My primary area of study is Mathematical Oncology, focusing on the modeling and analysis of cancer dynamics through Reaction-Diffusion Equations. My current work uses physics-informed strategies, but my future work aims to utilize methods such as Sparse Identification of Nonlinear Dynamics (SINDy) to uncover underlying mechanisms and predict tumor behavior. This work aims to optimize cancer treatment strategies and improve therapeutic outcomes. More information about my previous and ongoing research projects is provided below. 

Current Projects

     Title: A Reaction-Diffusion Model of Vascular Tumor Growth: Bifurcation, Stability, Periodic Behavior, and Relapse

Summary: This study explores the effectiveness of chemotherapy and anti-angiogenic therapy in controlling cancer growth using an extended Reaction-Diffusion (RD) model. Incorporating cell growth dynamics and metastasis through angiogenesis, the model refines the original framework by Pinho et al. Numerical simulations, assess tumor dynamics and therapeutic outcomes, offering insights into stability, bifurcation behavior, and optimized treatments.

        This project is currently being developed into a research paper with collaborators Dr. Bani-Yagoub and Dr. Bi-Botti Youan                      (manuscript in preparation).

Key Highlights:

• • • Incorporation of extended logistic growth models.

    • Reaction-diffusion dynamics for metastasis and angiogenesis.

    • Stability and bifurcation analysis to identify treatment thresholds.

Tools & Techniques: MATLAB PDE solver, numerical simulations, bifurcation analysis, mathematical modeling.

Collaborators: Dr. Bani-Yagoub, Dr. Bi-Botti Youan.

Outcome:  Presented in the 9th Annual Meeting of SIAM Central States Section https://sse.umkc.edu/siam-2024/

 Completed Projects

     Title: Effectiveness of Chemotherapy and Anti-Angiogenic Therapy in Controlling Cancer Growth

Summary: This study investigates the effectiveness of chemotherapy and anti-angiogenic therapy in controlling cancer growth through an extended mathematical model. Numerical simulations, utilizing MATLAB’s ODE45 and the Runge-Kutta method, explore how healthy cell growth behaviors influence vascular tumor dynamics under varying initial conditions. The findings provide insights into therapeutic strategies and tumor growth patterns, contributing to ongoing advancements in cancer modeling.

Key Highlights: Modeled cell growth dynamics.

Tools & Techniques: Runge-Kutta method, MATLAB ODE 45 solver.

Outcome: Presented at the 10th Annual UMKC Math and Stat Research Day. https://sites.google.com/view/mathrd/home

   Future Directions

     Transitioning from Physics-Informed to Data-Driven Cancer Modeling using Sparse Identification of Nonlinear Dynamics (SINDy) and SINDy-c.

Objectives:

• • • Build models using data from literature to predict cancer dynamics.

    • Identify effective treatment strategies to prevent relapse.

    • Collaborate with medical researchers to parameterize models using patient data.

Tools & Techniques: PySINDy, sparse regression, Reaction-diffusion modeling, Sparse Identification of Nonlinear Dynamics (SINDy), SINDy with Control (SINDy-c).

    Software: MATLAB, Python (PySINDy), WebPlotDigitizer, LaTeX.

    Data Sources: Literature-based data extraction.           

         Anticipated Impact: Develop personalized therapeutic strategies and optimize cancer treatment protocols.

 Publications & Presentations

• Sekyere, P. O., Bani-Yaghoub, M., Youan, B. C. A Reaction-Diffusion Model of Vascular Tumor Growth: Bifurcation, Stability, Periodic Behavior, and Relapse (manuscript in preparation).

•  The 9th Annual Meeting of SIAM Central States Section https://sse.umkc.edu/siam-2024/

• The 10th Annual UMKC Math and Stat Research Day. https://sites.google.com/view/mathrd/home