APP MTH 4047 - Applied Mathematics Topic B - Honours
North Terrace Campus - Semester 1 - 2019
General Course Information
Course Code APP MTH 4047 Course Applied Mathematics Topic B - Honours Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 2.5 hours per week Available for Study Abroad and Exchange Y Restrictions Honours students only Course Description Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au
Course Coordinator: Professor Joshua RossThis is the same course as APP MTH 7045 - Applied Mathematics Topic B
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesThe topic of this course is Infectious disease dynamics: Stochastic models and associated statistical methods.
Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology one of the most exciting topics in applied mathematics. During the course, you will be introduced to mathematical epidemiology and some fundamental theory and numerical methods for studying and parametrising stochastic models of infectious disease dynamics. This will provide an ideal basis for addressing key research questions in this area; several such questions will be introduced and explored in this course.
Assumed knowledge for the course is DTMCs and CTMCs as, for example, covered in Applied Probability III and Random Processes III, ODEs as, for example, covered in Differential Equations II; and, some knowledge of Bayesian statistics would be useful, but not required.
On successful completion of this course, students will be able to:
1. understand and explain the basic model structures uesd in Mathematical Epidemiology;
2. develop ODE and CTMC models of infectious disease dynamics, giving consideration to the suitability of assumptions;
3. to derive and explain the Threshold, Escape and Final size results for the SIR ODE model;
4. understand and exploit linearisation, and associated Branching Processes, to study the early stages of epidemics;
5. numerically evaluate the distribution of the state of an epidemic model given initial conditions, through simulation and numerically-exact methods;
6. understand and derive the relationship between some CTMC and ODE epidemic models;
7. numerically evaluate the mean, and distribution, of the final size and duration of an epidemic for basic CTMC epidemic models, inluding Laplace-Stieljtes transform inversion and a general appreciation of Path Integral methods for CTMCs;
8. parameterise simple CTMC epidemic models within a Bayesian framework, including the use of the Metropolis-Hastings algorithm.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
all Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
Required ResourcesAccess to the internet.
Recommended Resources1. Keeling and Rohani, Modeling infectious diseases in humans and animals, PUP, 2008.
2. Black, House, Keeling and Ross (2013) (http://dx.doi.org/10.1098/rsif.2012.1019)
Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza.
3. Black and Ross (2015) (https://doi.org/10.1016/j.jtbi.2014.11.029)
Computation of epidemic final size distributions.
4. Black and Ross (2013) (https://doi.org/10.1371/journal.pone.0073420)
Estimating a Markovian epidemic model using household serial interval data from the early phase of an epidemic.
5. Diekmann, Heesterbeek and Britton, Mathematical tools for understanding infectious disease dynamics, PUP, 2013.
6. Daley and Gani, Epidemic modelling: an introduction, CUP, 2001.
7. Gilks, Richardson and Spiegelhalter, Markov chain Monte Carlo in practice, Chapman and Hall/CRC, 1996.
8. Grimmett and Stirzaker, Probability and random processes, OUP, 2001.
9. Kreyszig, Advanced engineering mathematics, Wiley.
Online LearningThis course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources.
Learning & Teaching Activities
Learning & Teaching ModesThe lecturer guides the students through the course material in 23 lectures. Students are expected to engage with the material in the lectures. Interaction and discussion of any difficulties that arise with the lecturer during the lecture is encouraged. The lectures are supplemented with 7 practical/tutorial classes, that will in particular focus on the numerical aspects. Three homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lecture classes 23 92 Practicals / Tutorials 7 21 Assignments 3 43 Total 156
Learning Activities Summary1. Introduction to mathematical epidemiology (Lecture 1);
2. Deterministic models of infectious disease dynamics (Lectures 2 - 4);
3. CTMC models of infectious disease dynamics, including numerical evaluation of transients, simulation, deterministic approximations, branching process approximations, path integrals, and duration and final size random variables (Lectures 5 - 25);
4. Bayesian inference, including the Metropolis-Hastings algorithm (Lectures 26 - 30).
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Objective Assessed Assignments 30% all Exam 70% all
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment item Distributed Due date Weighting Assignment 1 week 2 week 4 5% Assignment 2 week 6 week 9 10% Assignment 3 week 9 week 12 15%
SubmissionAssignments and projects must be left in the course hand-in box or given to the lecturer in person by the specified deadline. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported on Official Transcript Fail A mark between 1-49 F Third Class A mark between 50-59 3 Second Class Div B A mark between 60-69 2B Second Class Div A A mark between 70-79 2A First Class A mark between 80-100 1 Result Pending An interim result RP Continuing Continuing CN
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
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