Post-Pandemic Sector-Based Investment Model Using Generalized Liouville–Caputo Type

In this article, Euler's technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter (ρ) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator's suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances.

Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation

This study presents a novel approach for simulating the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and the Haar wavelet collocation method. The proposed model considers various factors that affect virus transmission, while the Haar wavelet collocation method provides an efficient and accurate solution for the fractional derivatives used in the model. This study analyzes the impact of the Omicron variant and provides valuable insights into its transmission dynamics, which can inform public health policies and strategies that are aimed at controlling its spread. Additionally, this study's findings represent a significant step forward in understanding the COVID-19 pandemic and its evolving variants. The results of the simulation showcase the effectiveness of the proposed method and demonstrate its potential to advance the field of COVID-19 research. The COVID epidemic model is reformulated by using fractional derivatives in the Caputo sense. The existence and uniqueness of the proposed model are illustrated in the model, taking into account some results of fixed point theory. The stability analysis for the system is established by incorporating the Hyers–Ulam method. For numerical treatment and simulations, we apply the Haar wavelet collocation method. The parameter estimation for the recorded COVID-19 cases in Pakistan from 23 June 2022 to 23 August 2022 is presented.

Probability fixed points, (in)adequate concept possession and covid-19 irrationalities

We argue that probability mistakes indicate that at least some of us often do not adequately possess the concept of probability (and its cognates) and that the digital dissemination of such misinformation helps foster collective irrationalities (e.g., COVID-19 underestimation and vaccination hesitancy), with detrimental effect for society. Such probability mistakes betray that at least some of us often do not grasp necessary conditions on the concept of probability, what we call probability fixed points. Our case study that illustrates this phenomenon in action is the recent COVID-19 pandemic. We present paradigmatic examples of probability mistakes during the COVID-19 pandemic and explain how such mistakes are especially prone to help create digital epistemic bubbles and echo chambers (cf. Nguyen (2020)) that foster collective irrationalities, such as COVID-19 underestimation and skepticism and vaccination hesitancy. (PsycInfo Database Record (c) 2023 APA, all rights reserved)

EXISTENCE RESULTS AND NUMERICAL STUDY ON NOVEL CORONAVIRUS 2019-NCOV/SARS-COV-2 MODEL USING DIFFERENTIAL OPERATORS BASED ON THE GENERALIZED MITTAG-LEFFLER KERNEL AND FIXED POINTS

The use of mathematical modeling in the exploration of epidemiological disorders has increased dramatically. Mathematical models can be used to forecast how viral infections spread, as well as to depict the likely outcome of an outbreak and to support public health measures. In this paper, we present useful ideas for finding existence of solutions of the novel coronavirus 2019-nCoV/SARS-CoV-2 model via fractional derivatives by using fuzzy mappings. Three classes of fractional operators were considered including Atangana-Baleanu, Caputo-Fabrizio and Caputo. For each case, we introduce the fuzzination in the study of the existence of a system of solutions. A fresh numerical scheme was proposed for each scenario, and then numerical simulations involving various parameters of Atangana-Baleanu fractional-order were shown utilizing numerical solutions. © 2022

Discrete models for analyzing the behavior of COVID-19 pandemic in the State of Mexico, Mexico.

In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.

Existence Results for Impulsive Fractional Integrodifferential Equations Involving Integral Boundary Conditions

This research paper is devoted to investigating the existence results for impulsive fractional integrodifferential equations in the form of Atangana - Baleanu - Caputo (ABC) fractional derivative, by using Gronwall–Bellman inequality and Krasnoselskii’s fixed point theorem to study the existence and uniqueness of the problem with integral boundary conditions. At the end, the examples are illustrated to verify results.

(k,ψ)-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions

In this paper, we establish existence and uniqueness results for single-valued as well as multi-valued (k,ψ)-Hilfer boundary value problems of order in (1,2], subject to nonlocal integro-multi-point boundary conditions. In the single-valued case, we use Banach and Krasnosel’skiĭ fixed point theorems as well as a Leray–Schauder nonlinear alternative to derive the existence and uniqueness results. For the multi-valued problem, we prove two existence results for the convex and non-convex nature of the multi-valued map involved in a problem by applying a Leray–Schauder nonlinear alternative for multi-valued maps, and a Covitz–Nadler fixed point theorem for multi-valued contractions, respectively. Numerical examples are presented for illustration of all the obtained results.

Study of COVID-19 epidemiological evolution in India with a multi-wave SIR model.

The global pandemic due to the outbreak of COVID-19 ravages the whole world for more than two years in which all the countries are suffering a lot since December 2019. In this article characteristics of a multi-wave SIR model have been studied which successfully explains the features of this pandemic waves in India. Origin of the multi-wave pattern in the solution of this model is explained. Stability of this model has been studied by identifying the equilibrium points as well as by finding the eigenvalues of the corresponding Jacobian matrices. In this model, a finite probability of the recovered people for becoming susceptible again is introduced which is found crucial for obtaining the oscillatory solution in other words. Which on the other hand incorporates the effect of new variants, like delta, omicron, etc in addition to the SARS-CoV-2 virus. The set of differential equations has been solved numerically in order to obtain the variation of susceptible, infected and removed populations with time. In this phenomenological study, some specific sets of parameters are chosen in order to explain the nonperiodic variation of infected population which is found necessary to capture the feature of epidemiological wave prevailing in India. The numerical estimations are compared with the actual cases along with the analytic results.

Development of a Human Flow Visualization System Using Video Streams from Fixed Point Cameras

Currently, due to the changes in social conditions caused by the spread of Covid19 infection, the increase and decrease in the stream of people in major downtown areas and tourist spots such as holiday resorts are attracting attention. These data have been analyzed from the accumulation of smartphone location data and sensor information, but their availability is limited. To solve this problem, we use the images from fixed-point cameras installed in each city, which are available on YouTube as open data, and analyze the flow of people using OpenCV to reflect and visualize the real-time congestion status in a 3D city model. © 2022 IEEE.

Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative

A mathematical model of the nutrient-phytoplankton-zooplankton associated with viral infection in phytoplankton under the Atangana-Baleanu derivative in Caputo sense is investigated in this study. We prove the theoretical results for the existence and uniqueness of the solutions by using Banach’s and Sadovskii’s fixed point theorems. The notion of various Ulam’s stability is used to guarantee the context of the stability analysis. Furthermore, the equilibrium points and the basic reproduction numbers for the proposed model are provided. The Adams type predictor-corrector algorithm has been applied for the theoretical confirmation to establish the approximate solutions. A variety of numerical plots corresponding to various fractional orders between zero and one are presented to describe the dynamical behavior of the fractional model under consideration.

Darbo Fixed Point Criterion on Solutions of a Hadamard Nonlinear Variable Order Problem and Ulam-Hyers-Rassias Stability

The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundary value problem to an equivalent standard Hadamard fractional boundary problem of the fractional constant order. Further, Darbo’s fixed point criterion along with Kuratowski’s measure of noncompactness is used in this direction. As well as, the Ulam-Hyers-Rassias stability of the proposed Hadamard variable order fractional boundary value problem is established. A numerical example is presented to express our results’ validity.

Trial of Building a Resilient Face-To-Face Classroom Based on CO2-Based Risk Awareness

The COVID-19 pandemic forced many schools to switch to online classes. Although there has been a movement to return to face-to-face classes since then, many schools are still struggling to ensure safety during classes and subsequent examinations in a face-to-face environment. In this study, we attempted to visualize the relationship between class usage and building air conditioning management by installing CO2 sensors at fixed points in classrooms and also applied them to environmental monitoring during examinations to grasp the risks in real time and provide a response. © 2022, IFIP International Federation for Information Processing.

Stability Results of Some Fractional Neutral Integrodifferential Equations with Delay

Differential equations with fractional derivative are being extensively used in the modelling of the transmission of many infective diseases like HIV, Ebola, and COVID-19. Analytical solutions are unreachable for a wide range of such kind of equations. Stability theory in the sense of Ulam is essential as it provides approximate analytical solutions. In this article, we utilize some fixed point theorem (FPT) to investigate the stability of fractional neutral integrodifferential equations with delay in the sense of Ulam-Hyers-Rassias (UHR). This work is a generalized version of recent interesting works. Finally, two examples are given to prove the applicability of our results.

Epidemiological theory of virus variants.

We propose a physics-inspired mathematical model underlying the temporal evolution of competing virus variants that relies on the existence of (quasi) fixed points capturing the large time scale invariance of the dynamics. To motivate our result we first modify the time-honoured compartmental models of the SIR type to account for the existence of competing variants and then show how their evolution can be naturally re-phrased in terms of flow equations ending at quasi fixed points. As the natural next step we employ (near) scale invariance to organise the time evolution of the competing variants within the effective description of the epidemic Renormalisation Group framework. We test the resulting theory against the time evolution of COVID-19 virus variants that validate the theory empirically.

Ulam-Hyers-Rassias Stability of Nonlinear Differential Equations with Riemann-Liouville Fractional Derivative

Fractional derivatives are used to model the transmission of many real world problems like COVID-19. It is always hard to find analytical solutions for such models. Thus, approximate solutions are of interest in many interesting applications. Stability theory introduces such approximate solutions using some conditions. This article is devoted to the investigation of the stability of nonlinear differential equations with Riemann-Liouville fractional derivative. We employed a version of Banach fixed point theory to study the stability in the sense of Ulam-Hyers-Rassias (UHR). In the end, we provide a couple of examples to illustrate our results. In this way, we extend several earlier outcomes.

Optimization of Object Detection CNN with Weight Quantization and Scale Factor Consolidation

Due to the current Covid-19 pandemic, Convolutional Neural Networks (CNN) models attract attention in the applications to identify people with no masks. Developing an optimal CNN model is a challenging task especially for embedded deceives with limited hardware resources. To overcome the above challenge, we present a weight quantization technique aimed to produce compact CNN model for detection of people with mask or no mask. Its weights and feature maps are optimized using minimal fixed-point quantization at little or no sacrifice of its detection accuracy. The proposed weight quantization has been evaluated using a modified tiny-YOLOv2 model with the Mask and no-mask. Furthermore, we modified the internal model architecture to further reduce the model size and inference calculation by optimizing the order of max-pooling layers, consolidating the scale factors of batch normalization into only two pre-calculated parameters, and modifying the leaky ReLU activation function. The evaluation demonstrated that it saves more than 50 % of parameter memory and 56.21 % of inference computation. © 2021 IEEE.

Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”

The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications due to their properties of interpolation between operators of integer order. In [2], Salem and Alghamdi considered a nonlinear sequential-type Caputo fractional ordinary differential equation on a finite interval, with nonlocal multi-point boundary conditions and an overall fractional order between 1 and 3. A comparative analysis was performed to compare the results achieved by using the M-derivative and by using the usual Caputo derivative with respect to t. In [7], Uçar et al. considered a system of first-order ordinary differential equations, which is used to model the effect of computer worms, and replaced the first-order derivatives with fractional derivatives of Atangana–Baleanu type to obtain a different system, which they studied using fixed-point and Laplace transform techniques to prove existence, uniqueness, and stability properties.

Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations

We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn)+az+c, where a,c∈C, n≥2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants.

Mathematical modelling of the epidemiology of COVID-19 infection in Ghana.

In this paper, Covid-19 patients with self-immunity is incorporated in the Susceptible-Exposed-Infected-Quarantined-Recovered ( S E I Q R ) model is applied to describe the epidemiology of Covid-19 infection in Ghana. Based on data on the epidemiology of the Covid-19 infection in Ghana, we observed that, on an average, three persons contract the Covid-19 infection from an infected person daily based using the basic reproductive number ( R o ) derived from the SEIQR model. In addition, the threshold condition for the long term stability of the Covid-19 infection in Ghana is derived from this model. Based on the Dulac criterion, it was observed that for a long period of time the epidemiology of Covid-19 in Ghana will be under control. Again, we observed that both the transmission rate natural death rate of a person in the various classes mostly influence the spread of Covid-19 infection followed by the exposed rate from exposure class to the infected class, then the rate at which an infected person is quarantined and finally, the rate at an exposed person is quarantined. On the other hand, the rate at which an exposed person recovers from his/her have least influence on the spread of Covid-19 infection in the country. Nevertheless, the rates of birth, transmission of Covid-19 infection to a susceptible person, exposure to Covid-19 infection and Covid-19 patient who is quarantined by the facilities provided by the Ghana Health Service ( G H S ) are in direct relationship with R o . However, the rates at which a quarantiner dies from a Covid-19 infection, an infected person dies from a Covid-19 infection, natural death from each class and the recoveries from an infected class, exposed class and quarantined class are in relationship with R o .