Optimal analysis of adaptive type-II progressive censored for new unit-lindley model

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton–Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators' asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The Metropolis–Hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios. © 2022 The Author(s)

An Artificial Approach for the Fractional Order Rape and Its Control Model

The current investigations provide the solutions of the nonlinear fractional order mathematical rape and its control model using the strength of artificial neural networks (ANNs) along with the Levenberg-Marquardt back -propagation approach (LMBA), i.e., artificial neural networks-Levenberg-Marquardt backpropagation approach (ANNs-LMBA). The fractional order investigations have been presented to find more realistic results of the mathe-matical form of the rape and its control model. The differential mathematical form of the nonlinear fractional order mathematical rape and its control model has six classes: susceptible native girls, infected immature girls, sus-ceptible knowledgeable girls, infected knowledgeable girls, susceptible rapist population and infective rapist population. The rape and its control differ-ential system using three different fractional order values is authenticated to perform the correctness of ANNs-LMBA. The data is used to present the rape and its control differential system is designated as 70% for training, 14% for authorization and 16% for testing. The obtained performances of the ANNs-LMBA are compared with the dataset of the Adams-Bashforth-Moulton scheme. To substantiate the consistency, aptitude, validity, exactness, and capability of the LMBA neural networks, the obtained numerical values are provided using the state transitions (STs), correlation, regression, mean square error (MSE) and error histograms (EHs).

A higher order Galerkin time discretization scheme for the novel mathematical model of COVID-19

In the present period, a new fast-spreading pandemic disease, officially recognised Coronavirus disease 2019 (COVID-19), has emerged as a serious international threat. We establish a novel mathematical model consists of a system of differential equations representing the population dynamics of susceptible, healthy, infected, quarantined, and recovered individuals. Applying the next generation technique, examine the boundedness, local and global behavior of equilibria, and the threshold quantity. Find the basic reproduction number R0 and discuss the stability analysis of the model. The findings indicate that disease fee equilibria (DFE) are locally asymptotically stable when R0 < 1 and unstable in case R0 > 1. The partial rank correlation coefficient approach (PRCC) is used for sensitivity analysis of the basic reproduction number in order to determine the most important parameter for controlling the threshold values of the model. The linearization and Lyapunov function theories are utilized to identify the conditions for stability analysis. Moreover, solve the model numerically using the well known continuous Galerkin Petrov time discretization scheme. This method is of order 3 in the whole-time interval and shows super convergence of order 4 in the discrete time point. To examine the validity and reliability of the mentioned scheme, solve the model using the classical fourth-order Runge-Kutta technique. The comparison demonstrates the substantial consistency and agreement between the Galerkin-scheme and RK4-scheme outcomes throughout the time interval. Discuss the computational cost of the schemes in terms of time. The investigation emphasizes the precision and potency of the suggested schemes as compared to the other traditional schemes. © 2023 the Author(s), licensee AIMS Press.