| dc.description.abstract | Despite the success of traditional cancer treatments, a definite cure to several cancers
does not exist. Further, the traditional cancer treatments are highly toxic
and have a relatively low efficacy. Current research and clinical trials have indicated
that virotherapy, a procedure which uses replication-competent viruses
to kill cancer cells, is less toxic and highly effective. Some recent studies suggest
that the success of combating cancer lies in the understanding of tumour-immune
interactions. However, the interaction dynamics of recent cancer treatments with
the tumour and immune system response are still poorly understood.
In this thesis we construct and analyse mathematical models in the form of ordinary
and partial differential equations in order to explain tumour invasion dynamics
and new forms of cancer treatment. We use these models to suggest
possible measures needed in order to combat cancer. The thesis seeks to determine
the most critical biological factors during tumour invasion, describe how the
virus and immune system response influences the outcome of oncolytic virotherapy
treatment, investigate how drug infusion methods determine the success of
chemotherapy and virotherapy, and determine the efficacy of chemotherapy and
virotherpy in depleting tumour cells from body tissue.
We present a travelling wave analysis of a tumour-immune interaction model with
immunotherapy. Here we aim to investigate the existence of travelling wave solutions
of the model equations with and without immunotherapy and calculate the
minimum wave speed with which tumour cells invade healthy tissue. This investigation
highlights the properties which are most vital during tumour invasion.
We use the geometric treatment of an apt-phase space to establish the intersection
between stable and unstable manifolds. Numerical simulations are performed
to support the analytical results. The analysis reveals that the main factors involved
during tumour invasion include the tumour growth rate, resting immune
cell growth rate, carrying capacity of the resting immune cells, resting cell supply,
diffusion rate of the tumour cells, and the local kinetic interaction parameters. We
also present a mathematical analysis of models that study tumour-immune-virus
interactions using differential equations with spatial effects. The major aim is to
investigate how virus and immune responses influence the outcome of oncolytic
treatment. Stability analysis is carried out to determine the long term behaviour
of the model solutions. Analytical traveling wave solutions are obtained using
factorization of differential operators and numerical simulations are carried out
using Runge-Kutta fourth order method and Crank-Nicholson methods. Our results
show that the use of viruses as a means of cancer treatment can reduce the
tumour cell concentration to a very low cancer dormant state or possibly eradicate
all tumour cells in body tissue. The traveling wave solutions indicate an
exponential increase and decrease in the immune cells density and tumour load
in the long term respectively.
A mathematical model of chemovirotherapy, a recent experimental treatment
which combines virotherapy and chemotherapy, is constructed and analyzed. The
aim is to compare the efficacy of three drug infusion methods and predict the
outcome of oncolytic virotherapy-drug combination. A comparison of the efficacy
of using each treatment individually, that is, chemotherapy and virotherapy,
is presented. Analytical solutions of the model are obtained where possible and
stability analysis is presented. Numerical solutions are obtained using the Runge-
Kutta fourth order method. This study shows that chemovirotherapy may have a
higher chance of reducing the tumour cell density in body tissue in a relatively
short time. To the best of our knowledge, there has not been a mathematical study
on the combination of both chemotherapy and virotherapy.
Lastly, the chemovirotherapy model is extended to include spatial distribution
characteristics, thus developing a model which describes avascular tumour growth
under chemovirotherapy in a two dimensional spatial domain. Numerical investigation
of the model solutions is carried out using a multi domain monomial
based collocation method and pdepe, a finite element based method in Matlab.
This study affirmed that chemovirotherapy may possibly eradicate all tumour
cells in body tissue. | en_US |
