A fitted operator method for tumor cells dynamics in their micro-environment

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dc.contributor.authorKolade, Owolabi
dc.contributor.authorKailash, Patidar
dc.contributor.authorShikongo, Albert
dc.date.accessioned2020-06-04T15:01:40Z
dc.date.available2020-06-04T15:01:40Z
dc.date.issued2019
dc.description.abstractIn this paper, we consider a quasi non-linear reaction-diffusion model designed to mimic tumor cells’ proliferation and migration under the influence of their micro-environment in vitro. Since the model can be used to generate hypotheses regarding the development of drugs which confine tumor growth, then considering the composition of the model, we modify the model by incorporating realistic effects which we believe can shed more light into the original model. We do this by extending the quasi non-linear reaction-diffusion model to a system of discrete delay quasi non-linear reaction-diffusion model. Thus, we determine the steady states, provide the conditions for global stability of the steady states by using the method of upper and lower solutions and analyze the extended model for the existence of Hopf bifurcation and present the conditions for Hopf bifurcation to occur. Since it is not possible to solve the models analytically, we derive, analyze, implement a fitted operator method and present our results for the extended model. Our numerical method is analyzed for convergence and we find that is of second order accuracy. We present our numerical results for both of the models for comparison purposes.en_US
dc.identifier.citationKolade, M. 2019. A fitted operator method for tumor cells dynamics in their micro-environment. Commun. Math. Biol. Neurosci. 2019:18. doi: https://doi.org/10.28919/cmbn/3885en_US
dc.identifier.urihttps://doi.org/10.28919/cmbn/3885
dc.identifier.urihttp://hdl.handle.net/10566/5220
dc.language.isoenen_US
dc.publisherTianjin Polytechnic Universityen_US
dc.subjectTumor cellsen_US
dc.subjectMicro-environmenten_US
dc.subjectHopf bifurcationen_US
dc.subjectStability analysisen_US
dc.subjectNumerical methodsen_US
dc.subjectMathematical modellingen_US
dc.titleA fitted operator method for tumor cells dynamics in their micro-environmenten_US
dc.typeArticleen_US

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