Modelling repeated epidemics with general infection kernels : this thesis is presented in partial fulfilment of the requirements for the degree of Masters of Information Science in Mathematics at Massey University
This thesis is on mathematical modelling in epidemiology, exploring the generic characteristics of diseases in two different population structures. Integral equations are used, to model the epidemics in each generation (of the epidemic). Difference equations are then used to model the change in the populations between epidemics. Initially, single dimension populations are modelled, where the entire population is considered to be one class. Then the population is split into two classes and a similar analysis is performed, with critical differences noted between the two structures. An analytical approach is taken, with numerical examples. The work in this thesis is not specific to one disease, the main focus is to develop a stepped process between generations of the epidemic and analyse the behaviour.