The interaction model is deduced from the concept of the flux motion of heat transfer, and the movement is constrained by space limitation. Furthermore, we analyze the model to obtain the behavior of two-cell populations at time close to initial state and far into the future.
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References
1.
BottinoD.C., FauciL. J.1998. A computational model of ameboid deformation and locomotion. Eur. Biophys. J., 27:532–539.
2.
BottinoD., MogilnerA., RobertsT.et al.2002. How nematode sperm crawl. J. Cell Sci., 115:367–384.
3.
ChaplainM.A.J., StuartA.M.1993. A model mechanism for the chemotactic response of endothelial cells to tumor angiogenesis factor. IMA J. Math. Appl. Med. Biol., 10:149–168.
4.
HillenT., OthmerH.G.2000. The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math., 61:751–775.
5.
HöferT., SherrattJ.A., MainiP.K.1995. Dictyostelium discoideum: cellular self-organization in an excitable biological medium. Proc. Biol. Sci., 259:249–257.
6.
KellerE.F., SegelL.A.1970. Initiation of slide mold aggregation viewed as an instability. J. Theor. Biol., 26:99415.
7.
MazumdarJ.1999. An Introduction to Mathematical Physiology and Biology. Combridge University Press: Combridge, UK.
8.
OsterG.1984. On the crawling of cells. J. Embryol. Exp. Morphol., 83:329–364.
9.
OsterG., PerelsonA.1985. Cell spreading and motility: a model lamellipod. J. Math. Biol., 21:383–388.
10.
PainterK.J., MainiP.K., OthmerH.G.2000. A chemotactic model for the advance and retreat of the primitive streak in avian development. Bull. Math. Biol., 62:501–525.
11.
PainterK.J., SherrattJ.A.2003. Modelling the movement of interacting cell populations. J. Theor. Biol., 225:327–339.
12.
PettetG.J., ByrneH.M., McElwainD.L.S.et al.1996. A model of wound-healing angiogenesis in soft tissue. Math. Biosci., 136:35–63.
13.
LiM.-R., LinY.-J., ShiehT.-H.2010. The space-jump model of the movement of tumor cells and health cells (Preprint).
14.
LiM.-R.2008. Estimates for the life-span of the solutions of some semilinear wave equations. Commun. Pure Appl. Anal., 7:417–432.
15.
DuanR., LiM.-R., YangT.2008. Propagation of singularities in the solutions to the Boltzmann equation near equilibrium. Math. Models Methods Appl. Sci., 18:1093–1114.
16.
ShiehT.H., LiouT.M., LiM.R.et al.2009. Analysis on numerical results for stage separation with different exhaust holes. Int. Commun. Heat Mass Transfer, 36:342–345.
17.
LiM.-R., ChangY.L.2007. On a particular Emden-Fowler equation with non-positive energy—Mathematical model of enterprise competitiveness and performance. Appl. Math. Lett., 20:1011–1015.
18.
LiM.-R., PaiJ.-T.2008. Quenching problem in some semilinear wave equations. A. MATH. SCI., 28:523–529.
