Numerical Computation of SEIR Model for the Zika Virus Spreading

The purpose of this study is to present the numerical performancesand interpretations of the SEIR nonlinear system based on the Zika virusspreading by using the stochastic neural networks based intelligent computingsolver. The epidemic form of the nonlinear system represents the four dynamicsof the patients, susceptible patients S(y), exposed patients hospitalized inhospital E(y), infected patients I(y), and recovered patients R(y), i.e., SEIRmodel. The computing numerical outcomes and performances of the systemare examined by using the artificial neural networks (ANNs) and the scaledconjugate gradient (SCG) for the training of the networks, i.e., ANNs-SCG.The correctness of the ANNs-SCG scheme is observed by comparing theproposed and reference solutions for three cases of the SEIR model to solvethe nonlinear system based on the Zika virus spreading dynamics throughthe knacks of ANNs-SCG procedure based on exhaustive experimentations.The outcomes of the ANNs-SCG algorithm are found consistently in goodagreement with standard numerical solutions with negligible errors. Moreover,the procedure’s constancy, dependability, and exactness are perceived by usingthe values of state transitions, error histogram measures, correlation, andregression analysis.

The Dual Spaces of Sets of Difference Sequences of Order m and Matrix Transformations

Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.