Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom

Exploring optimal control strategies in a nonlinear fractional bi-susceptible model for Covid-19 dynamics using Atangana-Baleanu derivative

In this article, a nonlinear fractional bi-susceptible [Formula: see text] model is developed to mathematically study the deadly Coronavirus disease (Covid-19), employing the Atangana-Baleanu derivative in Caputo sense (ABC). A more profound comprehension of the system's intricate dynamics using fractional-order derivative is explored as the primary focus of constructing this model. The fundamental properties such as positivity and boundedness, of an epidemic model have been proven, ensuring that the model accurately reflects the realistic behavior of disease spread within a population. The asymptotic stabilities of the dynamical system at its two main equilibrium states are determined by the essential conditions imposed on the threshold parameter. The analytical results acquired are validated and the significance of the ABC fractional derivative is highlighted by employing a recently proposed Toufik-Atangana numerical technique. A quantitative analysis of the model is conducted by adjusting vaccination and hospitalization rates using constant control techniques. It is suggested by numerical experiments that the Covid-19 pandemic elimination can be expedited by adopting both control measures with appropriate awareness. The model parameters with the highest sensitivity are identified by performing a sensitivity analysis. An optimal control problem is formulated, accompanied by the corresponding Pontryagin-type optimality conditions, aiming to ascertain the most efficient time-dependent controls for susceptible and infected individuals. The effectiveness and efficiency of optimally designed control strategies are showcased through numerical simulations conducted before and after the optimization process. These simulations illustrate the effectiveness of these control strategies in mitigating both financial expenses and infection rates. The novelty of the current study is attributed to the application of the structure-preserving Toufik-Atangana numerical scheme, utilized in a backward-in-time manner, to comprehensively analyze the optimally designed model. Overall, the study's merit is found in its comprehensive approach to modeling, analysis, and control of the Covid-19 pandemic, incorporating advanced mathematical techniques and practical implications for disease management.

Long-term effect of SARS-CoV-2 variant : Challenging issues and controlling strategies

In this study, a latest version of COVID-19 pandemic is hand overed. A Stochastic post COVID-19 delayed model is developed to explore the spread of COVID-19 as well as omicron variant with the correlation of heart attack. This article provides an eradication of the COVID-19 and omicron variant as well as the population who have heart attack after post COVID-19 of these epidemic diseases. Then the existence and uniqueness of global positive solution are studied. Ensuing, In this article, we classify COVID-19 virus and omicron variant which go to extinction and become persistent in mean. By using Lyapunov function, the existence of ergodic stationary distribution are established. Later from the persistent disease as well as extinction, heart disease are ready to develop in the human body. By Eventually, an optimal control strategies are introduced in the form of stochastic post COVID-19 delayed model to control two different types of virus. Finally, the numerical simulation are presented to determine the behavior of dynamical system by utilizing the real data of United Kingdom.

New computations of the fractional worms transmission model in wireless sensor network in view of new integral transform with statistical analysis; an analysis of information and communication technologies

Wireless sensor networks (WSNs) have attracted a lot of interest due to their enormous potential for both military and civilian uses. Worm attacks can quickly target WSNs because of the network's weak security. The worm can spread throughout the network by interacting with a single unsafe node. Moreover, the analysis of worm spread in WSNs can benefit from the use of mathematical epidemic models. We suggest a five-compartment model to characterize the mechanisms of worm proliferation with respect to time in WSN. Taking into account the Z Z transform convoluted with the Atangana-Baleanu-Caputo (ABC) fractional derivative operator, we employ it to analyze the characteristics and applications of the Z Z transformation using the Mittag-Leffler kernel. Moreover, we construct a new algorithm for the homotopy perturbation method (HPM) in conjunction with the Z Z transform technique to generate analytical solutions for the worm transmission model. Also, we address the qualitative aspects such as positivity, boundness, worm-free state, endemic state, basic reproduction number ( R 0 ) and worm-free equilibrium stability. Furthermore, we prove that the virus rate in sensor nodes is extinct ifR 0 < 1 and the virus persists ifR 0 > 1 . In addition, we develop analytical findings to evaluate the series of solutions. Furthermore, a detailed statistical analysis is conducted to verify the nonlinear dynamics of the system by verifying the 0 - 1 test to determine whether uncertainty exists using approximation entropy and theC 0 data. An extensive analysis of the vaccination class with respect to the transmitting class as well as the susceptible class is being used to investigate the effects of stepping up precautions on WP in WSN. Moreover, the modeling of the WSN revealed that reducing the fractional-order from 1 requires that the recommended approach be implemented at the highest rate so that there is no long-lasting immunization; instead, nodes remain briefly defensive before becoming vulnerable to future worm attacks.

Analysis of learning curves in predictive modeling using exponential curve fitting with an asymptotic approach

The existence of large volumes of data has considerably alleviated concerns regarding the availability of sufficient data instances for machine learning experiments. Nevertheless, in certain contexts, addressing limited data availability may demand distinct strategies and efforts. Analyzing COVID-19 predictions at pandemic beginning emerged a question: how much data is needed to make reliable predictions? When does the volume of data provide a better understanding of the disease's evolution and, in turn, offer reliable forecasts? Given these questions, the objective of this study is to analyze learning curves obtained from predicting the incidence of COVID-19 in Brazilian States using ARIMA models with limited available data. To fulfill the objective, a retrospective exploration of COVID-19 incidence across the Brazilian States was performed. After the data acquisition and modeling, the model errors were assessed by employing a learning curve analysis. The asymptotic exponential curve fitting enabled the evaluation of the errors in different points, reflecting the increased available data over time. For a comprehensive understanding of the results at distinct stages of the time evolution, the average derivative of the curves and the equilibrium points were calculated, aimed to identify the convergence of the ARIMA models to a stable pattern. We observed differences in average derivatives and equilibrium values among the multiple samples. While both metrics ultimately confirmed the convergence to stability, the equilibrium points were more sensitive to changes in the models' accuracy and provided a better indication of the learning progress. The proposed method for constructing learning curves enabled consistent monitoring of prediction results, providing evidence-based understandings required for informed decision-making.

Stability Analysis of SARS-CoV-2 with Heart Attack Effected Patients and Bifurcation

The aim of this study is to analyze and investigate the SARS-CoV-2 (SC-2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC-2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC-2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID-19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC-2 in the United Kingdom as well as its global effects, also show the actual behavior of SC-2 which will be helpful to understand the outbreak of SC-2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies.

Modeling of psoriasis by considering drug influence: A mathematical approach with memory trace

Psoriasis is an immune-mediated genetic disease, characterized by its manifestation on the skin, the joints, or both. In this paper, our primary aim is to increase awareness about the intricate nature of this multifaceted condition, highlight the potential of therapeutic approaches, and examine the factors affecting the future course of psoriasis. This paper introduces a mathematical model for psoriasis, formulated by fractional order differential equations (FODE) with Caputo sense. The model also includes the drug effect of immune-boosting drugs on psoriasis. It has been shown that the solution of the proposed system exists and is unique, and its positivity and boundedness have been proven. Additionally, the local stability and global stability of the co-existing equilibrium point have been investigated. Numerical solutions have been conducted using the Adams Bashforth PECE method to analyze the influence of fractional order derivatives (FODs) and distinct parameters on population dynamics. The graphics have been acquired using the L1 scheme, incorporating a memory trace (MT) mechanism capable of comprehensively capturing and amalgamating historical system dynamics to visualize the memory trace in detail. One of the results deduced from this paper is that the MT disappears when α equals 1. Upon decreasing the fractional order α from 1, the MT experiences a non-linear augmentation starting from zero. This observed MT emphasizes the distinction between derivatives of fractional and integer orders. Within the proposed model, our findings suggest that introducing the immune booster drug efficiently controls psoriasis. Furthermore, when appropriate clinical patient data are available, the proposed results can be used for a specific psoriasis patient. Our study suggests that treatment with the drug may be a new insight into psoriasis treatment and may be proposed as a treatment policy for future clinical trials.

Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space

This paper conducts a systematic statistical analysis of the characteristics of the geographical empirical distributions for the numbers of both cumulative and daily confirmed COVID-19 cases and deaths at county, city, and state levels over a time span from January 2020 to June 2022. The mathematical heavy-tailed distributions can be used for fitting the empirical distributions observed in different temporal stages and geographical scales. The estimations of the shape parameter of the tail distributions using the Generalized Pareto Distribution also support the observations of the heavy-tailed distributions. According to the characteristics of the heavy-tailed distributions, the evolution course of the geographical empirical distributions can be divided into three distinct phases, namely the power-law phase, the lognormal phase I, and the lognormal phase II. These three phases could serve as an indicator of the severity degree of the COVID-19 pandemic within an area. The empirical results suggest important intrinsic dynamics of a human infectious virus spread in the human interconnected physical complex network. The findings extend previous empirical studies and could provide more strict constraints for current mathematical and physical modeling studies, such as the SIR model and its variants based on the theory of complex networks.

A novel fractional order model of SARS-CoV-2 and Cholera disease with real data

This study presents a novel approach to investigating COVID-19 and Cholera disease. In this situation, a fractional-order model is created to investigate the COVID-19 and Cholera outbreaks in Congo. The existence, uniqueness, positivity, and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, the basic reproduction number (the virus transmission coefficient) is calculated that simply refers to the number of people, to whom an infected person can make infected, as R 0 = 6 . 7442389 e - 10 by using the next generation matrix method. Next, the sensitivity analysis of the parameters is performed according to R 0 . To determine the values of the parameters in the model, the least squares curve fitting method is utilized. A total of 22 parameter values in the model are estimated by using real Cholera data from Congo. Finally, to find out the dynamic behavior of the system, numerical simulations are presented. The outcome of the study indicates that the severity of the Cholera epidemic cases will decrease with the decrease in cases of COVID-19, through the implementation and follow-up of safety measures that have been taken to reduce COVID-19 cases.

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

Modeling the SARS-CoV-2 Omicron variant dynamics in the United States with booster dose vaccination and waning immunity

We carried out a theoretical and numerical analysis for an epidemic model to analyze the dynamics of the SARS-CoV-2 Omicron variant and the impact of vaccination campaigns in the United States. The model proposed here includes asymptomatic and hospitalized compartments, vaccination with booster doses, and the waning of natural and vaccine-acquired immunity. We also consider the influence of face mask usage and efficiency. We found that enhancing booster doses and using N95 face masks are associated with a reduction in the number of new infections, hospitalizations and deaths. We highly recommend the use of surgical face masks as well, if usage of N95 is not a possibility due to the price range. Our simulations show that there might be two upcoming Omicron waves (in mid-2022 and late 2022), caused by natural and acquired immunity waning with respect to time. The magnitude of these waves will be 53% and 25% lower than the peak in January 2022, respectively. Hence, we recommend continuing to use face masks to decrease the peak of the upcoming COVID-19 waves.

Understanding COVID-19-related myocarditis: pathophysiology, diagnosis, and treatment strategies

Coronavirus disease 2019 (COVID-19) disease has infected nearly 600 million people, resulting in > 6 million deaths, with many of them dying from cardiovascular diseases. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is caused by a combination of the virus surface spike protein and the human angiotensin-converting enzyme 2 (ACE2) receptor. In addition to being highly expressed in the lungs, ACE2 is widely distributed in the heart, mainly in myocardial cells and pericytes. Like other types of viruses, SARS-CoV-2 can cause myocarditis after infecting the myocardial tissue, which is attributed to the direct damage of the virus and uncontrolled inflammatory reactions. Patients with chest tightness, palpitation, abnormal electrocardiogram, and cardiac troponin elevation, should be suspected of myocarditis within 1-3 weeks of COVID-19 infection. When the hemodynamics change rapidly, fulminant myocarditis should be suspected. Cardiac ultrasound, myocardial biopsy, cytokine detection, cardiac magnetic resonance imaging, 18F-fluorodeoxyglucose positron emission tomography, and other examination methods can assist in the diagnosis. Although scientists and clinicians have made concerted efforts to seek treatment and prevention measures, there are no clear recommendations for the treatment of COVID-19-related myocarditis. For most cases of common myocarditis, general symptomatic and supportive treatments are used. For COVID-19-related fulminant myocarditis, it is emphasized to achieve "early identification, early diagnosis, early prediction, and early treatment" based on the "life support-based comprehensive treatment regimen." Mechanical circulatory support therapy can rest the heart, which is a cure for symptoms, and immune regulation therapy can control the inflammatory storms which is a cure for the disease. Furthermore, complications of COVID-19-related myocarditis, such as arrhythmia, thrombosis, and infection, should be actively treated. Herein, we summarized the incidence rate, manifestations, and diagnosis of COVID-19-related myocarditis and discussed in detail the treatment of COVID-19-related myocarditis, especially the treatment strategy of fulminant myocarditis.

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

On the analysis of the fractional model of COVID-19 under the piecewise global operators

An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.

Analysis of food chain mathematical model under fractal fractional Caputo derivative

In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.

Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

The Unique ergodic stationary distribution of two stochastic SEIVS epidemic models with higher order perturbation

Two types of susceptible, exposed, infectious, vaccinated/recovered, susceptible (SEIVS) epidemic models with saturation incidence and temporary immunity, driven by higher order white noise and telegraph noise, are investigated. The key aim of this work is to explore and obtain the existence of the unique ergodic stationary distribution for the above two models, which reveals whether the disease will be prevalent and persistent under some noise intensity assumptions. We also use meticulous numerical examples to validate the feasibility of the analytical findings. Finally, a brief biological discussion shows that the intensities of noises play a significant role in the stationary distributions of the two models.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

It is well established that COVID-19 incidence data follows some power law growth pattern. Therefore, it is natural to believe that the COVID-19 transmission process follows some power law. However, we found no existing model on COVID-19 with a power law effect only in the disease transmission process. Inevitably, it is not clear how this power law effect in disease transmission can influence multiple COVID-19 waves in a location. In this context, we developed a completely new COVID-19 model where a force of infection function in disease transmission follows some power law. Furthermore, different realistic epidemiological scenarios like imperfect social distancing among home-quarantined individuals, disease awareness, vaccination, treatment, and possible reinfection of the recovered population are also considered in the model. Applying some recent techniques, we showed that the proposed system converted to a COVID-19 model with fractional order disease transmission, where order of the fractional derivative ( α ) in the force of infection function represents the memory effect in disease transmission. We studied some mathematical properties of this newly formulated model and determined the basic reproduction number (R 0 ). Furthermore, we estimated several epidemiological parameters of the newly developed fractional order model (including memory index α ) by fitting the model to the daily reported COVID-19 cases from Russia, South Africa, UK, and USA, respectively, for the time period March 01, 2020, till December 01, 2021. Variance-based Sobol's global sensitivity analysis technique is used to measure the effect of different important model parameters (including α ) on the number of COVID-19 waves in a location (W C ). Our findings suggest that α along with the average transmission rate of the undetected (symptomatic and asymptomatic) cases in the community (β 1 ) are mainly influencing multiple COVID-19 waves in those four locations. Numerically, we identified the regions in the parameter space of α andβ 1 for which multiple COVID-19 waves are occurring in those four locations. Furthermore, our findings suggested that increasing memory effect in disease transmission ( α → 0) may decrease the possibility of multiple COVID-19 waves and as well as reduce the severity of disease transmission in those four locations. Based on all the results, we try to identify a few non-pharmaceutical control strategies that may reduce the risk of further SARS-CoV-2 waves in Russia, South Africa, UK, and USA, respectively.

Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model

Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.

A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response

The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.

Mathematical modeling of corona virus (COVID-19) and stability analysis

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us.

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.

Analysis of mobility based COVID-19 epidemic model using Federated Multitask Learning

Aggregating a massive amount of disease-related data from heterogeneous devices, a distributed learning framework called Federated Learning(FL) is employed. But, FL suffers in distributing the global model, due to the heterogeneity of local data distributions. To overcome this issue, personalized models can be learned by using Federated multitask learning(FMTL). Due to the heterogeneous data from distributed environment, we propose a personalized model learned by federated multitask learning (FMTL) to predict the updated infection rate of COVID-19 in the USA using a mobility-based SEIR model. Furthermore, using a mobility-based SEIR model with an additional constraint we can analyze the availability of beds. We have used the real-time mobility data sets in various states of the USA during the years 2020 and 2021. We have chosen five states for the study and we observe that there exists a correlation among the number of COVID-19 infected cases even though the rate of spread in each case is different. We have considered each US state as a node in the federated learning environment and a linear regression model is built at each node. Our experimental results show that the root-mean-square percentage error for the actual and prediction of COVID-19 cases is low for Colorado state and high for Minnesota state. Using a mobility-based SEIR simulation model, we conclude that it will take at least 400 days to reach extinction when there is no proper vaccination or social distance.

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana-Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case ifR 0 < 1 . We show the global asymptotically stable of the model for the disease free case whenR 0 ≤ 1 . We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021-Sep 2021 and estimate the model parameters and getR 0 ≈ 1 . 4004 . The real parameters values are used to show the graphical results for the fractional and piecewise model.