# h-Discrete Fractional Model of Tumor Growth and Anticancer Effects of Mono and Combination Therapies

## Publication Date

Spring 2020

Dr. Ferhan Atici (Director), Dr. Mark Robinson, and Dr. John Spraker

## Degree Program

Department of Mathematics

## Degree Type

Master of Science

## Abstract

In this thesis, we focus on h–discrete and h–discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model which describes tumor growth considering time on hNa, where h>0. First, we introduce some deﬁnitions, lemmas and theorems on both h–discrete and h–discrete fractional calculus in the preliminary section. In Chapter 3, we work on the PD model with delay by exam ining nabla h–discrete equations and nabla h–discrete fractional equations as well as variation of constants formulas, accordingly. We introduce our model and solve it using theorems we proved in the last section of the indicated chapter. When we do simulation for the solutions we found that jumps occur when drug was given the ﬁrst time. Therefore, we decide to work on PD model without delay in Chapter 4. We also obtain theorems regarding nabla h–discrete equations and nabla h–discrete fractional equations ignoring delay. We apply our results to the tumor growth model to ﬁnd solutions. We observe that jumps disappear on this model once we put new solutions into code. Although, we do not attain our wanted goal for tumor growth model having delay, we decide to write it as a chapter in this thesis because the theorems and lemmas found in Chapter 3 might be useful for another research work in the future. In Chapter 5, we give our PK model considering both delay and without delay case, then solutions of the models are stated accordingly. In the last chapter, we summarize what we have done so far and mention future works regarding continuation of this work.

## Disciplines

Applied Mathematics | Discrete Mathematics and Combinatorics | Disease Modeling | Medical Pharmacology | Other Mathematics

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