Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,exposed,infected,symptomatically infected,asymptomatically infected and recovered)infection model of COVID-19 with a constant rate of advection is studied for the disease propagation.A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system.The continuous model is transposed into a discrete numerical model by discretizing the domains,finitely.To analyze the disease dynamics,a structure preserving non-standard finite difference scheme is designed.Two steady states of the continuous system are described i.e.,virus free steady state and virus existing steady state.Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model.Positivity of the state variables is ensured by applying the M-matrix theory.A result for the positivity property is established.For the proposed numerical design,two different types of the stability are investigated.Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results.Von Neuman stability test is applied to ensure linear stability.The reproductive number is described and its pivotal role in stability analysis is also discussed.Consistency and convergence of the numerical model is also studied.Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically,which is helpful in controlling the disease dynamics.In the end,the conclusion of the study is also rendered.

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.

Unification and Application of 3-point Approximating Subdivision Schemes of Varying Arity

In this paper, we propose and analyze a subdivision scheme which unifies 3-point approximating subdivision schemes of any arity in its compact form and has less support, computational cost and error bounds.? The usefulness of the scheme is illustrated by considering different examples along with its comparison with the established subdivision schemes. Moreover, B-splines of degree 4and well known 3-point schemes [1, 2, 3, 4, 6, 11, 12, 14, 15] are special cases of our proposed scheme.

Dynamic Properties of Neutral Stochastic Differential Equations with Markovian Switching

A generalized neutral stochastic functional differential equation(NSFDE) with Markovian switching is studied. We will discuss some important properties of the solutions including boundedness and exponential stability by using Lyapunov-Krasovskii functional,Matrix inequality and some analysis techniques. Finally, an numerical example for neutral stochastic neural networks with Markovian switching is given to show the effectiveness of the results in this paper.

Extended Wiener Measure by Nonstandard Analysis for Financial Time Series

We propose a new approach to construct an extended Wiener measure using nonstandard analysis by E. Nelson. For the new definition we construct non-standardized convolution of probability measure for independent random variables. As an application, we consider a simple calculation of financial time series.

Chaos for Subshifts of Finite Type

This paper deals with chaos for subshifts of finite type. We show that for any subshift of finite type determined by an irreducible and aperiodic matrix, there is a finitely chaotic set with full Hausdorff dimension. Moreover, for any subshift of finite type determined by a matrix, we point out that the cases including positive topological entropy, distributional chaos, chaos and Devaney chaos are mutually equivalent.

Distributed adaptive Kalman filter based on variational Bayesian technique

In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The con vergence of the proposed algorithm is proved in two main steps: n oise statistics is estimated, where each age nt only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.