Modification of the random differential transformation method and its applications to compartmental models

Stability and Numerical Solutions of Second Wave Mathematical Modeling on COVID-19 and Omicron Outbreak Strategy of Pandemic: Analytical and Error Analysis of Approximate Series Solutions by Using HPM

“…M. A. Khan, A. Atangana [26], A Mathematical Modeling of novel Corona-virus (2019-nCoV) is studied with numerical simulation and asymptomatic carrier transmission [27]. The compartment models are defined by [28] with phase based [29]. The numerical data's are in all countries, we used this procedure the calculations [30][31][32].…”

A modification of approximate random characteristics for a model of Zika virus transmission

“…The modified random DTM has been recently introduced and the method relies upon the Laplace-Pade modification of the random DTM [8]. Assume that the fourth order stochastic process u(t), t ∈ T has a mean fourth derivative of a non-negative integer order k at t ∈ T denoted by u (k) (t).…”

“…Random effects can be implemented into the system to model the variations in disease dynamics. The motivation for such an analysis is the previous studies of the authors [8,9]. Using a random framework, it is possible to analyze various random disease characteristics such as expected time for disease eradication or expected spread of disease in the total population as well as other concepts in engineering [10].…”

“…The MRDTM is the modification of DTM in the random framework using Laplace-Pade modification technique. Random DTM has been used to analyze random differential equations by many researchers [14,8]. Its modification, MRDTM, is an improved method for obtaining approximate characteristics of random equations.…”

Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

“…The concept of differential transform method was first proposed by Zhou [33] in 1986 and it was applied to solve linear and non-linear initial value problems in electric circuit analysis and later it was used to solve linear and non-linear initial value problems, boundary value problems, fractional order derivative problems, fluid flow models and so on, one can refer [1,5,12,15,21,23,24,26,27,29] and references therein for history and properties of DTM. Also, at the present time, this method get much attention to solve SIS (susceptible-infectedsusceptible) and SI (susceptible-infected) epidemic models [2,3], SIR (susceptible-infectedrecovered) epidemic models [16,28], influenza epidemic model [18], compartmental models [7], transmission of seasonal diseases model [4], analysis of computer virus propagation model [24], the transmission dynamical of syphilis disease model [17], SEIR (susceptible-exposed -infectedrecovered) epidemic model [14], SAEIQRS (susceptible-antidotal-exposed-infected-quarantinedrecovered-susceptible) model [8] and for HBV infection model [?, 11], also one can refer the references therein for more details. To speak about the advantages and generic nature of the DTM, it is worthwhile to mention that the method can be applied to linear and nonlinear ODEs not requiring discretization, linearization or perturbation.…”