Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem

In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.

Dynamical Behaviors of Nonlinear Coronavirus (COVID-19) Model with Numerical Studies

The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.

Solution of the time-fractional generalized Burger-Fisher equation using the fractional re duce d differential transform method

“The time-fractional generalized Burger-Fisher equation(TF-GBFE)”is used in various applied sciences and physical applications,including simulation of gas dynamics,financial mathematics,fluid mechan-ics,and ocean engineering.This equation represents a concept for the coordination of reaction systems,as well as advection,and conveys the understanding of dissipation.The Fractional Reduced Differential Transform Method(FRDTM)is used to evaluate“the time-fractional generalized Burger-Fisher equation(TF-GBFE).”Todeterminethemethod’s validity,whenthesolutionsareobtained,theyarecorrelatedto exact solutions ofα=1 order,and even for various values ofα.Three-dimensional graphs are used to depict the solutions.Additionally,the analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.

Tsunami wave propagation model:A fractional approach

This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.