Iterative approximate solutions of kinetic equations for reversible enzyme reactions

Khoshnaw, Sarbaz H. A.

doi:10.4236/ns.2013.56091

Cited by 6 publications

(7 citation statements)

References 19 publications

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“…Figure 6 shows the dynamics behaviours at an affine plane and also at infinity, which exams a good understanding of the global behaviours of the Equation (12). We note that, the sum of the ratio of eigenvalues of either line is unity according to an index formula Lins Neto [39].…”

Section: The Global Behaviours Of the Simplified Modelmentioning

confidence: 99%

“…The SIR epidemic disease model is given as the non-linear system of ODE's. Equation (12) can not be solved analytically. Therefore, calculating some analytical approximate solutions for the system provides more information about the behaviours of the model dynamics.…”

Section: The Sir Epidemic Disease Modelmentioning

confidence: 99%

“…Therefore, calculating some analytical approximate solutions for the system provides more information about the behaviours of the model dynamics. Applying the idea of Elzaki transform, we can obtain some analytical approximate solutions of the Equation (12). Take Elzaki transform of Equation (12) to get:…”

Section: The Sir Epidemic Disease Modelmentioning

confidence: 99%

“…(20) and (21) respectively. These are the singular points of the new system that are corresponding to the singular points at infinity for simplified Equation (12).…”

Section: The Global Behaviours Of the Simplified Modelmentioning

confidence: 99%

“…We use Pplane8 for Mathlab to study the stability analysis of the Equation (12) and to compute numerical simulations in * * S I -plane, we also identify model nullclines; see Figure 2. It can be concluded that the model has the same stability properties at different values for the parameter used.…”

Section: Local Behaviours Of the Simplified Modelmentioning

confidence: 99%

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Identifying Critical Parameters in SIR Model for Spread of Disease

Khoshnaw¹,

Mohammad²,

Salih³

2017

OJMSi

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Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some theoretical and practical applications in systems biology. They represent key critical elements and give some approximate solutions for such systems. The SIR epidemic disease model is given as the non-linear system of ODE's. Then, we use a proper scaling to reduce the number of parameters. We suggest Elzaki transform method to find analytical approximate solutions for the simplified model. The technique plays an important role in calculating the analytical approximate solutions. The local and global dynamics of the model are also studied. An investigation of the behaviour at infinity was conducted via finding the lines and singular points at infinity. Model dynamic results are computed in numerical simulations using Pplane8 and SimBiology Toolbox for Mathlab. Results provide a good step forward for describing the model dynamics. More interestingly, the simplified model could be accurate, robust, and used by biologists for different purposes such as identifying critical model elements.

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Section: The Global Behaviours Of the Simplified Modelmentioning

confidence: 99%

Section: The Sir Epidemic Disease Modelmentioning

confidence: 99%

Section: The Sir Epidemic Disease Modelmentioning

confidence: 99%

“…(20) and (21) respectively. These are the singular points of the new system that are corresponding to the singular points at infinity for simplified Equation (12).…”

Section: The Global Behaviours Of the Simplified Modelmentioning

confidence: 99%

Section: Local Behaviours Of the Simplified Modelmentioning

confidence: 99%

See 3 more Smart Citations