MASTER’S THESIS

Md Tariqul Islam

Matriculation Number: 218100921

Mathematical Modeling of Complex Systems

Email- tariquldipu@uni-koblenz.de

Universität Koblenz - Landau, Germany

Topic- Mathematical Modeling and Simulation of A Zombie Epidemic

This repository contains all the code files that were written during the Master's Thesis for various mathematical analysis and calculation purposes.

All the codes are available in two formats. Firstly, the codes are available in Anaconda Jupyter Notebook (as in .ipynb) format and are organized inside the Jupyter folder. The codes and their outputs are also saved in PDF formats inside this directory.

And secondly, the codes are also available as separate python files (as in .py format) and are organized in different folders as per their chapter names.

Some brief information about each and every code file are provided below--

Chapter02

1. SIR_model.py- Provides numerical solution for the SIR Model.
2. SIR_PhasePortrait.py- Draws phase portrait for the SIR model.

Chapter03

1. Basic_SZR_PhasePortrait.py- Draws phase portrait for the SZR model.
2. Basic_SZR_solution.py- Provides numerical solution for the SZR Model.
3. PerturbedSZR_PhasePortrait_GUI.py- Interactive graphical interface for the Perturbed SZR model.
4. PerturbedSZR_PhasePortrait.py- Draws phase portrait for the perturbed SZR model.
5. PerturbedSZR_Relation_ZombieWithMU.py- Shows first relation between zombie population and perturbation parameter for the perturbed SZR model.
6. PerturbedSZR_Relation_ZombieWithMu02.py- Shows second relation between zombie population and perturbation parameter for the perturbed SZR model.
7. PerturbedSZR_solution.py- Provides numerical solution for the perturbed SZR model.
8. PerturbedSZR_StabilityCheck_Bifurcation.py- Checks stability condition and draws the bifurcation diagram for the perturbed SZR model.

Chapter04

1. InverseMatrix.m- Calculates inverse matrix, determinant and adjugate matrix for the modified SEZQR model. This is a Matlab/Octave source file.
2. ModifiedSEZQR_Bifurcation.py- Draws the bifurcation diagram for the modified SEZQR model.
3. ModifiedSEZQR_PhasePortrait.py- Draws the phase portrait for the modified SEZQR model.
4. ModifiedSEZQR_Relation_ZombieWithMu.py- Shows first relation between zombie population and perturbation parameter for the modified SEZQR model.
5. ModifiedSEZQR_Relation_ZombieWithMu02.py- Shows second relation between zombie population and perturbation parameter for the modified SEZQR model.
6. ModifiedSEZQR_Solution.py- Provides numerical solution for the modified SEZQR model.
7. ModifiedSEZQR_SpecialCase.py- Provides numerical solution for the special case of the modified SEZQR model.
8. SEZQR_Bifurcation.py- Draws bifurcation diagram for the SEZQR model.
9. SEZQR_Solution.py- Provides numerical solution for the SEZQR model.

Jupyter

Inside this directory, all the code files are provided as Anaconda Jupyter Notebook file formats. The PDF folder contains all the codes and their outputs within the notebook files as simple pdf files.

1. ModifiedSEZQR_Model.ipynb- Contains all the relevant codes for the modified SEZQR model (chapter 04).
2. ModifiedSEZQR_SpecialCase.ipynb- Contains all the codes for the special cases of the modified SEZQR model (chapter 04).
3. PerturbedSZR_model.ipynb- Contains all the relevant codes for the perturbed SZR model (chapter 03).
4. PerturbedSZR_PhasePortrait_GUI.ipynb- The interactive graphical user interface program for drawing the phase portraits of the perturbed SZR model (chapter 03).
5. SEZQR_model.ipynb- Contains all the codes for the SEZQR model (chapter 04).
6. SIR_model.ipynb- Contains all the codes for the basic SIR model (chapter 02).
7. SZR_model.ipynb- Contains all the codes for the SZR model (chapter 03).