Solutions of the SIR models of epidemics using HAM

Awawdeh, Fadi; Adawi, A.; Mustafa, Zead

doi:10.1016/j.chaos.2009.04.012

Cited by 54 publications

(33 citation statements)

References 10 publications

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“…They mainly focused on presenting effective mathematical methods in order to solve the corresponding differential equations [49,[55][56][57]. For instance, in [57] a mathematical tool (the multistep generalized differential transform method) is introduced to approximate the numerical solution of the SIR model with fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

et al. 2017

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Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume "fully mixed" approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory "length" decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a "constraint" is analyzed and discussed.

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Section: Introductionmentioning

confidence: 99%

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

et al. 2017

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“…In the past, HAM has been successfully used to solve many problems in science and engineering [8][9][10][11][12][13][14][15], and also in epidemic models such as SIR [16] and SIS models [17].…”

Section: Introductionmentioning

confidence: 99%

Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Guerrero

Santonja

Micó

2013

Nonlinear Analysis: Real World Applications

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. a b s t r a c tWe obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Padé technique. We present and discuss graphical results for our solutions.

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“…The graphical results in all the studies [4][5][6][7] reveal that the results are valid for small values of time and beyond that these analytic expressions fail to give results that can be compared with the existing numerical solutions. However, the authors in [1] obtained same expressions as presented in [4][5][6][7], but the graphical results are different from all these studies which are not possible. Thus Figure 1 present in [1] is not found through 20-term HAM solution.…”

Section: Introductionmentioning

confidence: 44%

“…The constant population in SIR model is divided into susceptible, infectious, and recovered classes [2,3]. The expressions for the susceptible, infectious, and recovered population presented in [1] for five-and nine-term HAM solutions clearly indicate that, for = 0, the initial population size is 20, 15, and 10, respectively. However, Figure 1 illustrates a different population size.…”

Section: Introductionmentioning

confidence: 99%