This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.

We consider Markov models for growth of populations subject to catastrophes. Emphasis is placed on discrete-state models where immigration is possible and the catastrophe rate is population-dependent. Explicit formulas for descriptive quantities of interest are derived when catastrophes reduce population size by a random amount which is either geometrically, binomially or uniformly distributed. Comparison is made with continuous-state Markov models in the literature in which population size evolves continuously and deterministically upwards between random jumps downward.

Part 3, SUMMARY The paper is concerned with formulae for estimating student enrolments and degrees to be awarded in Australian universities over the next few years. A simplified model for student progress through a university course is constructed from which such formulae can be derived. An illustrative example for projecting the number of bachelor's degrees awarded is given; numerical formulae are obtained by following through the cohorts of new enrolments, while a theoretical solution is also provided using matrix methods. The results obtained prove to fit the actual number of degrees awarded between 1955 and 1960 fairly closely. Some refinements such as the estimation of students enrolled term by term are suggested.

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