Some population and epidemic models revisited.
Three problems of population and epidemic models formulated between ten and thirty years ago are reconsidered. In each case, a modified approach to the problem leads to its solution. For the two-sex population model, the solution of a Riccati equation results in an expression for the generating function of the process. The fully stochastic, as against the previously studied semistochastic, model of population growth with random catastrophes yields to hard analysis. Finally a generalized form of the general stochastic epidemic is solved using matrix geometric methods.

title: Point Processes in Epidemiology
abstract: The paper consists of six sections. The first is devoted to chain binomial methods and their use in the statistical analysis of measles and hepatitis data. A second considers time dependent results for carrier-borne epidemics, and the use of matrix methods in computing probabilities of their final size. The third surveys the application of perturbation techniques to the general stochastic epidemic, and the estimation of infection and removal parameters in this model on the basis of smallpox data. The fourth section summarizes asymptotic results for the general stochastic epidemic when the initial populations of susceptibles and infectives are both very large. In the fifth, some recent results are outlined on the costs of epidemics; these depend on the stochastic path integral under the infective curve. Finally, a brief account is given of the analysis of space-time interactions in epidemic processes.

title: A simple deterministic epidemic in several related growing communities
abstract: This paper first considers a simple deterministic epidemic in a growing population. It then examines a simple deterministic epidemic in several related growing communities, where infection is transmitted between individuals both within and across the communities. An explicit parametric solution is derived for the number of susceptibles in these communities as a function of time.

title: Random Allocation Methods in an Epidemic Model
abstract: A random allocation model is developed for the numbers of susceptibles in a group of n IVDU’s who become infected by i HIV-infectives sharing needles. A comparison of this model and the classical Reed-Frost model is outlined.

title: Approaches to the Modelling of Aids
abstract: The spread of AIDS in Africa, Europe, North America and elsewhere in the world is causing considerable concern. It is known that the human immunodeficiency virus (HIV) attacks T-4lymphocytes in the bloodstream, thus causing a decline in the immune system. Serious infection by organisms usually kept under control follows: patients develop Pneumocystis carinii pneumonia, Kaposi’s sarcoma, chronic lymphadenopathy, dementia and various opportunistic infections. Infection by the HIV almost always leads to overt AIDS symptoms, which appear to be inevitably fatal; one problem of interest is the length of the incubation period, that is the time between HIV infection and the diagnosis of AIDS.

title: Modelling the spread of HIV in prisons
abstract: This paper is concerned with models for the spread of HIV in prisons. We first consider a single prison of size N in which there is homogeneous mixing, and where there is an inflow and outflow of n< N prisoners at times t= 0, 1, 2,... Conditions are derived for the stability of the system. The interaction of such a prison with the outside world is then studied, and stability conditions obtained for this case. Finally, a quarantine policy is examined and its cost analyzed, both in the non-stable and stable cases.

title: OBITUARY: EDWARD JAMES HANNAN