Fractional-type integral operators and their applications to trend estimation of COVID-19

In this paper, we construct a novel family of fractional-type integral operators of a function (Formula presented.) by replacing sample values (Formula presented.) with the fractional mean values of that function. We give some explicit formulas for higher order moments of the proposed operators and investigate some approximation properties. We also define the fractional variants of Mirakyan–Favard–Szász and Baskakov-type operators and calculate the higher order moments of these operators. We give an explicit formula for fractional derivatives of proposed operators with the help of the Caputo-type fractional derivative Furthermore, several graphical and numerical results are presented in detail to demonstrate the accuracy, applicability, and validity of the proposed operators. Finally, an illustrative real-world example associated with the recent trend of Covid-19 has been investigated to demonstrate the modeling capabilities of fractional-type integral operators. © 2023 John Wiley & Sons, Ltd.

Model selection with decision support model for US natural gas consumption forecasting

Reliable prediction of natural gas consumption helps make the right decisions ensuring sustainable economic growth. This problem is addressed here by introducing a hybrid mathematical model defined as the Choquet integral-based model. Model selection is based on decision support model to consider the model performance more comprehensively. Different from the previous literature, we focus on the interaction between models when combine models. This paper adds grey accumulation generating operator to Holt-Winters model to capture more information in time series, and the grey wolf optimizer obtains the associated parameters. The proposed model can deal with seasonal (short-term) variability using season auto-regression moving average computation. Besides, it uses the long short term memory neural network to deal with long-term variability. The effectiveness of the developed model is validated on natural gas consumption due to the COVID-19 pandemic in the USA. For this, the model is customized using the publicly available datasets relevant to the USA energy sector. The model shows better robustness and outperforms other similar models since it consider the interaction between models. This means that it ensures reliable perdition, taking the highly uncertain factor (e.g., the COVID-19) into account. © 2023 Elsevier Ltd

Integral Model of COVID-19 Spread and Mitigation in UK: Identification of Transmission Rate

The integral model with finite memory is employed to analyze the time-line of COVID-19 epidemic in the United Kingdom and government actions to miti-gate it. The model uses a realistic infection distribution. The time-varying transmission rate is determined from Volterra integral equation of the first kind. The authors construct and justify an efficient regularization algorithm for finding the transmission rate. The model and algorithm are approbated on the UK data with several waves of COVID-19 and demonstrate a remarkable resemblance between real and simulated dynamics. The timing of government preventive measures and their impact on the epidemic dynamics are discussed. © The Author(s).

Analysis of optimal lockdown in integral economic-epidemic model.

We analyze the optimal lockdown in an economic-epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

Population growth equation by fuzzy common integral transforms

In this work, three famous different fuzzy integral transforms have been attempted to evaluate the exact solution of fuzzy equation based on fuzzy convolution Volterra integral equation of the second kind due to the fact that such transforms reduce the integral problem to algebraic problem. Moreover, this article examines three aspects, a brief conversation about the classification of integral equations, some important instruments as well as a real-world problem related with population growth is considered. Population growth increases due to the increase in the number of humans. For better understanding of the growth meaning, we can relate it with renewal and industrialization, more precisely, when food, water, energy and medical care become more available. As an expectation for the growth in population, however, due to the Covid-19 pandemic, millions of people worldwide have died since 2020. It has increased to 8.5 billion by 2030 and the global population will reach 9.7 billion in 2050, whereas 10.9 billion in 2100 [11]. In order to address population growth equation, three common fuzzy transforms are used for estimating its exact solution. [ FROM AUTHOR] Copyright of Journal of Interdisciplinary Mathematics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Simulation of Evaporative Flow and Coupled Transport Behaviors of Aerosol Particles

Intense scientific interest in the mechanisms of aerosol transport has been aroused due to the global COVID-19 pandemic. In this study, a new droplet evaporation model considering solid components such as salt, has proposed to simulate the diffusion and evaporative flow behaviors of saliva-forming aerosols droplets, caused by human breathing, coughing and sneezing. The model considers the evaporation process on the surface of aerosols and couples the droplet kinetic equations, including the incorporation of influencing factors such as flow resistance, gravity, droplet-like size and initial velocity. Different ambient temperatures, relative humidity and wind speed have been simulated and the mechanisms of aerosols migration behaviors have been analyzed. For individual droplet, the results not only show that the larger the droplet size, the longer it remains suspended in airborne, but also the lower the humidity and the higher the temperature, the faster the evaporation rate. © 2022, Science Press. All right reserved.

Scaffolding Spatial Abilities in Integral Calculus Eric Davishahl (Professor and Program Coordinator)

This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with hands-on models and manipulatives. We are exploring how best to design these activities to support learners' development of conceptual understanding and representational competence in integral calculus and engineering statics, two foundational courses for most engineering majors. A second goal is to leverage the model-based activities to scaffold spatial skills development in the context of traditional course content. As widely reported in the literature, well-developed spatial abilities correlate with student success and persistence in many STEM majors. We provided calculus students in selected intervention sections taught by four instructors at three different community colleges with take-home model kits that they could reference for a series of asynchronous learning activities. Students in these sections completed the Purdue Spatial Visualization Test: Rotations (PSVT:R) in the first and last weeks of their course. We also administered the assessment in multiple control sections (no manipulatives) taught by the same faculty. This paper analyzes results from fall 2020 through fall 2021 to see if there is any difference between control and intervention sections for the courses as a whole and for demographic subgroups including female-identifying students and historically-underserved students of color. All courses were asynchronous online modality in the context of the COVID-19 pandemic. We find that students in intervention sections of calculus made slightly larger gains on the PSVT:R, but this result is not statistically significant as a whole or for any of the demographic subgroups considered. We also analyzed final course grades for differences between control and intervention sections and found no differences. We found no significant effect of the presence of the model-based activities leading to increased PSVT:R gains or improved course grades. We would not extend this conclusion to face-to-face implementation, however, due primarily to the compromises made to adapt the curriculum from in-person group learning to asynchronous individual work and inconsistent engagement of the online students with the modeling activities. © American Society for Engineering Education, 2022.

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.

Efficient Function Integration and a Case Study with Gompertz Functions for Covid-19 Waves

Numerical algorithms are widely used in different applications, therefore, the execution time of the functions involved in numerical algorithms is important, and, in some cases, decisive, for example, in machine learning algorithms. Given a finite set of independent functions A(x), B(x), …, Z(x) with domains defined by disjoint, consecutive, and not necessarily adjacent intervals, the main goal is to integrate into a single function F(x) = k1×A(x) + k2×B(x) + … + kn×Z(x), where each activation coefficient k, is one if x is in the interval of the respective domain and zero otherwise. The novelty of this work is the presentation and formal demonstration of two general forms of integration of functions in a single function: The first is the mathematical version and the second is the computational version (with the AND function at the bit level), which is characterized by its efficiency. The result is applied in a case study (Peru), where two regression functions were obtained that integrate all the waves of Covid-19, that is, the epidemic curve of the variable global number of deaths/infected per day, the adjustment provided a highly statistically significant measure of correlation, a Pearson's product-moment correlation of 0.96 and 0.98 respectively. Finally, the size of the epidemic was projected for the next 30 days © 2022, International Journal of Advanced Computer Science and Applications.All Rights Reserved.

Sugeno Integral Based Pandemic Risk Assessment

Complex situations such as pandemics generally lead to consider different sources of information in the analysis. We propose a general framework for coronavirus risk assessment based on multi-criteria decision aiding (MCDA) where input variables are indicators expressed on the basis of qualitative-ordinal scales. The proposed approach, based on Sugeno Utility Functionals, makes the problem setting easy to interpret and allows us to reflect the policy-makers’ opinions on the importance of each indicator or subset of indicators. Interestingly, our approach is related to if-then rule-based systems adopted by some Governments for pandemic risk assessment and restriction policy planning. © 2022, Springer Nature Switzerland AG.

A DISTRIBUTED OPTIMAL CONTROL MODEL APPLIED to COVID-19 PANDEMIC

In this paper, a distributed optimal control epidemiological model is presented. The model describes the dynamics of an epidemic with social distancing as a control policy. The model belongs to the class of continuous-time models, usually involving ordinary/partial differential equations, but has a novel feature. The core model-a single integral equation-does not explicitly use transition rates between compartments. Instead, it is based on statistical information on the disease status of infected individuals, depending on the time since infection. The approach is especially relevant for the coronavirus disease 2019 (COVID-19) in which infected individuals are infectious before onset of symptoms during a relatively long incubation period. Based on the analysis of the proposed optimal control problem, including necessary optimality conditions, this paper outlines some efficient numerical approaches. Numerical solutions show some interesting features of the optimal policy for social distancing, depending on the weights attributed to the number of isolated individuals with symptoms and to economic losses due to the enforcement of the control policy. The general nature of the model allows for inclusion of additional epidemic features with minor adaptations in the basic equations. Therefore, the modeling approach may contribute to the analysis of combined intervention strategies and to the guidance of public health decisions. © 2022 Society for Industrial and Applied Mathematics

Model Checking Functional Integration of Human Cognition and Machine Reasoning

Functional integration of human cognition and machine reasoning is an industry-wide problem where failure risks health or safety. Differences in human versus machine functioning obscure conventional integration. We introduce cognitive work problems (CWP) for rigorous, verifiable functional integration. CWP specify the cognitive problem that integrated designs must solve. They are technology-neutral, work objects, allowing people and computing to share and transform them in coordination. The end-to-end method is illustrated on a system that employs AI for remote patient monitoring (RPM) during COVID-19 home care. The CWP specified actionable risk awareness as the medical problem RPM must solve. Graphical modeling standards enabled user participation: CWP as finite state machines and system behavior in BPMN. For model checking, the CWPs logical content was translated to linear temporal logic (LTL) and the BPMN into Promela as inputs to the SPIN model checker. SPIN verified the Promela implements the LTL correctly. We conclude this CWP-derived RPM design solves the medical problem and enhances patient safety. The method appears general to many critical systems. © 2022 IEEE.

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.

Dynamic Modeling of COVID-19 Disease with Impact of Lockdown in Pakistan & Malaysia

Being researchers, it is an utmost responsibility to provide insight on social issues thus, this work addresses the dynamic modeling of first and most contagious disease named as COVID-19 caused by coronavirus. The first case of COVID-19 appeared in Pakistan was on 26th February 2020 and in Malaysia on 27th February 2020;both patients had foreign travel history. In the paper, the number of total affected cases and total deaths in both countries, are quite the same up till 12th April 2020 but the frequency of new cases per day and recovery rate are different from one another. The movement control approach had also been imposed on 18th March 2020 by both countries. Keeping these facts and figures, the paper proposes a mathematical model based on Lotka-Volterra equations and provides numerical solution of differential equations using the suspectable, exposed, infected, and recovered people data to estimate future consequences and address the difference in the growth rate of COVID-19 patients before and after locked down to reduce the spread further by taking pro-active approaches i.e., social distancing and being quarantined for the essential time frame. © 2021 IEEE

COVID-19 Pandemic Analysis by the Volterra Integral Equation Models: A Preliminary Study of Brazil, Italy, and South Africa

The COVID-19 pandemic has affected many people throughout the world. The objective of this research project was to find numerical solutions through the Gaussian Quadrature Method for the Volterra Integral Equation Model. The non-homogenous Volterra Integral Equation of the second kind is used to capture a broader range of disease distributions. Volterra Integral equation models are used in the context of applied mathematics, public health, and evolutionary biology. The mathematical models of this integral equation gave valid convergence results for the COVID-19 data for 3 countries Italy, South Africa and Brazil. The modeling of these countries was done using the Volterra Integral Equation, using the Gaussian Quadrature nodes. Inspired by the COVID-19 pandemic, the IRCD model included the number of initially infected individuals, the rate of infection, contact rate, death rate, fraction of recovered individuals, and the mean time an individual remains infected. This research investigated the feasibility of obtaining accurate convergence results for two models of the Volterra Integral Equation for the geographic locations of Italy, South Africa and Brazil. The IRCD model accounted for the infected rate, number of recovered, contact rate, and the death rate. The first 365 days of the pandemic were analyzed for the IRCD model. The ISR model accounted for the number of initially infected individuals, susceptible individuals, removed individuals, number of contacts per person, the recovery rate, and the total population. The ISR model specifically looked at COVID-19 in Brazil and South Africa for the first 300 days of the pandemic. Both models are mathematically and epidemiologically well posed. © 2022, IAENG International Journal of Applied Mathematics. All Rights Reserved.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique.

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it Our signal-processing approach to this problem yields both Rt and a restored it corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

COVID-19: data-driven dynamics, statistical and distributed delay models, and observations.

COVID-19 was declared as a pandemic by the World Health Organization on March 11, 2020. Here, the dynamics of this epidemic is studied by using a generalized logistic function model and extended compartmental models with and without delays. For a chosen population, it is shown as to how forecasting may be done on the spreading of the infection by using a generalized logistic function model, which can be interpreted as a basic compartmental model. In an extended compartmental model, which is a modified form of the SEIQR model, the population is divided into susceptible, exposed, infectious, quarantined, and removed (recovered or dead) compartments, and a set of delay integral equations is used to describe the system dynamics. Time-varying infection rates are allowed in the model to capture the responses to control measures taken, and distributed delay distributions are used to capture variability in individual responses to an infection. The constructed extended compartmental model is a nonlinear dynamical system with distributed delays and time-varying parameters. The critical role of data is elucidated, and it is discussed as to how the compartmental model can be used to capture responses to various measures including quarantining. Data for different parts of the world are considered, and comparisons are also made in terms of the reproductive number. The obtained results can be useful for furthering the understanding of disease dynamics as well as for planning purposes.