Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

Gepree, K.A.; Mahdy, A. M. S.; Mohamed, M.S.; Al-Amiri, A.

doi:10.32604/cmc.2019.07701

Cited by 33 publications

(15 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was first introduced by Zhou [34] for solving linear and non-linear initial value problems in electrical circuit analysis. Subsequently, several authors have applied the differential transformation method (DTM) and further multi-step differential transform method (MsDTM) to solve systems of nonlinear differential equations that describe dynamical systems [30], biomathematics models [18] and epidemic models [1][2][3]14,23,26,33]. Several variants have been suggested for differential transformation method like modified DTM [5], reduced DTM [17,22,28] and partitioned DTM [4].…”

Section: Formulation Of Sir Model For Dengue Fevermentioning

confidence: 99%

Numerical Simulation of Dengue Fever (Sir Model) Using Differential Transform Method, Multi-Step Differential Transform Method and Rk4 Method

Tuteja¹

2021

ITII

View full text Add to dashboard Cite

This study investigates the application of the differential transformation method(DTM), multi-step differential transform method(MsDTM) with step-size and RK4 method (Mathematica) for finding the numerical solution of the SIR model of dengue fever in epidemiology. This model is a system of non-linear ordinary differential equations that have no analytic solution. Both the methods DTM and MsDTM are applied directly without any linearization, perturbation or discretization in the model equations to obtain semi-analytic solutions. The accuracy of the MSDTM is excellent and comparable to the RK4 method of Mathematica.

show abstract

Section: Formulation Of Sir Model For Dengue Fevermentioning

confidence: 99%

Numerical Simulation of Dengue Fever (Sir Model) Using Differential Transform Method, Multi-Step Differential Transform Method and Rk4 Method

Tuteja¹

2021

ITII

View full text Add to dashboard Cite

show abstract

“…We can use this algorithm with one dimension and two dimensions data. For more reading see [24][25][26][27][28][29][30][31].…”

Section: The Metropolis-hasting Algorithmmentioning

confidence: 99%

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Hussam¹,

Riad

Mubarak

et al. 2020

Symmetry

View full text Add to dashboard Cite

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

show abstract

“…Fractional order differential equations (FDEs) are usually used to model systems that have a memory that occurs in sundry physical phenomenas, models in the thermoelasticity field, and biological ideals see ( [9][10][11], [12][13][14], [15][16][17], [18][19][20], [21][22][23], [24][25][26], [27][28][29], [30][31][32]).…”

Section: Introductionmentioning

confidence: 99%

Describe the Mathematical Model for Exchanging Waves Between Bacterial and Cellular DNA

Mohamed¹,

Elagan²,

Mohamed³

et al. 2021

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

In this article, we have shown that bacterial DNA could act like some coils which interact with coil-like DNA of host cells. By decreasing the separating distance between two bacterial cellular DNA, the interaction potential, entropy, and the number of microstates of the system grow. Moreover, the system gives its energy to the medium and the temperature of the host body grows. This could be seen as fever in diseases. By emitting some special waves and changing the temperature of the medium, the effects of bacterial waves could be reduced and bacterial diseases could be controlled. Many investigators have shown that bacterial DNA could emit or absorb electromagnetic waves. One of the main experiments about bacterial waves has been done by Montagnier and his group. They have shown that the genomic DNA of most pathogenic bacteria includes sequences that are able to emit electromagnetic waves. The results have shown that wave affects the crucial physicochemical processes in both Gram-positive and Gram-negative bacteria. The emphasis in this survey is on the development of controlling model equations and computer emulation of the model equations rather than on mathematical methods for solving the model equations and differential equations of epidemics.

show abstract

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

Cited by 33 publications

References 7 publications

Numerical Simulation of Dengue Fever (Sir Model) Using Differential Transform Method, Multi-Step Differential Transform Method and Rk4 Method

Numerical Simulation of Dengue Fever (Sir Model) Using Differential Transform Method, Multi-Step Differential Transform Method and Rk4 Method

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Describe the Mathematical Model for Exchanging Waves Between Bacterial and Cellular DNA

Contact Info

Product

Resources

About