A mathematical model of coronavirus transmission by using the heuristic computing neural networks.

In this study, the nonlinear mathematical model of COVID-19 is investigated by stochastic solver using the scaled conjugate gradient neural networks (SCGNNs). The nonlinear mathematical model of COVID-19 is represented by coupled system of ordinary differential equations and is studied for three different cases of initial conditions with suitable parametric values. This model is studied subject to seven class of human population N(t) and individuals are categorized as: susceptible S(t), exposed E(t), quarantined Q(t), asymptotically diseased IA (t), symptomatic diseased IS (t) and finally the persons removed from COVID-19 and are denoted by R(t). The stochastic numerical computing SCGNNs approach will be used to examine the numerical performance of nonlinear mathematical model of COVID-19. The stochastic SCGNNs approach is based on three factors by using procedure of verification, sample statistics, testing and training. For this purpose, large portion of data is considered, i.e., 70%, 16%, 14% for training, testing and validation, respectively. The efficiency, reliability and authenticity of stochastic numerical SCGNNs approach are analysed graphically in terms of error histograms, mean square error, correlation, regression and finally further endorsed by graphical illustrations for absolute errors in the range of 10-05 to 10-07 for each scenario of the system model.

Analytical Solution to the Generalized Complex Duffing Equation.

Future scientific and technological evolution in many areas of applied mathematics and modern physics will necessarily depend on dealing with complex systems. Such systems are complex in both their composition and behavior, namely, dealing with complex dynamical systems using different types of Duffing equations, such as real Duffing equations and complex Duffing equations. In this paper, we derive an analytical solution to a complex Duffing equation. We extend the Krýlov-Bogoliúbov-Mitropólsky method for solving a coupled system of nonlinear oscillators and apply it to solve a generalized form of a complex Duffing equation.

A Cloud-Based Machine Learning Approach to Reduce Noise in ECG Arrhythmias for Smart Healthcare Services.

ECG (electrocardiogram) identifies and traces targets and is commonly employed in cardiac disease detection. It is necessary for monitoring precise target trajectories. Estimations of ECG are nonlinear as the parameters TDEs (time delays) and Doppler shifts are computed on receipt of echoes where EKFs (extended Kalman filters) and electrocardiogram have not been examined for computations. ECG, certain times, results in poor accuracies and low SNRs (signal-to-noise ratios), especially while encountering complicated environments. This work proposes to track online filter performances while using optimization techniques to enhance outcomes with the removal of noise in the signal. The use of cost functions can assist state corrections while lowering costs. A new parameter is optimized using IMCEHOs (Improved Mutation Chaotic Elephant Herding Optimizations) by linearly approximating system nonlinearity where multi-iterative function (Optimized Iterative UKFs) predicts a target's unknown parameters. To obtain optimal solutions theoretically, multi-iterative function takes less iteration, resulting in shorter execution times. The proposed multi-iterative function provides numerical approximations, which are derivative-free implementations. Signals are updated in the cloud environment; the updates are received by the patients from home. The simulation evaluation results with estimators show better performances in terms of reduced NMSEs (normalized mean square errors), RMSEs (root mean squared errors), SNRs, variances, and better accuracies than current approaches. Machine learning algorithms have been used to predict the stages of heart disease, which is updated to the patient in the cloud environment. The proposed work has a 91.0% accuracy rate with an error rate of 0.05% by reducing noise levels.

Solution to a Damped Duffing Equation Using He's Frequency Approach.

In this paper, we generalize He's frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt-Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.