Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario.

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model.

In this paper, we develop a new mathematical model for an in-depth understanding of COVID-19 (Omicron variant). The mathematical study of an omicron variant of the corona virus is discussed. In this new Omicron model, we used idea of dividing infected compartment further into more classes i.e asymptomatic, symptomatic and Omicron infected compartment. Model is asymptotically locally stable whenever R0<1 and when R0≤1 at disease free equilibrium the system is globally asymptotically stable. Local stability is investigated with Jacobian matrix and with Lyapunov function global stability is analyzed. Moreover basic reduction number is calculated through next generation matrix and numerical analysis will be used to verify the model with real data. We consider also the this model under fractional order derivative. We use Grunwald-Letnikov concept to establish a numerical scheme. We use nonstandard finite difference (NSFD) scheme to simulate the results. Graphical presentations are given corresponding to classical and fractional order derivative. According to our graphical results for the model with numerical parameters, the population's risk of infection can be reduced by adhering to the WHO's suggestions, which include keeping social distances, wearing facemasks, washing one's hands, avoiding crowds, etc.

Total Value Adjustment of Multi-Asset Derivatives under Multivariate CGMY Processes

Counterparty credit risk (CCR) is a significant risk factor that financial institutions have to consider in today's context, and the COVID-19 pandemic and military conflicts worldwide have heightened concerns about potential default risk. In this work, we investigate the changes in the value of financial derivatives due to counterparty default risk, i.e., total value adjustment (XVA). We perform the XVA for multi-asset option based on the multivariate Carr–Geman–Madan–Yor (CGMY) processes, which can be applied to a wider range of financial derivatives, such as basket options, rainbow options, and index options. For the numerical methods, we use the Monte Carlo method in combination with the alternating direction implicit method (MC-ADI) and the two-dimensional Fourier cosine expansion method (MC-CC) to find the risk exposure and make value adjustments for multi-asset derivatives.

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.

Fractional Optimal Control Model of SARS-CoV-2 (COVID-19) Disease in Ghana

Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana–Baleanu–Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v≥0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.

Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach's accuracy and utility, and it is presented in symmetric forms.

Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach

We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. The objective of this research was to halt the global spread of a disease. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.

A Chaotic-Based Interactive Autodidactic School Algorithm for Data Clustering Problems and Its Application on COVID-19 Disease Detection

In many disciplines, including pattern recognition, data mining, machine learning, image analysis, and bioinformatics, data clustering is a common analytical tool for data statistics. The majority of conventional clustering techniques are slow to converge and frequently get stuck in local optima. In this regard, population-based meta-heuristic algorithms are used to overcome the problem of getting trapped in local optima and increase the convergence speed. An asymmetric approach to clustering the asymmetric self-organizing map is proposed in this paper. The Interactive Autodidactic School (IAS) is one of these population-based metaheuristic and asymmetry algorithms used to solve the clustering problem. The chaotic IAS algorithm also increases exploitation and generates a better population. In the proposed model, ten different chaotic maps and the intra-cluster summation fitness function have been used to improve the results of the IAS. According to the simulation findings, the IAS based on the Chebyshev chaotic function outperformed other chaotic IAS iterations and other metaheuristic algorithms. The efficacy of the proposed model is finally highlighted by comparing its performance with optimization algorithms in terms of fitness function and convergence rate. This algorithm can be used in different engineering problems as well. Moreover, the Binary IAS (BIAS) detects coronavirus disease 2019 (COVID-19). The results demonstrate that the accuracy of BIAS for the COVID-19 dataset is 96.25%.

Modeling of Computer Virus Propagation with Fuzzy Parameters

Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus. Considering this, the parameters beta and gamma being functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses. Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.

Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

In this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.

DESIGN AND NUMERICAL ANALYSIS OF FACE MASK POLYMER SHIELD AGAINST INFECTIOUS DISEASES

Viruses that cause infections spread very quickly and has a fatal risk to people with chronic diseases. Since the virus vaccine and the drugs to be used in treatment are not fully developed, alternative ways to protect from the virus are being investigated. The Covid-19 virus has been recognized by the World Health Organization (WHO) as a pandemic. In this study, the effect of face mask shield against Covid-19 and other infections were investigated using finite element analysis (FEA). Three-dimensional model of the conventional face mask, equipment and shield was performed with the SolidWorks software. Computer-aided simulations were performed using AnsysWorkbench explicit dynamics module. The loading, boundary conditions and material properties were defined in the AnsysWorkbench. The effects of droplets formed because of cough or sneezing on the human model with mask and shield were analyzed. It has been confirmed from the analyzes that both the mask and the shield are effective against the virus.

Numerical Analysis and Scientific Calculation Considering the Management Mechanism of College Students’ Innovation and Entrepreneurship Education

Purpose. This article aims to study how to analyze and study the numerical value of education management mechanisms based on cloud computing and describe the innovation and entrepreneurship of college students. Methodology. This article addresses the problems of numerical analysis and scientific computing. This problem is based on cloud computing, so it elaborates on the concepts and related algorithms of cloud computing and big data and designs and analyzes cases of numerical analysis and scientific computing of educational management mechanisms. Research Findings. Through the research of different kernel functions, the IG_CDmRMR algorithm can obtain relatively high accuracy results for numerical analysis and scientific computing. The IG_CDmRMR algorithm is the closest to expert evaluation. The maximum difference is 0.002, which is consistent in sample three. The maximum difference of the IG algorithm is 0.005, and the minimum difference is 0.002. The evaluation effect of the IG_CDmRMR algorithm is closer to the evaluation effect of experts. Practical Implications. It analyzes the numerical value of the education management mechanism and finds that the accuracy has a certain height. This has certain evaluation significance for the management mechanism of college students’ innovation and entrepreneurship education.

Improvement of Split-Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics

In the present investigation, new explicit approaches by the Milstein method and increment function of the Jacobian derivative of the drift coefficient are designed. Several numerical tests such as Cox–Ingersoll–Ross process, stochastic Brusselator, and Davis-Skodje system are presented to illustrate the accuracy and the efficiency of our schemes. Furthermore, we show that the strong convergence rate of our procedures is approximately one.

The Mathematical Analysis of the New Fractional Order Ebola Model

This research study focuses on the analytical behavior and numerical computation of the fractional order Ebola model. In this study we have calculated the conditions for the existence, uniqueness, and stability of the solution with the help of the fixed point results. In addition to this, we calculated the numerical solution of the fractional order smoke model with the help two-step fractional Adam’s Bashforth method using the Caputo’s fractional derivative of order μ. Furthermore, the results obtained for different orders of the fractional derivative μ have been shown graphically with the help of Matlab.

A Hybrid Interpolation Method for Fractional PDEs and Its Applications to Fractional Diffusion and Buckmaster Equations

This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. In this method, we apply the Newton interpolation numerical scheme in Laplace space, and then, the solution is returned to real space through the inverse Laplace transform. The Newton polynomial provides good results as compared to the Lagrangian polynomial, which is used to construct the Adams–Bashforth method. This procedure is used to solve fractional Buckmaster and diffusion equations. Finally, a few numerical simulations are presented, ensuring that this strategy is highly stable and quickly converges to an exact solution.

Progress and Challenges in Modeling Dynamics–Microphysics Interactions: From the Pi Chamber to Monsoon Convection

The CAIPEEX (Cloud Aerosol Interaction and Precipitation Enhancement Experiment) monsoon convective clouds case was designed to explore the impacts of environmental and cloud condensation nuclei (CCN) conditions on monsoon convection. Pi chamber warm cloud case The scientific objectives are 1) to demonstrate the model capability of representing the detailed microphysical processes happening in the cloud chamber and how different models behave in different aerosol injection rates, 2) to reveal the model uncertainties and limitations in the existing modeling tools, and 3) to provide guidance and recommendations for future work to improve cloud chamber simulations and model–laboratory comparisons. The comparison was performed among a diverse set of model categories, including four types of LES models (Dziekan et al. 2019;Shima et al. 2009, 2020;Niedermeier et al. 2020;Khairoutdinov and Randall 2003) performed by the University of Warsaw, University of Hyogo, Leibniz Institute for Tropospheric Research, and Brookhaven National Laboratory;two types of direct numerical simulation (DNS) models (Chen et al. 2021;Richter et al. 2021) by the National Center for Atmospheric Research (NCAR) and the University of Notre Dame;and the Linear Eddy Model (LEM;Su et al. 1998) by the University of Utah. Interestingly, however, the amount of updraft tilting was sensitive not only to the vertical wind shear used in the model, but also to the method of cloud initiation, i.e., forcing using warm bubbles or surface heat fluxes.

Prediction of Epidemic Transmission Path and Risk Management Method in Urban Subway

With the development of COVID-19, the epidemic prevention requirements of city subway system have become stricter. This study studies the transmission path of epidemic disease in city subway system. Using FLUENT software and AnyLogic software, the simulation models of subway platform ventilation structure and crowd behavior mode in subway system are constructed, respectively, and SEIR (vulnerable exposed affected recovered) is used as the general infection model of epidemic disease. According to the actual situation, the parameters such as shoulder width, flow, and moving speed of crowd are determined, and the simulation analysis of epidemic disease transmission in subway system is carried out. The analysis results show that the transmission speed of the disease in the subway will increase with the enhancement of the transmission capacity of the disease and the increase of the contact rate. When the disease transmission capacity is 0.14, the number of latent persons reaches the peak at 14.115 time units, which is 1374, and the number of patients reaches the peak at 28.541 time units, which is 1925. According to the simulation results, the simulation analysis results show that with the enhancement of disease transmission ability and the increase of exposure rate, the maximum number of latent and sick people in the subway environment will increase. The corresponding suggestions on risk management and control of infectious disease transmission in subway are put forward. The research results can provide a useful reference for the epidemic prevention management of urban subway transportation system in China.

The susceptible-infected-recovered-dead model for long-term identification of key epidemiological parameters of COVID-19 in Indonesia

The COVID-19 epidemic has spread massively to almost all countries including Indonesia, in just a few months. An important step to overcoming the spread of the COVID-19 is understanding its epidemiology through mathematical modeling intervention. Knowledge of epidemic dynamics patterns is an important part of making timely decisions and preparing hospitals for the outbreak peak. In this study, we developed the susceptible-infected-recovered-dead (SIRD) model, which incorporates the key epidemiological parameters to model and estimate the long-term spread of the COVID-19. The proposed model formulation is data-based analysis using public COVID-19 data from March 2, 2020 to May 15, 2021. Based on numerical analysis, the spread of the pandemic will begin to fade out after November 5, 2021. As a consequence of this virus attack, the cumulative number of infected, recovered, and dead people were estimated at ≈ 3,200,000, ≈ 3,437,000 and ≈ 63,000 people, respectively. Besides, the key epidemiological parameter indicates that the average reproduction number value of COVID-19 in Indonesia is 7.32. The long-term prediction of COVID-19 in Indonesia and its epidemiology can be well described using the SIRD model. The model can be applied in specific regions or cities in understanding the epidemic pattern of COVID-19.

Bio-Inspired Numerical Analysis of COVID-19 with Fuzzy Parameters

Fuzziness or uncertainties arise due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of susceptible, infectious and recovered are uncertain due to the different degrees in susceptibility, infectivity and recovery among the individuals of the population. The differences can arise, when the population groups under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. More realistic models are needed which consider these different degrees of susceptibility infectivity and recovery of the individuals. In this paper, a Susceptible, Infected and Recovered (SIR) epidemic model with fuzzy parameters is discussed. The infection, recovery and death rates due to the disease are considered as fuzzy numbers. Fuzzy basic reproduction number and fuzzy equilibrium points have been derived for the studied model. The model is then solved numerically with three different techniques, forward Euler, Runge-Kutta fourth order method RK-4) and the nonstandard finite difference (NSFD) methods respectively. The NSFD technique becomes more efficient and reliable among the others and preserves all the essential features of a continuous dynamical system.