Chaos, Solitons and Fractals: X最新文献

Dengue is a significant factor to the global public health issue, including Nepal. In Nepal from $2004-2022$, the largest outbreak occurred in the year 2022. Dengue infection cases appeared all over 77 districts of Nepal. The Caputo fractional order SEIR-SEI epidemic model is able to describe dengue disease transmission dynamics of present situation. For fundamental mathematical guarantees of epidemic model equations, we studied the Lipschitz and Banach contraction theorems to show that the model equations have a unique solution. The Ulam-Hyres stability is established in the model. Next generation matrix approach is used to calculate the associated basic reproduction number $R_0$. The model equilibrium points are identified, and the local asymptotic stability for disease-free equilibrium point is analyzed. Normalized forward and partial rank correlation coefficient are used for sensitivity study to identify the factors that affect dengue infection with respect to basic reproduction number. Using real data of Nepal, the model is fitted and the least square method is used for estimating parameters. Numerical scheme has been illustrated using a two-step Lagrange interpolation approach and the solution is approximated. With numerical results and sensitivity analysis, it is concluded that biting rate and death rate of mosquito are extremely sensitive to the disease transmission. The transmission increases with increasing biting rate and decreases with decreasing mosquito death rate. For the year 2022, $R_0=1.7739>1$ showing that the disease is endemic. Thus, effective control measure should be implemented to combat the dengue virus. However, further research needs to be undertaken to assess the impact of such control measures.

In the current work, we examine $\eta$-Ricci-Yamabe solitons in a Bochner flat Lorentzian K$\ddot{a}$hler space-time manifolds. We have addressed various circumstances for Ricci-Yamabe solitons to be steady, shrinking or expanding in terms of isotropic pressure, the cosmological constant, energy density and gravitational constant in different perfect fluids such as dark fluid, Stiff matter, dust fluid and radiation fluid.

We consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and compare the average to existing numerical results. Computer simulations show that the proposed analytic solution is highly accurate when compared to the existing benchmark. This confirms that the proposed approach to deal with such non-linear problems can be used to treat similar non-classical boundary-value problems.

COVID-19 pandemic affects 213 countries and regions around the world. Which the number of people infected with the virus exceeded 26 millions infected and more than 870 thousand deaths until september 04, 2020, in the world, and Peru among the countries most affected by this pandemic. So we proposed a mathematical model describes the dynamics of spread of the COVID-19 pandemic in Peru. The optimal control strategy based on the model is proposed, and several reasonable and suitable control strategies are suggested to the prevention and reduce the spread COVID-19 virus, by conducting awareness campaigns and quarantine with treatment. coronavirus 2019 (COVID-19). Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.

Stochastic fractional integrodifferential models are widely employed to model several natural phenomena these days. This current work focuses on the well-posedness results and numerical solutions of a specific form of these models considering the Leffler nonsingular kernels operator wherein the stochastic term is driven by the standard Brownian motion. Accordingly, a combination of sufficient conditions, topological theorems, and Banach space theory are utilized to construct the well-posedness proof. For treating the numerical issue, a familiar spectral collocation technique relying upon shifted Legendre series expansion theory is proposed. The basic properties of Brownian motion and a linear spline interpolation method are used to simulate the standard Brownian motion at a fixed time value. In addition, the idea of the Gauss-Legendre numerical integration rule is implemented to approximate the finite integral. We also devote our attention to the concept of convergence of the proposed method and demonstrate its analysis. Ultimately, the obtained theoretical results and the presented method are examined with five numerous applications. The obtained results indicate the high accuracy and efficiency of applying this method in solving stochastic models of the above-mentioned form.

Asymptomatic carriers serve as a potential source of transmission of epidemic diseases. Exposed people who develop symptoms only get tested and remain isolated in their homes or sometimes in hospitals when needed. In contrast, the asymptomatic individuals go untested and spread the disease silently as they roam freely throughout their entire infectious lifetime. The work intends to explore the role of asymptomatic carriers in the transmission of epidemic diseases and investigate suitable optimal control strategies. We propose a SEIAQR compartmental model subdividing the total population into six different compartments. To illustrate the model’s implication, we estimate the number of asymptomatic individuals using COVID-19 data during June 9–July 18, 2021 from Bangladesh. We then analyze the model to explore whether the epidemic subsides if the asymptomatic individuals are tested randomly and isolated. Finally, to gain a better understanding of the potential of this unidentified transmission route, we propose an optimal control model considering two different control strategies: personal protective measures and isolation of asymptomatic carriers through random testing. Our results show that simultaneous implementation of both control strategies can reduce the epidemic early. Most importantly, sustained effort in identifying and isolation of asymptotic individuals allows relaxation in personal protective measures.

As an important research direction of swarm intelligence algorithm, particle swarm optimization (PSO) has become a popular evolutionary method and received extensive attention in the past decades. Despite many PSO variants have been proposed, how to maintain a good balance between the exploration and exploitation abilities, and how to jump out of the local optimal position are still challenges. In this article, based on empirical balance strategy, a new particle swarm optimization (EBPSO) algorithm is presented. Firstly, based on an adaptive adjustment mechanism, the algorithm can choose a better strategy from two search equations, which can maintain the balance between the exploration and exploitation abilities. Secondly, to utilize the information of individual historical optimal solution and the optimal solution of the current population, a weight for adjusting their influence is introduced into the search equation. Thirdly, by introducing the diversity of population, a moving equation for dynamically adjusting the search ability of the algorithm is proposed. Finally, to avoid falling into local optimum and to search the potential location, a dynamic random search mechanism is proposed, which is designed by using the information of the current optimal solution. Compared with some state-of-the-art algorithms, the experimental results show that EBPSO has excellent solution quality and convergence characteristic on almost all test problems.

In this investigation, the dynamical model of social media addiction is considered in the spirit of the Caputo differential operator. The main utilization is to elucidate the importance of nonclassical derivatives order in the implementation of social media addiction complex phenomena. Herein, we first developed the model using the Caputo scheme and discussed some fundamental mathematical computations. Secondly, we adapt the Hilbert reproducing scheme to generate numerical appropriate solutions via Mathematica 12 software. The utilized fractional social media problem was formulated and configured to solve it by fitting two subspaces from the space of Hilbert. The convergence-error behavior results are established using functional analysis techniques. After utilizing several computational algorithms, the considered model results are tabularly and graphically demonstrated with different choices of arbitrary order parameter values. The outcomes show that when applying the fractional Caputo differential operator, such complicated events become more realistic and convincing. The summary of the presented work and various scientific recommendations in addition to the future work that complements this analysis has been utilized in the last part.

In 1982 in a series of works Vielliefosse [1, 2] discussed a nonlinear homogeneous evolution equation for the velocity gradient tensor in fluid dynamics. Later Cantwell [3] extended this formalism to the non-homogeneous case including the effects of viscous diffusion and cross derivatives of pressure field. Here, we derive the evolution equations of the geometrical invariants of the magnetic and velocity field gradient tensors in the case of magneto-hydrodynamics for both non-homogeneous and homogeneous cases, i.e., considering or neglecting viscous effects and source terms. The inclusion of dissipation effects and higher-order gradient terms introduces a non trivial evolution of invariants, which can be treated as a stochastic evolution equation. Conversely, in the homogeneous case, the magnetic field invariants do not evolve, i.e., the magnetic field line topology is conserved, while the corresponding velocity invariants are affected by magnetic forces. By writing the equations of the velocity field invariants as a dynamical system we can identify the role of the different terms in the evolution equations. In detail, in the homogenous case we show that the term associated with the current density drives transitions between hyperbolic and elliptical structures. Evolution equations are also discussed in the perspective of an application to the analysis of magneto-hydrodynamic turbulence.

In this research, we study the fetal heart rate from abdominal signals using multi-fractal spectra and fractal analysis. We use the Abdominal and Direct Fetal Electrocardiogram Database contains multichannel fetal electrocardiogram (FECG) recordings obtained from 5 different women in labor, between 38 and 41 weeks of gestation. We apply autocorrelation or power spectral densities (PSD) analysis on these five FECG recordings to estimate the exponent from realizations of these processes and to find out if the signal of interest exhibits a power-law PSD. We perform multi-fractal analysis to discover whether some type of power-law scaling exists for various statistical moments at different scales of these FECG signals. We plot the multi-fractal spectra of this database to compare the width of the scaling exponent for each spectrum. A quantitative analysis commonly known as the Fractal Dimension (FD) using the Higuchi algorithm has been carried out to illustrate the fractal complexity of input signals. Our finding shows that the fractal geometry can be used as a mathematical model and computational framework to further analysis and classification of clinical database. Moreover, it can be considered as a framework to compare the complexity of FECG signals and a useful tool to differentiate between their patterns.