APP MTH 7049 - Applied Mathematics Topic D

North Terrace Campus - Semester 2 - 2018

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at

  • General Course Information
    Course Details
    Course Code APP MTH 7049
    Course Applied Mathematics Topic D
    Coordinating Unit Mathematical Sciences
    Term Semester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Assessment ongoing assessment 30%, exam 70%
    Course Staff

    Course Coordinator: Dr Andrew Black

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2016, the 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.

    Learning Outcomes

    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;

    6. 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;

    7. 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)
    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
    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
    Career and leadership readiness
    • technology savvy
    • professional and, where relevant, fully accredited
    • forward thinking and well informed
    • tested and validated by work based experiences
    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
  • Learning Resources
    Required Resources
    Recommended Resources
    G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Models, ASA-SIAM Series on Statistics and Applied Probability, 1999.

    Marcel F. Neuts, Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Dover Publications, 1981.
    Online Learning
    The course will have an active MyUni website.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Fortnightly 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
    Lectures 30 90
    Assignments 4 66
    Total 156


    Learning Activities Summary
    Lecture outline

    Introduction to Matrix Analytic Methods and example applications (2 Lectures).

    Revision of Basic Probability, Discrete-time Markov chains, and Continuous-time Markov Chains (5 Lectures).

    Phase-type distributions, renewal processes and Markovian Arrival Processes (10 Lectures).

    The birth-and-death-process and Quasi-Birth-and-Death-process and the structure and derivation of the stationary distribution and other performance measures (13 Lectures).

    The GI/M/1 and M/G/1-type Markov chains as QBDs (2 Lectures).

    Summary (1 Lecture).
  • 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
    Assessment task Task type Weighting Learning outcomes
    Assignments Formative and summative 30% All
    Exam Summative 70% All
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    There will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam
    Assignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.

    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    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 ( 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
  • Fraud Awareness

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