- Title
- Mathematical modelling of the tumour treatment with chemotherapy
- Creator
- Nyaweni, Fundile Sindy
- Subject
- Mathematical models
- Subject
- Mathematics
- Subject
- Chemotherapy
- Date Issued
- 2024-04
- Date
- 2024-04
- Type
- Master's theses
- Type
- text
- Identifier
- http://hdl.handle.net/10948/64289
- Identifier
- vital:73672
- Description
- In this study, a cancer disease model incorporating predator-prey dynamics between immune cells and tumor cells, as well as competition between tumor cells and normal cells, is formulated in an attempt to understand the interaction dynamics that govern the complex interplay within the tumor microenvironment. Mathematical analysis is employed to derive conditions for the boundedness of solutions and to discuss disease thresholds such as the basic reproduction number, R0. Equilibrium points are identified, and stability conditions for the system are derived. Sensitivity analysis is used to assess uncertainties in the parameters of the model, specifically their impact on R0. Numerical simulations are conducted, utilizing the Runge-Kutta scheme to solve the model. Furthermore, optimal control (OC) techniques are applied to examine the role of chemotherapy in enhancing tumor cell elimination and minimizing adverse effects on immune cells and normal cells. The improved model, incorporating normal cells, anticancer drugs, and immune cells, allows for a more comprehensive analysis of the dynamic interactions within the biological system. The optimal control is determined using the forward-backward sweep numerical method. The numerical simulation is carried out in MATLAB to validate and complement the analytical findings. The results indicate that a low concentration of the drug leads to a prolonged period for tumor clearance. Conversely, a higher drug concentration results in quicker tumor clearance, albeit with adverse effects on normal and effector cells. The OC identifies when to stop the treatment once the tumor clears. Furthermore, OC facilitates the regeneration of normal and immune cells beyond treatment, in contrast to a control scenario without optimization. The findings highlight the importance of early detection and careful chemotherapy dosage selection for effective and personalized cancer treatment strategies.
- Description
- Thesis (MSc) -- Faculty of Science, School Computer Science, Mathematics, Physics and Statistics, 2024
- Format
- computer
- Format
- online resource
- Format
- application/pdf
- Format
- 1 online resource (125 pages)
- Format
- Publisher
- Nelson Mandela University
- Publisher
- Faculty of Science
- Language
- English
- Rights
- Nelson Mandela University
- Rights
- All Rights Reserved
- Rights
- Open Access
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NMU School of Computer Science, Mathematics, Physics and Statistics
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Nyaweni, FS.pdf | 2 MB | Adobe Acrobat PDF | View Details Download |