Bio Mathematics

Paper Code: 
DMAT 511B
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand the scientific study of normal functions in living systems.
  2. exposure to nonlinear differential equations with examples such as heartbeat, chemical reactions and nerve impulse transmission.

Course Outcomes (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

DMAT511B

 

 

 

 

 

 

 

 

Bio Mathematics

 (Theory)

 

 

 

 

 

 

 

The students will be able to –

 

CO111: Learn the development, analysis and interpretation of bio mathematical models.

CO112: Learn different growth models and be able to construct mathematical models for growth models.

CO113: Apply the concept of matrices, eigenvalues and eigenvectors in modeling.

CO114: Learn to apply the basic concepts of probability to different population models.

CO115: Analyze the blood flow models with the concept of fluid dynamics.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
18.00
Concept and formulation of mathematical modelling, Classification and limitation of mathematical models, Single species models, stability and classification of equilibrium points, Relation between eigenvalues and critical points.
 
Unit II: 
II
18.00
Introduction of Single species (non-age structured) models, Formulation, solution and limitation of the Exponential growth model, Effect of immigration and emigration on population. Formulation, solution and limitation of the Logistic Growth model. Extension of the Logistic model.
Unit III: 
III
18.00

Introduction of Single species (age structured) models continuous and discrete both, Lotka’s Model for population growth, BLL(Bernardelli, Lewis and Leslie) model, eigen values and eigen vectors of the leslie matrix, stable age structure, asymptotic formulae for the population of different age groups.

Unit IV: 
IV
18.00

Density-dependent population model, Formulation and solution of Continuous –Time Discrete –Age Population model, effect of change in birth rate and death rate. Age-structure of two populations. MC KendricK approach to age scale models.

Unit V: 
V
18.00
Introduction, basic concept of fluid dynamics, Poiseuille’s flow, Model for Blood flow, Properties of blood, Bifurcation in an artery, Pulsatile flow of blood, Trans-Capillary exchange, Sedimentation.
 
Essential Readings: 
  • Bhupendra singh & Neenu Agarwal, Bio-Mathematics, Krishna Prakashan Media (P) ltd.,2008.
  • J. D. Murray, Mathematical biology: An introduction, Springer, 2007.
  • J. N. Kapur, Mathematical Modelling, New Age international ltd., 2015.
References: 
  • Christina Kuttler, Mathematical Models in Biology, Springer, 2015.
  • F. Brauer, C.C-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2000.
  • N.F. Britton, Essential mathematical biology, Springer, 2004.
  • M. Kot, Elements of mathematical ecology, Cambridge University Press, 2001.
Academic Year: 
2023-2024
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