Brief Description ...

Mathematical Biology is an active and growing research area in general. My research interests in Mathematical biology focus Mathematical immunology, epidemiology, spatial ecology and population dynamics. I am interested in using theoretical, statistical and computational techniques to understanding the evolution and spread of diseases and controlling their extinctions. I embrace a multidisciplinary approach to problems, employing microbiological research, behavioral and social science, network analysis, mathematical modeling, computer simulations and theoretical frameworks. Click here for More ...

Computational Methods: This research interest within the Analysis of Differential Equations concentrates on nonlinear problems. The focus is on rigorous analysis of mathematical models motivated from applied mathematics involving nonlinear differential equations, dynamical systems, evolution equations and financial mathematics. Click here for more ...

Mathematical Physiology: Dr. Annan is modeling renal physiology which focuses on Blood Flow, Hemodialysis and Acid-Base Balance in End-Stage Renal Diseases (ESRD) Patients. The dynamic models are to capture key physiological processes that may be involved in acid-base homeostasis associated with ESRD, and show how they are formulated. Most ESRD patients receiving dialysis therapy are in a state of constant metabolic acidosis which is associated with high cardiovascular morbidity and mortality. The modeling mechanisms involve coupled transient partial differential equations (PDEs) that describe convection-diffusion and solute concentration transports. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiogists in many experimental trials. The models aim to gain insight into the factors regulating body bicarbonate stores in patients receiving hemodialysis treatment, and to use this knowledge to construct testable mathematical models that will allow us to investigate, in more detail, (i) the overall nature of solute exchange across dialysis membranes, (ii) the body's response to the alkalinization during the dialysis (intradialytic) session, (iii) the events influencing body alkali stores during the post-dialysis (interdialytic) period, and (iv) the overall variation in solute exchange between dialysate, blood and the body compartments. Click here for more ...

Mathematics Education: Dr. Annan’s research interest in this field is Mathematics teaching and learning. It focuses on the idea that learning takes place when students are actively engaged with each other, their teachers, and others in conversations, activities and content. He is very interested in the power of real-world contexts to drive learning, and researches how design thinking and technologies could become a powerful and effective pedagogy in K-12 classrooms. Click here for more ...

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