On the fractional SIRD mathematical model and control for the transmission of COVID-19: The first and the second waves of the disease in Iran and Japan

Memristor-induced hyperchaos, multiscroll and extreme multistability in fractional-order HNN: Image encryption and FPGA implementation

Fractional-order differentiation (FOD) can record information from the past, present, and future. Compared with integer-order systems, FOD systems have higher complexity and more accurate ability to describe the real world. In this paper, two types of fractional-order memristors are proposed and one type is proved to have extreme multistability, local activity, and non-volatility. By using memristors to simulate the autapse of a neuron and to describe the phenomenon of electromagnetic induction caused by electromagnetic radiation, we establish a new 5D FOD memristive HNN (FOMHNN). Through dynamic simulation, rich dynamic behaviors are found, such as hyperchaos, multiscroll, extreme multistability, and "overclocking" behavior caused by order reduction. To the best of our knowledge, this is the first time that such rich dynamic behaviors are found in FOMHNN simultaneously. Based on this FOMHNN, a very efficient and secure image encryption scheme is designed. Security analysis shows that the encrypted Lena image has extremely low adjacent pixel correlation and high randomness, with information entropy of 7.9995. Despite discarding diffusion and scrambling, it has excellent plaintext sensitivity, with NCPR = 99.6095% and UACI = 33.4671%. Finally, this paper implements the proposed FOMHNN and image encryption on field programmable gate array (FPGA). To our knowledge, the related work of fully hardware implementation of fractional-order neural networks and image encryption schemes based on this is rare.

Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model

The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.

A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event

In 2020 the world faced with a pandemic spread that affected almost everything of humans' social and health life. Regulations to decrease the epidemiological spread and studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back to the regular life, but on the other side there were also notable criticism about the vaccines itself. In this study, we established a fractional order differential equations system incorporating the vaccinated and re-infected compartments to a S I R frame to consider the expanded and detailed form as an S V I I v R model. We considered in the model some essential parameters, such as the protection rate of the vaccines, the vaccination rate, and the vaccine's lost efficacy after a certain period. We obtained the local stability of the disease-free and co-existing equilibrium points under specific conditions using the Routh-Hurwitz Criterion and the global stability in using a suitable Lyapunov function. For the numerical solutions we applied the Euler's method. The data for the simulations were taken from the World Health Organization (WHO) to illustrate numerically some scenarios that happened.

An innovative modulating functions method for pseudo-state estimation of fractional order systems

In this paper, the objective is to estimate the pseudo-state of fractional order systems defined by the Caputo fractional derivative from discrete noisy output measurement. For this purpose, an innovative modulating functions method is proposed, which can provide non-asymptotic estimation within finite-time and is robust against corrupting noises. First, the proposed method is directly applied to the Brunovsky's observable canonical form of the considered system. Then, the initial value of the pseudo-state is exactly expressed by an algebraic integral formula, based on which the pseudo-state is estimated. Second, the properties and construction of the required modulating functions are studied. Furthermore, error analysis is provided in discrete noise cases, which is useful for improving the estimation accuracy. In order to show the advantages of the proposed method, two numerical examples are given, where both rational order and irrational order dynamical systems are considered. After selecting the design parameters using the provided noise error bound, the pseudo-states of considered systems are estimated. The fractional order Luenberger-like observer and the fractional order H_∞-like observer are also applied. Better than the applied fractional order observers, the proposed method can guarantee the convergence speed and robustness at the same time.

Mathematical Modeling of SARS-CoV-2 Omicron Wave under Vaccination Effects

Over the course of the COVID-19 pandemic millions of deaths and hospitalizations have been reported. Different SARS-CoV-2 variants of concern have been recognized during this pandemic and some of these variants of concern have caused uncertainty and changes in the dynamics. The Omicron variant has caused a large amount of infected cases in the US and worldwide. The average number of deaths during the Omicron wave toll increased in comparison with previous SARS-CoV-2 waves. We studied the Omicron wave by using a highly nonlinear mathematical model for the COVID-19 pandemic. The novel model includes individuals who are vaccinated and asymptomatic, which influences the dynamics of SARS-CoV-2. Moreover, the model considers the waning of the immunity and efficacy of the vaccine against the Omicron strain. This study uses the facts that the Omicron strain has a higher transmissibility than the previous circulating SARS-CoV-2 strain but is less deadly. Preliminary studies have found that Omicron has a lower case fatality rate compared to previous circulating SARS-CoV-2 strains. The simulation results show that even if the Omicron strain is less deadly it might cause more deaths, hospitalizations and infections. We provide a variety of scenarios that help to obtain insight about the Omicron wave and its consequences. The proposed mathematical model, in conjunction with the simulations, provides an explanation for a large Omicron wave under various conditions related to vaccines and transmissibility. These results provide an awareness that new SARS-CoV-2 variants can cause more deaths even if their fatality rate is lower.

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.

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.

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

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.

A New Homotopy Transformation Method for Solving the Fuzzy Fractional Black–Scholes European Option Pricing Equations under the Concept of Granular Differentiability

The Black–Scholes option pricing model is one of the most significant achievements in modern investment science. However, many factors are constantly fluctuating in the actual financial market option pricing, such as risk-free interest rate, stock price, option underlying price, and security price volatility may be inaccurate in the real world. Therefore, it is of great practical significance to study the fractional fuzzy option pricing model. In this paper, we proposed a reliable approximation method, the Elzaki transform homotopy perturbation method (ETHPM) based on granular differentiability, to solve the fuzzy time-fractional Black–Scholes European option pricing equations. Firstly, the fuzzy function is converted to a real number function based on the horizontal membership function (HMF). Secondly, the specific steps of the ETHPM are given to solve the fuzzy time-fractional Black–Scholes European option pricing equations. Finally, some examples demonstrate that the new approach is simple, efficient, and accurate. In addition, the fuzzy approximation solutions have been visualized at the end of this paper.

A mathematical model for the dynamics of SARS-CoV-2 virus using the Caputo-Fabrizio operator

The pandemic of SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics which spread worldwide through human interactions. The current study is focusing on the investigation and analysis of a fractional-order epidemic model that discusses the temporal dynamics of the SARS-CoV-2 virus in a community. It is well known that symptomatic and asymptomatic individuals have a major effect on the dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups of the population. Further, we assume that the vaccine confers permanent immunity because multiple vaccinations have commenced across the globe. The new fractional-order model for the transmission dynamics of SARS-CoV-2 virus is formulated via the Caputo-Fabrizio fractional-order approach with the maintenance of dimension during the process of fractionalization. The theory of fixed point will be used to show that the proposed model possesses a unique solution whereas the well-posedness (bounded-ness and positivity) of the fractional-order model solutions are discussed. The steady states of the model are analyzed and the sensitivity analysis of the basic reproductive number is explored. Moreover to parameterize the model a real data of SARS-CoV-2 virus reported in the Sultanate of Oman from January 1st, 2021 to May 23rd, 2021 are used. We then perform the large scale numerical findings to show the validity of the analytical work.

A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model

This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Our results show similar behavior as the classical order ones. This characteristic shows the applicability and usefulness of the derivative and our numerical scheme.