Multiple models for outbreak decision support in the face of uncertainty.

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.

Sensor Fault Diagnostics Using Physics-Informed Transfer Learning Framework.

The field of smart health monitoring, intelligent fault detection and diagnosis is expanding dramatically in order to maintain successful operation in many engineering applications. Considering possible fault scenarios that can occur in a system, indicating the type of fault in a sensor is one of the most important and challenging problems in the area of intelligent sensor fault diagnostics. Within this frame of reference, we extended the physics-informed transfer learning framework, first presented previously for a fault cause assignment, to the level of sensor fault diagnostics for a range of different fault scenarios. Hence, the framework is utilized to perform intelligent sensor fault diagnostics for the first time. The underlying dynamics of the reference system are extracted using a completely data-driven methodology and dynamic mode decomposition with control (DMDc) in order to generate time-frequency illustrations of each sample with continuous wavelet transform (CWT). Then, sensor fault diagnostics for bias, drift over time, sine disturbance and increased noise sensor fault scenarios are achieved using the idea of transfer learning with a pre-trained image classification algorithm. The classification results yields a good performance on sensor fault diagnostics with 91.5% training and 84.7% test accuracy along with a fair robustness level with a set of reference benchmark system parameters.

Stability analysis of a nonlocal SIHRDP epidemic model with memory effects.

The prediction and control of COVID-19 is critical for ending this pandemic. In this paper, a nonlocal SIHRDP (S-susceptible class, I-infective class (infected but not hospitalized), H-hospitalized class, R-recovered class, D-death class and P-isolated class) epidemic model with long memory is proposed to describe the multi-wave peaks for the spread of COVID-19. Based on the basic reproduction number R 0 , which is completely controlled by fractional order, the stability of the proposed system is studied. Furthermore, the numerical simulation is conducted to gauge the performance of the proposed model. The results on Hunan, China, reveal that R 0 < 1 suggests that the disease-free equilibrium point is globally asymptotically stable. Likewise, the situation of the multi-peak case in China is presented, and it is clear that the nonlocal epidemic system has a superior fitting effect than the classical model. Finally an adaptive impulsive vaccination is introduced based on the proposed system. Then employing the real data of France, India, the USA and Argentina, parameters identification and short-term forecasts are carried out to verify the effectiveness of the proposed model in describing the case of multiple peaks. Moreover, the implementation of vaccine control is expected once the hospitalized population exceeds 20 % of the total population. Numerical results of France, Indian, the USA and Argentina shed light on the varied effect of vaccine control in different countries. According to the vaccine control imposed on France, no obvious effect is observed even consider reducing human contact. As for India, although there will be a temporary increase in hospitalized admissions after execution of vaccination control, COVID-19 will eventually disappear. Results on the USA have seen most significant effect of vaccine control, the number of hospitalized individuals drops off and the disease is eventually eradicated. In contrast to the USA, vaccine control in Argentina has also been very effective, but COVID-19 cannot be completely eradicated.

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis, call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.

Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption.

The purpose of this paper is to explore a novel image encryption algorithm that is developed by combining the fractional-order Chua's system and the 1D time-fractional diffusion system of order α∈(0,1]. To this end, we first discuss basic properties of the fractional-order Chua's system and the 1D time-fractional diffusion system. After these, a new spatiotemporal chaos-based cryptosystem is proposed by designing the chaotic sequence of the fractional-order Chua's system as the initial condition and the boundary conditions of the studied time-fractional diffusion system. It is shown that the proposed image encryption algorithm can gain excellent encryption performance with the properties of larger secret key space, higher sensitivity to initial-boundary conditions, better random-like sequence and faster encryption speed. Efficiency and reliability of the given encryption algorithm are finally illustrated by a computer experiment with detailed security analysis.

RLIM: a recursive and latent infection model for the prediction of US COVID-19 infections and turning points.

Initially found in Hubei, Wuhan, and identified as a novel virus of the coronavirus family by the WHO, COVID-19 has spread worldwide at exponential speed, causing millions of deaths and public fear. Currently, the USA, India, Brazil, and other parts of the world are experiencing a secondary wave of COVID-19. However, the medical, mathematical, and pharmaceutical aspects of its transmission, incubation, and recovery processes are still unclear. The classical susceptible-infected-recovered model has limitations in describing the dynamic behavior of COVID-19. Hence, it is necessary to introduce a recursive, latent model to predict the number of future COVID-19 infection cases in the USA. In this article, a dynamic recursive and latent infection model (RLIM) based on the classical SEIR model is proposed to predict the number of COVID-19 infections. Given COVID-19 infection and recovery data for a certain period, the RLIM is able to fit current values and produce an optimal set of parameters with a minimum error rate according to actual reported numbers. With these optimal parameters assigned, the RLIM model then becomes able to produce predictions of infection numbers within a certain period. To locate the turning point of COVID-19 transmission, an initial value for the secondary infection rate is given to the RLIM algorithm for calculation. RLIM will then calculate the secondary infection rates of a continuous time series with an iterative search strategy to speed up the convergence of the prediction outcomes and minimize the maximum square errors. Compared with other forecast algorithms, RLIM is able to adapt the COVID-19 infection curve faster and more accurately and, more importantly, provides a way to identify the turning point in virus transmission by searching for the equilibrium between recoveries and new infections. Simulations of four US states show that with the secondary infection rate ω initially set to 0.5 within the selected latent period of 14 days, RLIM is able to minimize this value at 0.07 and reach an equilibrium condition. A successful forecast is generated using New York state's COVID-19 transmission, in which a turning point is predicted to emerge on January 31, 2021. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-021-06520-1.

A Simplified Fractional Order PID Controller's Optimal Tuning: A Case Study on a PMSM Speed Servo.

A simplified fractional order PID (FOPID) controller is proposed by the suitable definition of the parameter relation with the optimized changeable coefficient. The number of the pending controller parameters is reduced, but all the proportional, integral, and derivative components are kept. The estimation model of the optimal relation coefficient between the controller parameters is established, according to which the optimal FOPID controller parameters can be calculated analytically. A case study is provided, focusing on the practical application of the simplified FOPID controller to a permanent magnet synchronous motor (PMSM) speed servo. The dynamic performance of the simplified FOPID control system is tested by motor speed control simulation and experiments. Comparisons are performed between the control systems using the proposed method and those using some other existing methods. According to the simulation and experimental results, the simplified FOPID control system achieves the optimal dynamic performance. Therefore, the validity of the proposed controller structure and tuning method is demonstrated.

Why Do Big Data and Machine Learning Entail the Fractional Dynamics?

Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing of complex signals, enhance the control of complex systems, increase the performance of optimization, and even extend the enabling of the potential for creativity. In this article, the authors discuss the fractional dynamics, FOT and rich fractional stochastic models. First, the use of fractional dynamics in big data analytics for quantifying big data variability stemming from the generation of complex systems is justified. Second, we show why fractional dynamics is needed in machine learning and optimal randomness when asking: "is there a more optimal way to optimize?". Third, an optimal randomness case study for a stochastic configuration network (SCN) machine-learning method with heavy-tailed distributions is discussed. Finally, views on big data and (physics-informed) machine learning with fractional dynamics for future research are presented with concluding remarks.

Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System.

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (Kp, Kd, µ)-space corresponding to the observer bandwidth ωo can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral- Derivative (PID) controller. For example, the JITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the JITAE of IOADRC and PID controller, respectively. Besides, the JITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the JITAE of IOADRC and PID controller, respectively.

Evapotranspiration Estimation with Small UAVs in Precision Agriculture.

Estimating evapotranspiration (ET) has been one of the most critical research areas in agriculture because of water scarcity, the growing population, and climate change. The accurate estimation and mapping of ET are necessary for crop water management. Traditionally, researchers use water balance, soil moisture, weighing lysimeters, or an energy balance approach, such as Bowen ratio or eddy covariance towers to estimate ET. However, these ET methods are point-specific or area-weighted measurements and cannot be extended to a large scale. With the advent of satellite technology, remote sensing images became able to provide spatially distributed measurements. However, the spatial resolution of multispectral satellite images is in the range of meters, tens of meters, or hundreds of meters, which is often not enough for crops with clumped canopy structures, such as trees and vines. Unmanned aerial vehicles (UAVs) can mitigate these spatial and temporal limitations. Lightweight cameras and sensors can be mounted on the UAVs and take high-resolution images. Unlike satellite imagery, the spatial resolution of the UAV images can be at the centimeter-level. UAVs can also fly on-demand, which provides high temporal imagery. In this study, the authors examined different UAV-based approaches of ET estimation at first. Models and algorithms, such as mapping evapotranspiration at high resolution with internalized calibration (METRIC), the two-source energy balance (TSEB) model, and machine learning (ML) are analyzed and discussed herein. Second, challenges and opportunities for UAVs in ET estimation are also discussed, such as uncooled thermal camera calibration, UAV image collection, and image processing. Then, the authors share views on ET estimation with UAVs for future research and draw conclusive remarks.

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model.

In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R 0 is derived. When R 0 < 1 , the disease-free equilibrium point is unique and locally asymptotically stable. When R 0 > 1 , the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects.

In the end of 2019, a new type of coronavirus first appeared in Wuhan. Through the real-data of COVID-19 from January 23 to March 18, 2020, this paper proposes a fractional SEIHDR model based on the coupling effect of inter-city networks. At the same time, the proposed model considers the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period. By applying the least squares method and prediction-correction method, the proposed system is fitted and predicted based on the real-data from January 23 to March 18 - m where m represents predict days. Compared with the integer system, the non-network fractional model has been verified and can better fit the data of Beijing, Shanghai, Wuhan and Huanggang. Compared with the no-network case, results show that the proposed system with inter-city network may not be able to better describe the spread of disease in China due to the lock and isolation measures, but this may have a significant impact on countries that has no closure measures. Meanwhile, the proposed model is more suitable for the data of Japan, the USA from January 22 and February 1 to April 16 and Italy from February 24 to March 31. Then, the proposed fractional model can also predict the peak of diagnosis. Furthermore, the existence, uniqueness and boundedness of a nonnegative solution are considered in the proposed system. Afterward, the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number R 0 ≤ 1 , which provide a theoretical basis for the future control of COVID-19.

Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions.

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for single hidden layer feed-forward neural networks, such as Randomized Radial Basis Function (RBF) Networks and Random Vector Functional-link (RVFL), the SCN randomly assigns the input weights and biases of the hidden nodes in a supervisory mechanism. Since the parameters in the hidden layers are randomly generated in uniform distribution, hypothetically, there is optimal randomness. Heavy-tailed distribution has shown optimal randomness in an unknown environment for finding some targets. Therefore, in this research, the authors used heavy-tailed distributions to randomly initialize weights and biases to see if the new SCN models can achieve better performance than the original SCN. Heavy-tailed distributions, such as Lévy distribution, Cauchy distribution, and Weibull distribution, have been used. Since some mixed distributions show heavy-tailed properties, the mixed Gaussian and Laplace distributions were also studied in this research work. Experimental results showed improved performance for SCN with heavy-tailed distributions. For the regression model, SCN-Lévy, SCN-Mixture, SCN-Cauchy, and SCN-Weibull used less hidden nodes to achieve similar performance with SCN. For the classification model, SCN-Mixture, SCN-Lévy, and SCN-Cauchy have higher test accuracy of 91.5%, 91.7% and 92.4%, respectively. Both are higher than the test accuracy of the original SCN.

Subdiffusive Source Sensing by a Regional Detection Method.

Motivated by the fact that the danger may increase if the source of pollution problem remains unknown, in this paper, we study the source sensing problem for subdiffusion processes governed by time fractional diffusion systems based on a limited number of sensor measurements. For this, we first give some preliminary notions such as source, detection and regional spy sensors, etc. Secondly, we investigate the characterizations of regional strategic sensors and regional spy sensors. A regional detection approach on how to solve the source sensing problem of the considered system is then presented by using the Hilbert uniqueness method (HUM). This is to identify the unknown source only in a subregion of the whole domain, which is easier to be implemented and could save a lot of energy resources. Numerical examples are finally included to test our results.

Bifurcation dynamics of the tempered fractional Langevin equation.

Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

Explicit stability condition for delta fractional order systems with α∈(0,+∞).

This paper delves into the stability of time-advance delta fractional order systems, with a specific emphasis on the order range (0,+∞) rather than the conventional range (0,1). The delta Laplace transform is used to investigate the stability of the suggested system, and a mapping relation ρ=ss+1 is introduced. The explicit stability condition is provided, articulated in relation to a specific distribution of eigenvalues of the system matrix. To validate this condition, the paper establishes equivalence between the delta difference and the nabla difference. Furthermore, both quantitative and qualitative analyses are conducted on the range of the unstable region. Finally, the correctness of the developed results is validated by three examples.

A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler-Nichols approach.

The relay feedback auto-tuning method, which was an early commercialized approach, has maintained its popularity due to its simplicity and robustness. However, the classical proportional integral derivative (PID) controller auto-tuning method often results in unacceptable overshoot, especially for integrating and higher-order processes. By integrating the TID controller with the relay feedback technique, we significantly enhance dynamic control performance without relying on prior knowledge of the system. However, the direct application of the classical auto-tuning method to the TID controller encounters challenges due to the additional fractional-order transfer function s-1n. Therefore, we have developed a fractional-order Ziegler-Nichols (FOZ-N) approach, specifically designed to adjust the parameters of the TID controller. The proposed FOZ-N method is fast, simple, and capable of achieving the desired performance. In contrast to the previous Ziegler-Nichols tuning method, the TID controller parameters Kt and Ki are determined to shift the critical point (-1/Ku,j0) to the FOZ-N point (-0.5,-j0.7) on the Nyquist curve, ensuring system robustness and dynamic performance. The impact of the fractional order parameter s-1n and ratio r is explored through time-domain analysis, where these parameters are determined to ensure optimal dynamic performance. Additionally, we provide a detailed tuning procedure along with a helpful example. To demonstrate the advantages of the proposed auto-tuning TID controller over the Ziegler-Nichols PID controller, Optimal PID controller, simple internal model control (SIMC) PID controller, and Ziegler-Nichols FOPID controller, we present a simulation illustration involving multiple different systems. To validate the practical outcomes of this paper, we present experimental results on the temperature control of a Peltier cell.

Diagnosis of neurodegenerative diseases with a refined Lempel-Ziv complexity.

The investigation into the distinctive difference of gait is of significance for the clinical diagnosis of neurodegenerative diseases. However, human gait is affected by many factors like behavior, occupation and so on, and they may confuse the gait differences among Parkinson's disease, amyotrophic lateral sclerosis, and Huntington's disease. For the purpose of examining distinctive gait differences of neurodegenerative diseases, this study extracts various features from both vertical ground reaction force and time intervals. Moreover, refined Lempel-Ziv complexity is proposed considering the detailed distribution of signals based on the median and quartiles. Basic features (mean, coefficient of variance, and the asymmetry index), nonlinear dynamic features (Hurst exponent, correlation dimension, largest Lyapunov exponent), and refined Lempel-Ziv complexity of different neurodegenerative diseases are compared statistically by violin plot and Kruskal-Wallis test to reveal distinction and regularities. The comparative analysis results illustrate the gait differences across these neurodegenerative diseases by basic features and nonlinear dynamic features. Classification results by random forest indicate that the refined Lempel-Ziv complexity can robustly enhance the diagnosis accuracy when combined with basic features.

Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme.

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.