# Jose Tapia Quijada: Stability Analysis of Dynamic Mathematical Models in Systems Biology

MsC Project

**Time: **
Tue 2020-03-31 11.00 - 12.00

**Lecturer: **
Jose Tapia Quijada

**Location: ** Zoom, Meeting ID: 918 620 631

**Supervisor: **
Yishao Zhou

### Abstract

In this thesis, we analyze the dynamical behaviour of two biological systems, the three dimensional model of circadian rhythms in drosophila and the breast cancer model. Phase plane analysis and Bifurcation theory are applied to investigate the model of the circadian rhythm. Stability analysis on steady states, Center Manifold theorem and Bifurcation theory, are applied to study the dynamics of breast tumor in the presence and absence of estrogen supplements. We described the process via mathematical models in the form of differential equations when no external estrogen is supplied as well as in the case when external estrogen supplements are incorporated. Numerical simulations using R and Python are presented to validate our theoretical results. Finally, the anti-cancer drug parameter was included in the breast cancer model, and numerical simulations were done variating the parameter to ensure cancer persistence in the presence of an anti-cancer drug.