamical behaviour of the noncontrol model. We solved the model numerically by considering different simulation controls' pairing and examined their effectiveness.

Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic

COVID-19 is caused by the increase of SARS-CoV-2 viral load in the respiratory system. Epithelial cells in the human lower respiratory tract are the major target area of the SARS-CoV-2 viruses. To fight against the SARS-CoV-2 viral infection, innate and thereafter adaptive immune responses be activated which are stimulated by the infected epithelial cells. Strong immune response against the COVID-19 infection can lead to longer recovery time and less severe secondary complications. We proposed a target cell-limited mathematical model by considering a saturation term for SARS-CoV-2-infected epithelial cells loss reliant on infected cells level. The analytical findings reveal the conditions for which the system undergoes transcritical bifurcation and alternation of stability for the system around the steady states happens. Due to some external factors, while the viral reproduction rate exceeds its certain critical value, backward bifurcation and reinfection may take place and to inhibit these complicated epidemic states, host immune response, or immunopathology would play the essential role. Numerical simulation has been performed in support of the analytical findings.

Models to assess imported cases on the rebound of COVID-19 and design a long-term border control strategy in Heilongjiang Province, China

Since the outbreak of COVID-19 in Wuhan, China in December 2019, it has spread quickly and become a global pandemic. While the epidemic has been contained well in China due to unprecedented public health interventions, it is still raging or not yet been restrained in some neighboring countries. Chinese government adopted a strict policy of immigration diversion in major entry ports, and it makes Suifenhe port in Heilongjiang Province undertook more importing population. It is essential to understand how imported cases and other key factors of screening affect the epidemic rebound and its mitigation in Heilongjiang Province. Thus we proposed a time switching dynamical system to explore and mimic the disease transmission in three time stages considering importation and control. Cross validation of parameter estimations was carried out to improve the credibility of estimations by fitting the model with eight time series of cumulative numbers simultaneous. Simulation of the dynamics shows that illegal imported cases and imperfect protection in hospitals are the main reasons for the second epidemic wave, the actual border control intensities in the province are relatively effective in early stage. However, a long-term border closure may cause a paradox phenomenon such that it is much harder to restrain the epidemic. Hence it is essential to design an effective border reopening strategy for long-term border control by balancing the limited resources on hotel rooms for quarantine and hospital beds. Our results can be helpful for public health to design border control strategies to suppress COVID-19 transmission.

Fractional dynamical probes in COVID-19 model with control interventions: a comparative assessment of eight most affected countries

The ultimate aim of the article is to predict COVID-19 virus inter-cellular behavioral dynamics using an infection model with a quarantine compartment. Internal viral dynamics and stability attributes are thoroughly investigated around stable equilibrium states to probe possible ways in reducing rapid spread by incorporating fractional-order components into epidemic systems. Furthermore, a fractional optimal problem was built and studied with three control measures to restrict the widespread of COVID-19 infections and exhibit perfect protection. It is found that by following 60 % of control strategies can eradicate the infectives. Furthermore, the time frame of sixteen months has been divided into four short periods to grasp the pandemic, as the pandemic's parameters change over time. Finally, using real data, we estimated the parameters of the model system and the expression of the basic reproduction number R 0 for the most affected countries, China, USA, UK, Italy, France, Germany, Spain, and Iran.

Discrete-time COVID-19 epidemic model with bifurcation and control

The local dynamics with different topological classifications, bifurcation analysis and chaos control in a discrete-time COVID-19 epidemic model are investigated in the interior of $ \mathbb{R}_+^3 $. It is proved that discrete-time COVID-19 epidemic model has boundary equilibrium solution for all involved parameters, but it has an interior equilibrium solution under definite parametric condition. Then by linear stability theory, local dynamics with different topological classifications are investigated about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model. Further for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also investigated 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 exists hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Next by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally numerically verified theoretical results.

A spread model of COVID-19 with some strict anti-epidemic measures

In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.

Convolution model for COVID-19 rate predictions and health effort levels computation for Saudi Arabia, France, and Canada

Many published infection prediction models, such as the extended SEIR (E-SEIR) model, are used as a study and report tool to aid health authorities to manage the epidemic plans successfully. These models face many challenges, mainly the reliability of the infection rate predictions related to the initial boundary conditions, formulation complexity, lengthy computations, and the limited result scope. We attribute these challenges to the absence of a solution framework that encapsulates the interacted activities that manage: the infection growth process, the infection spread process and the health effort process. In response to these challenges, we formulated such a framework first as the basis of our new convolution prediction model (CPM). CPM links through convolution integration, three temporal profile levels: input (infected and active cases), transformational (health efforts), and output functions (recovered, quarantine, and death cases). COVID-19 data defines the input and output temporal profiles; hence it is possible to deduce the cumulative efforts temporal response (CETR) function for the health effort level. The new CETR function determines the health effort level over a period. Also, CETR plays a role in predicting the evolution of the underlying infection and active cases profiles without a system of differential equations. This work covers three countries: Saudi Arabia, France, and Canada.

Study of dynamic behaviour of psychological stress during COVID-19 in India: A mathematical approach

In this study, a new attempt has been made using mathematical modelling to study dynamic behaviour and estimate the final size of spread of the psychological stress arising due to sudden outbreak of COVID-19 in India. The proposed mathematical model examines and includes different behaviours of transition from one process to another in current situation and study their propagation mode. We propose a mathematical model, where two different type of psychological stresses occur due to COVID-19 situation and its impact on people's life such as their mental well being and happiness. We present some sufficient conditions for the vanishing or spreading of the psychological stress through qualitative and quantitative analysis. The basic reproduction number (R 0 ) of the model is computed and the local and the global stabilities of different equilibria are studied. Moreover, to better understand the level of psychological stress and decreasing mental well-being during the COVID-19 outbreak in India, we also conducted an online survey. Our findings establish several factors associated with level of psychological impact and mental health status. Based on the empirical analysis, we found that psychological stress has a significant negative influence on mental well being. Further, this study confirms that coping strategies with stress have significantly contributed towards the betterment in the mental well-being of the people. Numerical simulations are also given to illustrate the theoretical results. The results of the present study can be generalized to the society, Government, and others that they can adopt different strategies to avoid stressful situations during COVID-19 outbreak. The findings suggest that policy-makers, Government officials should focus on coping strategies to combat with pandemic disease.

Modeling and staged assessments of the controllability of spread for repeated outbreaks of COVID-19

SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) has been causing an outbreak of a new type of pneumonia globally, and repeated outbreaks have already appeared. Among the studies on the spread of the COVID-19, few studies have investigated the repeated outbreaks in stages, and the quantitative condition of a controllable spread has not been revealed. In this paper, a brief compartmental model is developed. The effective reproduction number (ERN) of the model is interpreted by the ratio of net newly infectious individuals to net isolation infections to assess the controllability of the spread of COVID-19. It is found that the value of the ERN at the inflection point of the pandemic is equal to one. The effectiveness of the quarantine, even the treatment, is parametrized in various stages with Gompertz functions to increase modeling accuracy. The impacts of the vaccinations are discussed by adding a vaccinated compartment. The results show that the sufficient vaccinations can make the inflection point appear early and significantly reduce subsequent increases in newly confirmed cases. The analysis of the ERNs of COVID-19 in the United States, Spain, France, and Peru confirms that the condition of a repeated outbreak is to relax or lift the interventions related to isolation and quarantine interventions to a level where the ERN is greater than one.

Stability and Hopf Bifurcation Analysis of an Epidemic Model with Time Delay

Epidemic models are normally used to describe the spread of infectious diseases. In this paper, we will discuss an epidemic model with time delay. Firstly, the existence of the positive fixed point is proven; and then, the stability and Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equations. Thirdly, the theory of normal form and manifold is used to drive an explicit algorithm for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions. Finally, some simulation results are carried out to validate our theoretic analysis.

Blockchain and AI-Based Solutions to Combat Coronavirus (COVID-19)-Like Epidemics: A Survey

The beginning of 2020 has seen the emergence of coronavirus outbreak caused by a novel virus called SARS-CoV-2. The sudden explosion and uncontrolled worldwide spread of COVID-19 show the limitations of existing healthcare systems in timely handling public health emergencies. In such contexts, innovative technologies such as blockchain and Artificial Intelligence (AI) have emerged as promising solutions for fighting coronavirus epidemic. In particular, blockchain can combat pandemics by enabling early detection of outbreaks, ensuring the ordering of medical data, and ensuring reliable medical supply chain during the outbreak tracing. Moreover, AI provides intelligent solutions for identifying symptoms caused by coronavirus for treatments and supporting drug manufacturing. Therefore, we present an extensive survey on the use of blockchain and AI for combating COVID-19 epidemics. First, we introduce a new conceptual architecture which integrates blockchain and AI for fighting COVID-19. Then, we survey the latest research efforts on the use of blockchain and AI for fighting COVID-19 in various applications. The newly emerging projects and use cases enabled by these technologies to deal with coronavirus pandemic are also presented. A case study is also provided using federated AI for COVID-19 detection. Finally, we point out challenges and future directions that motivate more research efforts to deal with future coronavirus-like epidemics.

Mathematical modeling of the COVID-19 pandemic with intervention strategies

Mathematical modeling plays an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat COVID-19 pandemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We performed sensitivity analysis forR 0 to investigate the relative importance of the system parameters. Also, we computed the sensitivity indices forR 0 to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficientβ s and clinical outbreak rateq a to control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibited the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal disease. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.

Study of SEIR epidemic model and scenario analysis of COVID-19 pandemic

In recent times, the Coronavirus disease (caused by COVID-19) is evidently observed to be the extremely contagious one with high fatality rate worldwide. In March 2020, the disease was declared a "global pandemic" by the World Health Organization (WHO). So far, there is no known/effective vaccine or medicine. In this paper, we propose and analyze an SEIR compartment model. We also compare and analyze the case study of India and Brazil. The model system is discussed by using MATLAB (2018a) software and the numerical results are verified graphically.

Study on the SEIQR model and applying the epidemiological rates of COVID-19 epidemic spread in Saudi Arabia

This article attempts to establish a mathematical epidemic model for the outbreak of the new COVID-19 coronavirus. A new consideration for evaluating and controlling the COVID-19 outbreak will be constructed based on the SEIQR Pandemic Model. In this paper, the real data of COVID-19 spread in Saudi Arabia has been used for the mathematical model and dynamic analyses. Including the new reproductive number and detailed stability analysis, the dynamics of the proposed SEIQR model have been applied. The local sensitivity of the reproduction number has been analyzed. The domain of solution and equilibrium based on the SEIQR model have been proved using a Jacobian linearization process. The state of equilibrium and its significance have been proved, and a study of the integrity of the disease-free equilibrium has been carried out. The Lyapunov stability theorem demonstrated the global stability of the current model equilibrium. The SEIQR model has been numerically validated and projected by contrasting the results from the SEIQR model with the actual COVID-19 spread data in Saudi Arabia. The result of this paper shows that the SEIQR model is a model that is effective in analyzing epidemic spread, such as COVID-19. At the end of the study, we have implemented the protocol which helped the Saudi population to stop the spread of COVID-19 rapidly.

Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

An outbreak of the COVID-19 pandemic is a major public health disease as well as a challenging task to people with comorbidity worldwide. According to a report, comorbidity enhances the risk factors with complications of COVID-19. Here, we propose and explore a mathematical framework to study the transmission dynamics of COVID-19 with comorbidity. Within this framework, the model is calibrated by using new daily confirmed COVID-19 cases in India. The qualitative properties of the model and the stability of feasible equilibrium are studied. The model experiences the scenario of backward bifurcation by parameter regime accounting for progress in susceptibility to acquire infection by comorbidity individuals. The endemic equilibrium is asymptotically stable if recruitment of comorbidity becomes higher without acquiring the infection. Moreover, a larger backward bifurcation regime indicates the possibility of more infection in susceptible individuals. A dynamics in the mean fluctuation of the force of infection is investigated with different parameter regimes. A significant correlation is established between the force of infection and corresponding Shannon entropy under the same parameters, which provides evidence that infection reaches a significant proportion of the susceptible.

COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution

We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of the dynamical equations and the poor knowledge of realistic values of the model parameters. The incidence time series of top ten corona infected countries are erratic and sparse. But in comparison, the incidence and disease fitness relationships are uniform and concave upward in nature. These simple profiles with the acceleration curves have fundamental implications in understanding the instinctive dynamics of the corona pandemic. We propose a simple population dynamics solution based on the incidence-fitness relationship in predicting that a plateau or steady state of SARS-CoV-2 will be reached using the basic concept of geometry.

A case study of Covid-19 epidemic in India via new generalised Caputo type fractional derivatives

The first symptomatic infected individuals of coronavirus (Covid-19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid-19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor-Corrector scheme. For the proposed model of Covid-19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non-integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's-Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non-linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non-linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non-integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results.

Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination

Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase in exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs.

Blockchain and AI-Based Solutions to Combat Coronavirus (COVID-19)-Like Epidemics: A Survey

The beginning of 2020 has seen the emergence of coronavirus outbreak caused by a novel virus called SARS-CoV-2. The sudden explosion and uncontrolled worldwide spread of COVID-19 show the limitations of existing healthcare systems in timely handling public health emergencies. In such contexts, innovative technologies such as blockchain and Artificial Intelligence (AI) have emerged as promising solutions for fighting coronavirus epidemic. In particular, blockchain can combat pandemics by enabling early detection of outbreaks, ensuring the ordering of medical data, and ensuring reliable medical supply chain during the outbreak tracing. Moreover, AI provides intelligent solutions for identifying symptoms caused by coronavirus for treatments and supporting drug manufacturing. Therefore, we present an extensive survey on the use of blockchain and AI for combating COVID-19 epidemics. First, we introduce a new conceptual architecture which integrates blockchain and AI for fighting COVID-19. Then, we survey the latest research efforts on the use of blockchain and AI for fighting COVID-19 in various applications. The newly emerging projects and use cases enabled by these technologies to deal with coronavirus pandemic are also presented. A case study is also provided using federated AI for COVID-19 detection. Finally, we point out challenges and future directions that motivate more research efforts to deal with future coronavirus-like epidemics.

Dynamics of coronavirus pandemic: effects of community awareness and global information campaigns

The effects of social media advertisements together with local awareness in controlling COVID-19 are explored in the present investigation by means of a mathematical model. The expression for the basic reproduction number is derived. Sufficient conditions for the global stability of endemic equilibrium are obtained. We perform sensitivity analysis to identify the key parameters of the model having great impacts on the prevalence and control of COVID-19. We calibrate the proposed model to fit the data set of COVID-19 cases for India. Our simulation results show that dissemination rate of awareness among susceptible individuals at community level and individual level plays pivotal role in curtailing the COVID-19 disease. Moreover, we observe that the global information distributing from social media and local awareness coming from mouth-to-mouth communication between unaware susceptible and aware people, together with hospitalization of symptomatic individuals and quarantine of asymptomatic individuals, are much beneficial in reducing COVID-19 cases in India. Our study suggests that both global and local awareness must be implemented effectively to manage the burden of COVID-19 pandemic.

The Recent Technologies to Curb the Second-Wave of COVID-19 Pandemic

Different epidemics, specially Coronavirus, have caused critical misfortunes in various fields like monetary deprivation, survival conditions, thus diminishing the overall individual fulfillment. Various worldwide associations and different hierarchies of government fraternity are endeavoring to offer the necessary assistance in eliminating the infection impacts but unfortunately standing up to the non-appearance of resources and expertise. In contrast to all other pandemics, Coronavirus has proven to exhibit numerous requirements such that curated appropriation and determination of innovations are required to deal with the vigorous undertakings, which include precaution, detection, and medication. Innovative advancements are essential for the subsequent pandemics where-in the forthcoming difficulties can indeed be approached to such a degree that it facilitates constructive solutions more comprehensively. In this study, futuristic and emerging innovations are analyzed, improving COVID-19 effects for the general public. Large data sets need to be advanced so that extensive models related to deep analysis can be used to combat Coronavirus infection, which can be done by applying Artificial intelligence techniques such as Natural Language Processing (NLP), Machine Learning (ML), and Computer vision to varying processing files. This article aims to furnish variation sets of innovations that can be utilized to eliminate COVID-19 and serve as a resource for the coming generations. At last, elaboration associated with future state-of-the-art technologies and the attainable sectors of AI methodologies has been mentioned concerning the post-COVID-19 world to enable the different ideas for dealing with the pandemic-based difficulties.

The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative

Novel coronavirus (COVID-19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID-19 SEIR epidemic model via Caputo fractional derivatives using a predictor-corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag-Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs.

Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives

In this manuscript, we solve a model of the novel coronavirus (COVID-19) epidemic by using Corrector-predictor scheme. For the considered system exemplifying the model of COVID-19, the solution is established within the frame of the new generalized Caputo type fractional derivative. The existence and uniqueness analysis of the given initial value problem are established by the help of some important fixed point theorems like Schauder's second and Weissinger's theorems. Arzela-Ascoli theorem and property of equicontinuity are also used to prove the existence of unique solution. A new analysis with the considered epidemic COVID-19 model is effectuated. Obtained results are described using figures which show the behaviour of the classes of projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of non-linear equations. The present study can confirm the applicability of the new generalized Caputo type fractional operator to mathematical epidemiology or real-world problems. The stability analysis of the projected scheme is given by the help of some important lemma or results.

Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan

Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana-Baleanu-Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number R 0 is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh-Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model's solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams-Bashforth-Moulton method, whereas for the Atangana-Baleanu-Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.