On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic

Real-time updating of dynamic social networks for COVID-19 vaccination strategies

Vaccination strategy is crucial in fighting the COVID-19 pandemic. Since the supply is still limited in many countries, contact network-based interventions can be most powerful to set an efficient strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamic systems where contact networks are highly time-variant. Furthermore, the numerous mutations of SARS-CoV-2 have a significant impact on the infectious probability, requiring real-time network updating algorithms. In this study, we propose a sequential network updating approach based on data assimilation techniques to combine different sources of temporal information. We then prioritise the individuals with high-degree or high-centrality, obtained from assimilated networks, for vaccination. The assimilation-based approach is compared with the standard method (based on partially observed networks) and a random selection strategy in terms of vaccination effectiveness in a SIR model. The numerical comparison is first carried out using real-world face-to-face dynamic networks collected in a high school, followed by sequential multi-layer networks generated relying on the Barabasi-Albert model emulating large-scale social networks with several communities.

Theoretical Analysis of a COVID-19 CF-Fractional Model to Optimally Control the Spread of Pandemic

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

Predicting COVID-19 using lioness optimization algorithm and graph convolution network

In this paper, a graph convolution network prediction model based on the lioness optimization algorithm (LsOA-GCN) is proposed to predict the cumulative number of confirmed COVID-19 cases in 17 regions of Hubei Province from March 23 to March 29, 2020, according to the transmission characteristics of COVID-19. On the one hand, Spearman correlation analysis with delay days and LsOA are used to capture the dynamic changes of feature information to obtain the temporal features. On the other hand, the graph convolutional network is used to capture the topological structure of the city network, so as to obtain spatial information and finally realize the prediction task. Then, we evaluate this model through performance evaluation indicators and statistical test methods and compare the results of LsOA-GCN with 10 representative prediction methods in the current epidemic prediction study. The experimental results show that the LsOA-GCN prediction model is significantly better than other prediction methods in all indicators and can successfully capture spatio-temporal information from feature data, thereby achieving accurate prediction of epidemic trends in different regions of Hubei Province.

Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods

The model of any epidemic illness is evolved from the current susceptibility. We aim to construct a model, based on the literature, different to the conventional examinations in epidemiology, i.e., what will occur depends on the susceptible cases, which is not always the case; one must consider a model with aspects such as infections, recoveries, deaths, and vaccinated populations. Much of this information may not be available. So without artificially assuming the unknown aspects, we frame a new model known as IVRD. Apart from qualitative evaluation, numerical evaluation has been completed to aid the results. A novel approach of calculating the fundamental reproduction/transmission range is presented, with a view to estimating the largest number of aspects possible, with minimal restrictions on the spread of any disease. An additional novel aspect of this model is that we include vaccines with the actively infected cases, which is not common. A few infections such as rabies, ebola, etc., can apply this model. In general, the concept of symmetry or asymmetry will exist in every epidemic model. This model and method can be applied in scientific research in the fields of epidemic modeling, the medical sciences, virology, and other areas, particularly concerning rabies, ebola, and similar diseases, to show how immunity develops after being infected by these viruses.

Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic

In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F0∗,F1∗ of the proposed model are stated. Threshold parameter R0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative ρ and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population.

On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19

In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.

Gauging the Impact of Artificial Intelligence and Mathematical Modeling in Response to the COVID-19 Pandemic: A Systematic Review

While the world continues to grapple with the devastating effects of the SARS-nCoV-2 virus, different scientific groups, including researchers from different parts of the world, are trying to collaborate to discover solutions to prevent the spread of the COVID-19 virus permanently. Henceforth, the current study envisions the analysis of predictive models that employ machine learning techniques and mathematical modeling to mitigate the spread of COVID-19. A systematic literature review (SLR) has been conducted, wherein a search into different databases, viz., PubMed and IEEE Explore, fetched 1178 records initially. From an initial of 1178 records, only 50 articles were analyzed completely. Around (64%) of the studies employed data-driven mathematical models, whereas only (26%) used machine learning models. Hybrid and ARIMA models constituted about (5%) and (3%) of the selected articles. Various Quality Evaluation Metrics (QEM), including accuracy, precision, specificity, sensitivity, Brier-score, F1-score, RMSE, AUC, and prediction and validation cohort, were used to gauge the effectiveness of the studied models. The study also considered the impact of Pfizer-BioNTech (BNT162b2), AstraZeneca (ChAd0x1), and Moderna (mRNA-1273) on Beta (B.1.1.7) and Delta (B.1.617.2) viral variants and the impact of administering booster doses given the evolution of viral variants of the virus.

A Novel Model for Distributed Denial of Service Attack Analysis and Interactivity

A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots throughout the network. A mathematical differential equation model is proposed to represent the dynamism of nodes at different compartments of the model. The model considers two levels of security, with the assumption that the recovered nodes do not return to the same security level. In previous models, the recovered nodes are returned to be suspect on the same security level, which is an unrealistic assumption. Moreover, it is assumed that the attacker can use the infected target nodes to attack again. With such epidemic-like assumptions of infection, different cases are presented and discussed, and the stability of the model is analyzed as well; reversing the symmetry transformation of attacking nodes population is also proven. The proposed model has many parameters in order to precisely describe the infection movement and propagation. Numerical simulation methods are used to solve the developed system of equations using MATLAB, with the intention of finding the best counteraction to control DDoS spread throughout a network.

On the effectiveness of tracking and testing in SEIR models for improving health vs. economy trade-offs

We study the effectiveness of tracking and testing policies for suppressing epidemic outbreaks. We evaluate the performance of tracking-based intervention methods on a network SEIR model, which we augment with an additional parameter to model pre-symptomatic and asymptomatic individuals, and study the effectiveness of these methods in combination with or as an alternative to quarantine and global lockdown policies. Our focus is on the basic trade-off between human-lives lost and economic costs, and on how this trade-off changes under different quarantine, lockdown, tracking, and testing policies. Our main findings are as follows: (1) Tests combined with patient quarantines reduce both economic costs and mortality, however, an extensive-scale testing capacity is required to achieve a significant improvement. (2) Tracking significantly reduces both economic costs and mortality. (3) Tracking combined with a moderate testing capacity can achieve containment without lockdowns. (4) In the presence of a flow of new incoming infections, dynamic "On-Off" lockdowns are more efficient than fixed lockdowns. In this setting as well, tracking strictly improves efficiency. The results show the extreme usefulness of policies that combine tracking and testing for reducing mortality and economic costs, and their potential to contain outbreaks without imposing any social distancing restrictions. This highlights the difficult social question of trading-off these gains against patient privacy, which is inevitably infringed by tracking.

Transmission dynamics of novel coronavirus SARS-CoV-2 among healthcare workers, a case study in Iran

One of the main concerns during the COVID-19 pandemic was the protection of healthcare workers against the novel coronavirus. The critical role and vulnerability of healthcare workers during the COVID-19 pandemic leads us to derive a mathematical model to express the spread of coronavirus between the healthcare workers. In the first step, the SECIRH model is introduced, and then the mathematical equations are written. The proposed model includes eight state variables, i.e., Susceptible, Exposed, Carrier, Infected, Hospitalized, ICU admitted, Dead, and finally Recovered. In this model, the vaccination, protective equipment, and recruitment policy are considered as preventive actions. The formal confirmed data provided by the Iranian ministry of health is used to simulate the proposed model. The simulation results revealed that the proposed model has a high degree of consistency with the actual COVID-19 daily statistics. In addition, the roles of vaccination, protective equipment, and recruitment policy for the elimination of coronavirus among the healthcare workers are investigated. The results of this research help the policymakers to adopt the best decisions against the spread of coronavirus among healthcare workers.

Dynamics of a COVID-19 Model with a Nonlinear Incidence Rate, Quarantine, Media Effects, and Number of Hospital Beds

In many countries the COVID-19 pandemic seems to witness second and third waves with dire consequences on human lives and economies. Given this situation the modeling of the transmission of the disease is still the subject of research with the ultimate goal of understanding the dynamics of the disease and assessing the efficacy of different mitigation strategies undertaken by the affected countries. We propose a mathematical model for COVID-19 transmission. The model is structured upon five classes: an individual can be susceptible, exposed, infectious, quarantined or removed. The model is based on a nonlinear incidence rate, takes into account the influence of media on public behavior, and assumes the recovery rate to be dependent on the hospital-beds to population ratio. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, stability analysis of the disease-free equilibrium (symmetry) and sensitivity analysis. We found that if the basic reproduction number is less than unity the system can exhibit Hopf and backward bifurcations for some range of parameters. Numerical simulations using parameter values fitted to Saudi Arabia are carried out to support the theoretical proofs and to analyze the effects of hospital-beds to population ratio, quarantine, and media effects on the predicted nonlinear behavior.

A Modified SIRD Model to Study the Evolution of the COVID-19 Pandemic in Spain

In this paper, we use an SIRD model to analyze the evolution of the COVID-19 pandemic in Spain, caused by a new virus called SARS-CoV-2 from the coronavirus family. This model is governed by a nonlinear system of differential equations that allows us to detect trends in the pandemic and make reliable predictions of the evolution of the infection in the short term. This work shows this evolution of the infection in various changing stages throughout the period of maximum alert in Spain. It also shows a quick adaptation of the parameters that define the disease in several stages. In addition, the model confirms the effectiveness of quarantine to avoid the exponential expansion of the pandemic and reduce the number of deaths. The analysis shows good short-term predictions using the SIRD model, which are useful to influence the evolution of the epidemic and thus carry out actions that help reduce its harmful effects.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses.

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.

On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

In this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.