A fitted numerical method for a model arising in HIV-related cancer-immune system dynamics
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Tianjin Polytechnic University
Abstract
The effect of diseases such as cancer and HIV among our societies is evident. Thus, from the mathematical
point of view many models has been developed with the aim to contribute towards understanding the dynamics
of diseases. Therefore, in this paper we believe by extending a system of delay differential equations (DDEs)
model of HIV related cancer-immune system to a system of delay partial differential equations (DPDEs) model of
HIV related cancer-immune dynamics, we can contribute toward understanding the dynamics more clearly. Thus,
we analyse the extended models and use the qualitative features of the extended model to derive, analyse and implement
a fitted operator finite difference method (FOFDM) and present our results. This FOFDM is analyzed for
convergence and it is seen that it has has second-order accuracy. We present some numerical results for some cases
of the the model to illustrate the reliability of our numerical method.
Description
Keywords
Reaction-diffusion, Delay differential equations, Cancer-immune system, Stability analysis, HIV/AIDS
Citation
Kolade, M. 2019. A fitted numerical method for a model arising in HIV-related cancer-immune system dynamics. Commun. Math. Biol. Neurosci., 2019:1. doi: https://doi.org/10.28919/cmbn/3866