## APP MTH 7048 - Applied Mathematics Topic A

### North Terrace Campus - Semester 1 - 2022

This course is available for students taking a Masters degree in Mathematical Sciences. The course will cover an advanced topic in applied mathematics. For details of the topic offered this year please refer to the Course Outline

• General Course Information
##### Course Details
Course Code APP MTH 7048 Applied Mathematics Topic A Mathematical Sciences Semester 1 Postgraduate Coursework North Terrace Campus 3 Y Ongoing assessment, exam
##### Course Staff

Course Coordinator: Professor Lewis Mitchell

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
In 2022 the topic of this course will be Stochastic Epidemic Modelling.

COVID-19 has highlighted the importance of mathematical modelling to support governmental decision-making in response to disease outbreaks. This course provides an introduction to epidemic modelling with a focus on stochastic models. Methods for linking models to data, in particular some Bayesian approaches, will also be covered. This course provides an ideal basis for addressing key research questions in the area and for using mathematical models to aid pandemic response; some examples of these will be presented.

Topics

Topics covered in this course will likely include:

- Introduction to epidemiology and simple models of epidemics.
- Simple probabilistic models of epidemics.
- Minor and major outbreaks, and their probabiliity of occurence.
- Continuous-time Markov chain models of epidemics.
- Final epidemic size.
- Branching processes.
- Sellke's construction.
- Coupling.
- Simple probabilistic household models.
- Simple probabilitic heterogeneous models.
- Markov chain Monte Carlo (MCMC) methods for inference in epidemic models.
- Density dependent epidemic models.
- Transmission intensity functions, and COVID-19 modelling.

Learning Outcomes

On successful completion of this course, students will be able to:

1. Understand and explain the basic model structures used in Mathematical Epidemiology.
2. Develop simple ODE and probabilistic models of epidemic dynamics, giving consideration to the suitability of assumptions.
3. Demonstrate understanding of the relationship between stochastic epidemic models, and branching proccess and ordinary differential equation approximations, and of minor/major outbreaks, including the use of coupling and limit theorems.
4. Numerically evaluate the probability of a major outbreak for simple epidemic models.
5. Numerically evaluate the final epidemic size of simple epidemic models, including Sellke's construction.
6. Demonstrate understanding of basic MCMC methods and apply these to simple problems in Mathematical Epidemiology.
7. Demonstrate understanding of transmission intensity functions and some models used for COVID-19 modelling in Australia.

Assumed knowledge

Applied Probability III or Random Processes III is the best preparation, but a thorough knowledge of Probability and Statistics II is enough.
Knowledge of basic Baysian inference and Markov chain Monte carlo would be useful, but not required.
This course will require some programming (students can use their preferred language).

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)

Attribute 1: Deep discipline knowledge and intellectual breadth

Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

all

Attribute 2: Creative and critical thinking, and problem solving

Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

all

Attribute 3: Teamwork and communication skills

Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.

all

Attribute 8: Self-awareness and emotional intelligence

Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

all
• Learning Resources
##### Recommended Resources
N.G. Becker (2015) Modeling to Inform Infectious Disease Control. CRC Press.

H. Andersson and T. Britton (2012) Stochastic Epidemic Models and their Statistical Analysis. Springer (Lecture Notes in Statistics).

M.J. Keeling and P. Rohani (2007) Modeling Infectious Diseases in Humans and Animals. Princeton University Press.
##### Online Learning
This 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 Modes
Students will work though the notes and reading materials guided by the lecturer. Weekly workshops will provide time for in depth discussion of the material. 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.

Study 30 108
Assignments 4 48
Total 156

##### Learning Activities Summary
Materials will be uploaded to, or noted on, MyUni at least one week in advance of being required.
##### Specific Course Requirements
None.
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Component Weighting Objective Assessed Assignments &/or Mini-projects 60% all Examination 40% all
##### Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.
##### Assessment Detail
TThere will be 4 Assignments &/or Mini-projects during semester, approximately equally-spaced, and Final Examination at the end of Semester.
##### Submission
All assignments are to be submitted online through MyUni. 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:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

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.

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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