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Modelling the aggregation process of cellular slime mold by the chemical attraction.

Atangana A, Vermeulen PD - Biomed Res Int (2014)

Bottom Line: We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system.Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values.The reliability of HDM and the reduction in computations give HDM a wider applicability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa.

ABSTRACT
We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM and the reduction in computations give HDM a wider applicability.

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Biological behaviour of concentrations of the chemical substance and amoebae as function of space.
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fig1: Biological behaviour of concentrations of the chemical substance and amoebae as function of space.

Mentions: Figures 1, 2, and 3 show the behaviour of the solution of the system of (15) describing the concentrations of the chemical substance and the amoebae in the human body. While on one hand, Figure 1 shows the behaviour as function of space, Figures 2 and 3 show the behaviour of these solutions as function of time. From the above figures, one can see that the concentration of amoebae reduces in space as the concentration of the chemical substance reduces. This simply implies that if the concentration of the chemical substance introduced in the human system to combat the spread of the disease is not sufficient enough, the amoebae will spread all over and the patient will certainly die. However, if this concentration is sufficient enough, the amoebae will decrease in space. It is observed from the graphical representation that the approximate solutions obtained here display the behaviour of the real world problem.


Modelling the aggregation process of cellular slime mold by the chemical attraction.

Atangana A, Vermeulen PD - Biomed Res Int (2014)

Biological behaviour of concentrations of the chemical substance and amoebae as function of space.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4121043&req=5

fig1: Biological behaviour of concentrations of the chemical substance and amoebae as function of space.
Mentions: Figures 1, 2, and 3 show the behaviour of the solution of the system of (15) describing the concentrations of the chemical substance and the amoebae in the human body. While on one hand, Figure 1 shows the behaviour as function of space, Figures 2 and 3 show the behaviour of these solutions as function of time. From the above figures, one can see that the concentration of amoebae reduces in space as the concentration of the chemical substance reduces. This simply implies that if the concentration of the chemical substance introduced in the human system to combat the spread of the disease is not sufficient enough, the amoebae will spread all over and the patient will certainly die. However, if this concentration is sufficient enough, the amoebae will decrease in space. It is observed from the graphical representation that the approximate solutions obtained here display the behaviour of the real world problem.

Bottom Line: We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system.Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values.The reliability of HDM and the reduction in computations give HDM a wider applicability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa.

ABSTRACT
We put into exercise a comparatively innovative analytical modus operandi, the homotopy decomposition method (HDM), for solving a system of nonlinear partial differential equations arising in an attractor one-dimensional Keller-Segel dynamics system. Numerical solutions are given and some properties show evidence of biologically practical reliance on the parameter values. The reliability of HDM and the reduction in computations give HDM a wider applicability.

Show MeSH