Ten-year phantom limb pain with only four sessions of Fu's subcutaneous needling: A case report and systematic review.

Phantom limb pain (PLP) is a distressing consequence commonly encountered by individuals who have undergone amputations. The efficacy of treatment options for PLP is limited. In this study, we present a case of a 64-year-old male who suffered from PLP for a duration of 10 years following an above-the-knee amputation. Despite unsuccessful attempts with painkillers and neurotrophic drugs over the course of a decade, the patient sought relief through Fu's Subcutaneous Needling (FSN), an innovative acupuncture therapy that specifically targets the subcutaneous tissue for pain management. Remarkably, the patient experienced a significant reduction in PLP and subsequently decreased his reliance on medication, as well as experiencing improved sleep after undergoing one session of FSN per day for four consecutive days. A follow-up conducted three years later demonstrated positive treatment outcomes. FSN demonstrated a significant influence on PLP, resulting in reduced analgesic requirements and enhanced quality of life. Therefore, FSN may be recommended as an additional treatment option for PLP. In order to gain a comprehensive understanding of the effects of acupuncture on PLP, a systematic review of relevant literature was conducted in PubMed, Embase, Cochrane Library and Web of Science in recent 20 years (from January 1, 2003 to October 16, 2023), using different combinations of the following terms: (phantom acrodynia), (residual limb pain), (phantom limb pain), (acupuncture), (electroacupuncture), (auriculoacupuncture), and (needling). 9 articles with 18 cases including one randomized controlled trial (n = 8) were obtained. This review provided additional evidence supporting the efficacy and safety of needling therapies for PLP. This systematic review offers additional evidence supporting the effectiveness and safety of needling therapies for PLP. However, there were no precedent reports using FSN treatment for PLP. Hence, this case may provide some implications for clinicians in practice.

Quasi-projective and complete synchronization of discrete-time fractional-order delayed neural networks.

This paper presents new theoretical results on quasi-projective synchronization (Q-PS) and complete synchronization (CS) of one kind of discrete-time fractional-order delayed neural networks (DFDNNs). At first, three new fractional difference inequalities for exploring the upper bound of quasi-synchronization error and adaptive synchronization are established by dint of Laplace transform and properties of discrete Mittag-Leffler function, which vastly expand a number of available results. Furthermore, two controllers are designed including nonlinear controller and adaptive controller. And on the basis of Lyapunov method, the aforementioned inequalities and properties of fractional-order difference operators, some sufficient synchronization criteria of DFDNNs are derived. Because of the above controllers, synchronization criteria in this paper are less conservative. At last, numerical examples are carried out to illustrate the usefulness of theoretical upshots.

The effect mitigation measures for COVID-19 by a fractional-order SEIHRDP model with individuals migration.

In this paper, the generalized SEIHRDP (susceptible-exposed-infective-hospitalized-recovered-death-insusceptible) fractional-order epidemic model is established with individual migration. Firstly, the global properties of the proposed system are studied. Particularly, the sensitivity of parameters to the basic reproduction number are analyzed both theoretically and numerically. Secondly, according to the real data in India and Brazil, it can all be concluded that the bilinear incidence rate has a better description of COVID-19 transmission. Meanwhile, multi-peak situation is considered in China, and it is shown that the proposed system can better predict the next peak. Finally, taking individual migration between Los Angeles and New York as an example, the spread of COVID-19 between cities can be effectively controlled by limiting individual movement, enhancing nucleic acid testing and reducing individual contact.

Stability analysis and optimal control of a fractional-order generalized SEIR model for the COVID-19 pandemic.

In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R0, the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann-Liouville (R-L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed.

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.

Necessary and Sufficient Conditions for Group Consensus of Fractional Multiagent Systems Under Fixed and Switching Topologies via Pinning Control.

The group consensus problem for fractional-order multiagent systems is investigated in this paper. With the help of double-tree-form transformations, the group consensus problem of fractional-order multiagent systems is proved to be equivalent to the asymptotical stability problem of reduced-order error systems. A class of distributed control protocols and some simple LMI sufficient conditions as well as necessary and sufficient conditions are proposed in this paper to solve the group consensus problem for fractional multiagent systems. Moreover, pinning control strategy has been taken into consideration. It is shown that the system converges more rapidly when the designed pinning protocols are adopted. In addition, the case of fractional system with switching topologies is also discussed and some corresponding sufficient conditions are obtained. Finally, some simulation results are presented to illustrate the theoretical results.

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.

Mean-square H∞ antagonistic formations of second-order multi-agent systems with multiplicative noises and external disturbances.

In physical systems, since the acceleration is always regard as the control input, it is meaningful to study the coordination problems of the second-order multi-agent system. This paper devotes to the mean-square H∞ antagonistic formation control of second-order multi-agent systems with multiplicative noises and external disturbances under directed signed topologies. To force all agents achieve antagonistic formation and attenuate the effect of communication noises and external disturbances, a novel distributed consensus control protocol with a time-invariant control gain is proposed where only the information that received from neighbors is utilized. And then, by combining the theories of graph, robust H∞ control and stochastic analysis, some matrix inequalities conditions are deduced. It is proved that under the designed control protocol, the state of each agent converge to its own desired formation in its allied groups in the sense of mean square. Furthermore, numerical simulations are given for the purpose of showing that the proposed theoretical results are effective.

Extinction Analysis of Stochastic Predator-Prey System with Stage Structure and Crowley-Martin Functional Response.

In this paper, we researched some dynamical behaviors of a stochastic predator-prey system, which is considered under the combination of Crowley-Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases.

LMI Conditions for Global Stability of Fractional-Order Neural Networks.

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

Function projective synchronization between integer-order and stochastic fractional-order nonlinear systems.

In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.

Stability analysis of fractional-order Hopfield neural networks with time delays.

This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper.

[Correlation between the changes of oxidation reduction potential values and postmortem interval of heart blood in rabbits after death].

OBJECTIVE: To investigate correlation between the changes of oxidation reduction potential (ORP) values of heart blood in rabbits after death and postmortem interval (PMI) at different temperatures. METHODS: Forty-eight rabbits were randomly divided into 6 groups and sacrificed by air embolism. Blood samples were taken from the right ventricle of each rabbit and stored at different temperatures of 10, 15, 20, 25, 30 and 35 degrees C, respectively. Every 4 hours from 0 h to 132 h postmortem, the ORP values of the blood samples were measured at different intervals by PB-21 electrochemical analyzer. The curvilinear regression equation was established by SPSS 17.0 software. The surface equation and 3D surface diagram were established by MATLAB 7.10.0 software. RESULTS: The ORP values at different temperatures of heart blood in rabbits were highly correlated with the PMI. The ORP values rised obviously when the temperature was high and rised slowly when the temperature was low. The surface equation and 3D surface diagram were obtained. CONCLUSION: The surface equation and 3D surface diagram of ORP values and PMI may be used for PMI estimation at different temperatures.