ECTS - Mathematical Models in Biology
Mathematical Models in Biology (MATH670) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Models in Biology | MATH670 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of the course is to describe the application of mathematical theory in difference and differential equations to biological phenomena. No knowledge of biology, and only basic knowledge in calculus, differential equations and linear algebra are required. The use of mathematics in biological sciences will be analyzed by using several mathematical models of biological systems |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Linear and nonlinear biological models via difference equations; linear and nonlinear biological models via differential equations; special topics in mathematical biology including predator-prey models, SI,SIS,SIR epidemic models, competition models of two and three species, Van Der Pol equation, Hodgkin-Huxley and FitzHugh-Nagumo models. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Linear difference equations: Basic definitions, first order equations, second order and higher-order equations | 1-14 |
| 2 | Linear difference equations: Firs-order linear systems; Leslie’s age-structure model; properties of Leslie matrix | 14-28 |
| 3 | Nonlinear difference equations: Basic definitions; Local stability in first-order equations | 36-45 |
| 4 | Nonlinear difference equations: A discrete-time SIR epidemic model | 69-73 |
| 5 | Biological applications of difference equations: Population models, Nicholson-Bailey model, predatory-prey model | 89-96, 99-103 |
| 6 | Linear ordinary differential equations: Routh-Hurwitz criteria, phase-plane analysis, Gershgorin’s theorem, Pharmacokinetics model | 150-152, 157-165 |
| 7 | Nonlinear ordinary differential equations: Basic definitions, local stability of first-order equations, | 177-184 |
| 8 | Midterm | |
| 9 | Nonlinear ordinary differential equations: Phase-Line diagram, local stability of first-order systems, | 184-191 |
| 10 | Nonlinear ordinary differential equations: Phase plane analysis, Periodic solutions | 191-198 |
| 11 | Biological applications of differential equations: Predatory-prey model | 240-248 |
| 12 | Biological applications of differential equations: Competitions models for two and three species | 248-253 |
| 13 | Biological applications of differential equations: Epidemic models (SI,SIS,SIR models) | 271-279 |
| 14 | Biological applications of differential equations: Excitable systems (Van Der Pol equation, Hodgkin-Huxley and FitzHugh-Nagumo models) | 279-283 |
| 15 | Review | |
| 16 | Final |
Sources
| Course Book | 1. L.J.S. Allen, An Introduction to Mathematical Biology, Pearson, 2006 |
|---|---|
| 2. J. D. Murray, Mathematical Biology I. An Introduction ,Third Edition, Springer , 2001 | |
| 3. G. Vries, J. Müller, T. Hillen, B. Schönfisch, M. Lewis, A Course of Mathematical Biology: Quantitative modelling with mathematical and computational methods, SIAM, 2006 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 10 |
| Presentation | 1 | 10 |
| Project | 1 | 10 |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | 1 | 3 | 3 |
| Project | 1 | 4 | 4 |
| Report | |||
| Homework Assignments | 3 | 2 | 6 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 12 | 12 |
| Total Workload | 125 | ||