Abstract:
This thesis investigates the role of spatial pattern formation in tumor{immune and
predator{prey systems. In the rst half of the thesis, we have proposed spatiotemporal
mathematical models using a system of non-linear partial di erential equations
(reaction-di usion equations), to study the qualitative and quantitative analysis of
tumor{immune interaction, and predator{prey interaction, considering the role of
di usion and other system parameters. The tumor{immune interaction consists
of two separate problems, namely, (i) interaction of solid tumor and e ector cells
(ii) interaction of malignant gliomas and four immune components with the administration
of immunotherapeutic agent T11 target structure (T11TS). Using the
combination of analytical and numerical techniques, we investigate spatiotemporal
dynamics due to the e ect of e ector cells and T11 target structure on the growth
and spread of solid tumor and malignant gliomas respectively. However, Turing zone
is absent in both the problems.
The second half of the thesis consists of di usive predator{prey system (i) with
hunting cooperation in predators and (ii) exhibiting herd behavior for prey with
linear and quadratic mortality. Using extensive numerical simulations, we obtain
complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the
Turing domain by varying (a) hunting cooperation parameter and (b) linear and
quadratic mortality's rates respectively. We also have a non-Turing pattern that
exhibits spatiotemporal chaos. Thus, the study of the predator{prey system focusses
in many pattern dynamics and help in better understanding of their interaction in
real environment.
