A Mathematical Model for the Effects of Incubation and Chemotherapy on the Dynamics of Tumor Growth

Abstract

The application of mathematical models in simulating processes that are biological in nature has been in effect for a long time. A great number of mathematical, Computational, Engineering and Physical approaches have been administered to several aspects of cancerous tumour development , with a view of appreciating how cancer cell population responds to medical intervention. In most of these models however, no much attention was given to the effects of incubation in the presence of chemotherapy on the dynamics of tumour growth. This research therefore considered a mathematical model for the consequences of incubation and Chemotherapy on cancerous tumour growth dynamics by formulating a deterministic S (susceptible), E (exposed), I (infectious), R (removed) model using Delay differential equations. The delay or incubation in this case accounted for the duration between the exposure of a cell to cancer causing viruses and the onset of disease symptoms. Reproduction number (R0) of the model was ascertained using next generation matrix approach. The stability analysis of Cancer Free Equilibrium Point (CFEP) and Cancer Endemic Equilibrium Point (CEEP) of the model were also investigated. MATLAB software was used for numerical simulations to validate the analytic results. The investigation and analysis of the consequences of incubation and Chemotherapy on the stability of the equilibrium points was also done. From the numerical findings it was found that R0 at CFEP was obtained at 0.6667 and at 1.1037 the CEEP was stable. This study of tumour growth dynamics was significant in that it helps establish the stage and the extent of cancer spread within the body cells. It shall also help develop a better drug administration procedure as well as provide mechanistic insights. Parameter values used were mostly hypothetical values.