A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects

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.

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.

Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.

Chaotic attractors that exist only in fractional-order case

INTRODUCTION

Studying chaotic dynamics in fractional- and integer-order dynamical systems has let researchers understand and predict the mechanisms of related non-linear phenomena.

OBJECTIVES

Phase transitions between the fractional- and integer-order cases is one of the main problems that have been extensively examined by scientists, economists, and engineers. This paper reports the existence of chaotic attractors that exist only in the fractional-order case when using the specific selection of parameter values in a new hyperchaotic (Matouk's) system.

METHODS

This paper discusses stability analysis of the steady-state solutions, existence of hidden chaotic attractors and self-excited chaotic attractors. The results are supported by computing basin sets of attractions, bifurcation diagrams and the Lyapunov exponent spectrum. These tools verify the existence of chaotic dynamics in the fractional-order case; however, the corresponding integer-order counterpart exhibits quasi-periodic dynamics when using the same choice of initial conditions and parameter set. Projective synchronization via non-linear controllers is also achieved between drive and response states of the hidden chaotic attractors of the fractional Matouk's system.

RESULTS

Dynamical analysis and computer simulation results verify that the chaotic attractors exist only in the fractional-order case when using the specific selection of parameter values in the Matouk's hyperchaotic system.

CONCLUSIONS

An example of the existence of hidden and self-excited chaotic attractors that appears only in the fractional-order case is discussed. So, the obtained results give the first example that shows chaotic states are not necessarily transmitted between fractional- and integer-order dynamical systems when using a specific selection of parameter values. Chaos synchronization using the hidden attractors' manifolds provides new challenges in chaos-based applications to technology and industrial fields.

Interaction of Virus in Cancer Patients: A Theoretical Dynamic Model

This study reports on a phase-space analysis of a mathematical model of tumor growth with the interaction between virus and immune response. In this study, a mathematical determination was attempted to demonstrate the relationship between uninfected cells, infected cells, effector immune cells, and free viruses using a dynamic model. We revealed the stability analysis of the system and the Lyapunov stability of the equilibrium points. Moreover, all endemic equilibrium point models are derived. We investigated the stability behavior and the range of attraction sets of the nonlinear systems concerning our model. Furthermore, a global stability analysis is proved either in the construction of a Lyapunov function showing the validity of the concerned disease-free equilibria or in endemic equilibria discussed by the model. Finally, a simulated solution is achieved and the relationship between cancer cells and other cells is drawn.

Vaccination control measures of an epidemic model with long-term memristive effect

COVID-19 is a drastic air-way tract infection that set off a global pandemic recently. Most infected people with mild and moderate symptoms have recovered with naturally acquired immunity. In the interim, the defensive mechanism of vaccines helps to suppress the viral complications of the pathogenic spread. Besides effective vaccination, vaccine breakthrough infections occurred rapidly due to noxious exposure to contagions. This paper proposes a new epidemiological control model in terms of Atangana Baleanu Caputo (ABC) type fractional order differ integrals for the reported cases of COVID-19 outburst. The qualitative theoretical and numerical analysis of the aforesaid mathematical model in terms of three compartments namely susceptible, vaccinated, and infected population are exhibited through non-linear functional analysis. The hysteresis kernel involved in AB integral inherits the long-term memory of the dynamical trajectory of the epidemics. Hyer-Ulam's stability of the system is studied by the dichotomy operator. The most effective approximate solution is derived by numerical interpolation to our proposed model. An extensive analysis of the vigorous vaccination and the proportion of vaccinated individuals are explored through graphical simulations. The efficacious enforcement of this vaccination control mechanism will mitigate the contagious spread and severity.

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.

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.

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.

Aggressive behavior, boredom, and protective factors among college students during closed-off management of the COVID-19 pandemic in China

Background

Chinese colleges have implemented strict closed-off management in response to the outbreak of a new variant of the new coronavirus, Omicron. But such management measures may lead to more aggressive behavior. The study aimed to determine the associations between boredom and aggressive behavior with aggression and to examine the impact of boredom on aggression through the moderating role of cognitive flexibility.

Methods

The Multidimensional State Boredom Scale, the Reactive-Proactive Aggression Questionnaire, and the Cognitive Flexibility Inventory were applied to a sample of 719 college students who were in a closed-off management environment.

Results

For individuals with high cognitive flexibility, the relationship between state boredom and proactive aggression was not significant. The relationship between state boredom and proactive aggression was significantly positively correlated for individuals with low cognitive flexibility, especially low substitutability. Cognitive flexibility has no significant moderating effect on the relationship between state boredom and reactive aggression.

Conclusion

The findings highlighted the importance of boredom as a potential risk factor for aggression, while cognitive flexibility appears as a potential protective factor.

Lyapunov stability and wave analysis of Covid-19 omicron variant of real data with fractional operator

The fractional derivative is an advanced category of mathematics for real-life problems. This work focus on the investigation of 2nd wave of the Corona virus in India. We develop a time-fractional order COVID-19 model with effects of the disease which consist of a system of fractional differential equations. The fractional-order COVID-19 model is investigated with Atangana-Baleanu-Caputo fractional derivative. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. The fractional-order system is analyzed qualitatively as well as verified sensitivity analysis. Fixed point theory is used to prove the existence and uniqueness of the fractional-order model. Analyzed the model locally as well as globally using Lyapunov first and second derivative. Boundedness and positive unique solutions are verified for the fractional-order model of infection of disease. The concept of fixed point theory is used to interrogate the problem and confine the solution. 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 behavior of the virus.

Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

In this paper, we explore local behavior at fixed points, chaos and bifurcations of a discrete COVID-19 epidemic model in the interior of R + 5 . It is explored that for all involved parametric values, COVID-19 model has boundary fixed point and also it has an interior fixed point under certain parametric condition(s). We have investigated local behavior at boundary and interior fixed points of COVID-19 model by linear stability theory. It is also explored the existence of possible bifurcations at respective fixed points, and proved that at boundary fixed point there exists no flip bifurcation but at interior fixed point it undergoes both flip and hopf bifurcations, and we have explored said bifurcations by explicit criterion. Moreover, chaos in COVID-19 model is also investigated by feedback control strategy. Finally, theoretical results are verified numerically.

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone's Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model's existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebola-malaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebola-malaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

Pediatric Residency Training amid the COVID-19 Pandemic: Exploring the Impact of Supervision and Clinical Practice Guidelines on Clinical and Financial Outcomes

Objective

This study is aimed at calculating the magnitude of the effect of clinical practice guidelines (CPG) and supervision in inhibiting the negative impact of the COVID-19 pandemic on clinical and financial outcomes of non-COVID-19 inpatient care by pediatric residents in academic medical center (AMC) hospitals during the COVID-19 pandemic.

Methods

The cohort retrospective study was conducted. This study collected patient data from pediatric residency programs. A research cohort consisted of non-COVID-19 pediatric patients at Dr. Soetomo General Academic Hospital. This study compared the subgroup of patients treated during the pandemic with those treated before the pandemic. The results were analyzed using SPSS 26.0 and Smart-PLS.

Results

There was a 41.4% decrease in pediatric inpatients during the pandemic with an increased severity level and complexity level, a reduction of 7.46% availability of supervisors, an increase of 0.4% in readmission < 30 days, an increase of 0.31% in-hospital mortality, an increase the total costs of care, and a decrease of insurance claim profit. CPG did not moderate the effect of the COVID-19 pandemic on the clinical outcomes (β = -0.006, P = 0.083) but moderated the financial outcomes (β = -0.022, P = 0.000), by reducing the total cost of care and increasing insurance claim profit. Supervision moderated the effect of the COVID-19 pandemic on the clinical outcomes (β = 0.040, P = 0.000) by increasing aLOS and on the financial outcomes (β = -0.031, P = 0.000) by reducing the total cost of care and increasing insurance claim profit. This study model had a 24.0% variance of explanatory power for clinical outcomes and 49.0% for financial outcomes. This study's structural model effectively predicted clinical outcomes (Q 2 = 0.238) and financial outcomes (Q 2 = 0.413).

Conclusion

Direct supervision inhibited the negative impact of the COVID-19 pandemic on both clinical and financial outcomes of non-COVID-19 inpatient care by pediatric residents, while CPG only inhibited the negative impact on financial outcomes. Implication of This Study. In a disaster, the availability of CPG and direct supervision makes AMC hospitals able to inhibit the negative impact of disasters on clinical and financial outcomes.

Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives

A new non-integer order mathematical model for SARS-CoV-2, Dengue and HIV co-dynamics is designed and studied. The impact of SARS-CoV-2 infection on the dynamics of dengue and HIV is analyzed using the tools of fractional calculus. The existence and uniqueness of solution of the proposed model are established employing well known Banach contraction principle. The Ulam-Hyers and generalized Ulam-Hyers stability of the model is also presented. We have applied the Laplace Adomian decomposition method to investigate the model with the help of three different fractional derivatives, namely: Caputo, Caputo-Fabrizio and Atangana-Baleanu derivatives. Stability analyses of the iterative schemes are also performed. The model fitting using the three fractional derivatives was carried out using real data from Argentina. Simulations were performed with each non-integer derivative and the results thus obtained are compared. Furthermore, it was concluded that efforts to keep the spread of SARS-CoV-2 low will have a significant impact in reducing the co-infections of SARS-CoV-2 and dengue or SARS-COV-2 and HIV. We also highlighted the impact of three different fractional derivatives in analyzing complex models dealing with the co-dynamics of different diseases.

Dynamical behaviours and stability analysis of a generalized fractional model with a real case study

Introduction

Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly.

Objectives

The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework.

Methods

The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated.

Results

Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied.

Conclusion

According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.

A Class of Deterministic and Stochastic Fractional Epidemic Models with Vaccination

In this paper, a class of fractional deterministic and stochastic susceptible-infected-removed- susceptible (SIRS) epidemic models with vaccination is proposed. For the fractional deterministic SIRS epidemic model, the existence of solution and the stability of equilibrium points are analyzed by using dynamic method. Then, the appropriate controls are established to effectively control the disease and eliminate it. On this basis, the fractional stochastic SIRS epidemic model with vaccination is further considered, and a numerical approximation method is proposed. The correctness of the conclusion is verified by numerical simulation.

The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling

Epidemic spread models are useful tools to study the spread and the effectiveness of the interventions at a population level, to an epidemic. The workhorse of spatially homogeneous class models is the SIR-type ones comprising ordinary differential equations for the unknown state variables. The transition between different states is expressed through rate functions. Inspired by -but not restricted to- features of the COVID-19 pandemic, a new framework for modeling a disease spread is proposed. The main concept refers to the assignment of properties to each individual person as regards his response to the disease. A multidimensional distribution of these properties represents the whole population. The temporal evolution of this distribution is the only dependent variable of the problem. All other variables can be extracted by post-processing of this distribution. It is noteworthy that the new concept allows an improved consideration of vaccination modeling because it recognizes vaccination as a modifier of individuals response to the disease and not as a means for individuals to totally defeat the disease. At the heart of the new approach is an infection age model engaging a sharp cut-off. This model is analyzed in detail, and it is shown to admit self-similar solutions. A hierarchy of models based on the new approach, from a generalized one to a specific one with three dominant properties, is derived. The latter is implemented as an example and indicative results are presented and discussed. It appears that the new framework is general and versatile enough to simulate disease spread processes and to predict the evolution of several variables of the population during this spread.

Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method

This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.

A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor

During the past several years, the deadly COVID-19 pandemic has dramatically affected the world; the death toll exceeds 4.8 million across the world according to current statistics. Mathematical modeling is one of the critical tools being used to fight against this deadly infectious disease. It has been observed that the transmission of COVID-19 follows a fading memory process. We have used the fractional order differential operator to identify this kind of disease transmission, considering both fear effects and vaccination in our proposed mathematical model. Our COVID-19 disease model was analyzed by considering the Caputo fractional operator. A brief description of this operator and a mathematical analysis of the proposed model involving this operator are presented. In addition, a numerical simulation of the proposed model is presented along with the resulting analytical findings. We show that fear effects play a pivotal role in reducing infections in the population as well as in encouraging the vaccination campaign. Furthermore, decreasing the fractional-order parameter α value minimizes the number of infected individuals. The analysis presented here reveals that the system switches its stability for the critical value of the basic reproduction number R0=1.

Short-Term and Long-Term COVID-19 Pandemic Forecasting Revisited with the Emergence of OMICRON Variant in Jordan

Three simple approaches to forecast the COVID-19 epidemic in Jordan were previously proposed by Hussein, et al.: a short-term forecast (STF) based on a linear forecast model with a learning database on the reported cases in the previous 5–40 days, a long-term forecast (LTF) based on a mathematical formula that describes the COVID-19 pandemic situation, and a hybrid forecast (HF), which merges the STF and the LTF models. With the emergence of the OMICRON variant, the LTF failed to forecast the pandemic due to vital reasons related to the infection rate and the speed of the OMICRON variant, which is faster than the previous variants. However, the STF remained suitable for the sudden changes in epi curves because these simple models learn for the previous data of reported cases. In this study, we revisited these models by introducing a simple modification for the LTF and the HF model in order to better forecast the COVID-19 pandemic by considering the OMICRON variant. As another approach, we also tested a time-delay neural network (TDNN) to model the dataset. Interestingly, the new modification was to reuse the same function previously used in the LTF model after changing some parameters related to shift and time-lag. Surprisingly, the mathematical function type was still valid, suggesting this is the best one to be used for such pandemic situations of the same virus family. The TDNN was data-driven, and it was robust and successful in capturing the sudden change in +qPCR cases before and after of emergence of the OMICRON variant.

Solving Fredholm Integral Equations Using Deep Learning

The aim of this paper is to provide a deep learning based method that can solve high-dimensional Fredholm integral equations. A deep residual neural network is constructed at a fixed number of collocation points selected randomly in the integration domain. The loss function of the deep residual neural network is defined as a linear least-square problem using the integral equation at the collocation points in the training set. The training iteration is done for the same set of parameters for different training sets. The numerical experiments show that the deep learning method is efficient with a moderate generalization error at all points. And the computational cost does not suffer from “curse of dimensionality” problem.

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

In this study, a new approach to COVID-19 pandemic is presented. In this context, a fractional order pandemic model is developed to examine the spread of COVID-19 with and without Omicron variant and its relationship with heart attack using real data from the United Kingdom. In the model, heart attack is adopted by considering its relationship with the quarantine strategy. Then, the existence, uniqueness, positivity and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, we calculate the basic reproduction number (the virus transmission coefficient) that simply refers to the number of people, to whom an infected person can make infected, asR 0 = 3.6456 by using the next generation matrix method. Next, we consider the sensitivity analysis of the parameters according to R 0 . In order to determine the values of the parameters in the model, the least squares curve fitting method, which is one of the leading methods in parameter estimation, is benefited. A total of 21 parameter values in the model are estimated by using real Omicron data from the United Kingdom. Moreover, in order to highlight the advantages of using fractional differential equations, applications related to memory trace and hereditary properties are given. Finally, the numerical simulations are presented to examine the dynamic behavior of the system. As a result of numerical simulations, an increase in the number of people who have heart attacks is observed when Omicron cases were first seen. In the future, it is estimated that the risk of heart attack will decrease as the cases of Omicron decrease.

Shape and size optimization of truss structures by Chaos game optimization considering frequency constraints

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Shape and size Optimization of truss Structures is considered.

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Chaos Game Optimization (CGO) is utilized for optimization purposes.

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Benchmark 10-bar, 37-bar, 52-bar, 72-bar and 120-bar truss structures are utilized.

Introduction

An engineering system consists of properly established activities and put together to achieve a predefined goal. These activities include analysis, design, construction, research, and development. Designing and constructing structural systems, including buildings, bridges, highways, and other complex systems, have been developed over the centuries. However, the evolution of these systems has been prolonged because the overall process is very costly and time-consuming, requiring primary human and material resources to be utilized. One of the options for overcoming these shortcomings is the utilization of metaheuristic algorithms as recently developed intelligent techniques. These algorithms can be utilized as upper-level search techniques for optimization procedures to achieve better results.

Objectives

Shape and size optimization of truss structures are considered in this paper utilizing the Chaos Game Optimization (CGO) as one of the recently developed metaheuristic algorithms. The principles of chaos theory and fractal configuration are considered inspirational concepts.

Methods

For the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar, and 120-bar truss structures as four of the benchmark problems in this field are considered as design examples in which the frequency constraints are considered as limits that have to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also conducted with other algorithms in the literature.

Results

Based on the results of the CGO and other approaches from the literature, the CGO can provide better and competitive results in dealing with the considered truss design problems.

Conclusion

In summary, the CGO can provide better solutions in dealing with the considered real-size structural design problems with higher levels of complexity.