Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Mathematical Biology
Code MATH335
Coordinator Dr M Domijan
Mathematical Sciences
Mirela.Domijan@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2023-24 Level 6 FHEQ First Semester 15

Aims

To develop expertise in dynamical systems in general and study particular systems in detail.

Learning Outcomes

(BH1) Demonstrate a familiarity with and ability to apply common types of mathematical common types of mathematical models used in population dynamics, biochemistry and biology.

(BH2) Identify basic scenarios for feedback mechanisms in biochemical systems and their impact on biological dynamics.

(BH3) Be able to apply analytic, graphical and computational methods to investigate the dynamic output of biological models.

(BH4) Relate the predictions of the mathematical models to experimental (biological) observations.

(BH5) Evaluate the limitations of mathematical models in relation to the understanding of the mechanics of complex biological systems.

(S1) Problem solving skills

(S2) Numeracy

Syllabus
 

1. Population models for single species:
a. continuous models represented by ODEs (Verhulst model)
b. equations with parameters and bifurcations (systems with harvest)
c. models with delay, oscillations
2. Models for interacting populations:
a. linear models, types of equilibria
b. nonlinear models, linear stability analysis
c. global dynamics, stable and unstable manifolds
d. non-linear oscillations (limit cycles)
e. SIR model.
3. Kinetics of biochemical reactions:
a. law of mass action, Michaelis-Menten kinetics
b. autocatalytic reactions (activation, inhibition)
c. Belousov-Zhabotinskii reaction, Brusselator
4. Complex biological systems:
a. Biological oscillators and switches
b. Excitable systems, FitzHugh model
5. Biological waves:
a. Fisher equation
b. FitzHugh-Nagumo model

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH101 Calculus I; MATH244 Linear Algebra and Geometry; MATH221 Differential Equations 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Written exam  120    70       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
group assessment involving use of computational simulations  0    15       
group assessment involving use of computational simulations  0    15