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Topic: | Survey paper(s) |

1: Heterogeneity of mixing and spatio-temporal models | Heterogeneity .. : advances and open problems (Bolker) (14 pages of postscript) |

2: Genetic, ecological and evolutionary dynamics | Recent progress in parasite ecology and evolutionary biology(Grenfell et al) |

Lymphocytes talk about modelling immunity (Apanius) | |

3: Immuno-epidemiology | Parasites of farmed animals (Roberts) (13 pages of postscript) |

A problem-oriented approach (Hellriegel) | |

4: Statistical issues | Statistical studies of disease transmission(Becker and Britton) (26 pages of postscript) |

List of references
(for the introductory paragraphs below) |

Heterogeneity among individuals is a central problem of epidemic theory. Differences between individuals affect both their susceptibility to disease and their infectiousness to others. It is important to determine those differences between individuals that have most influence on the spread of infection in space and time. These differences include those determined by age, and social, genetic and behavioural factors. The need for the formulation and analysis of models incorporating different types of heterogeneity is now widely accepted, and an important role of mathematical and statistical modelling is to assess which heterogeneities should be included in the model and data analysis and which can safely be ignored. A particular problem for discussion is the evaluation of control strategies in heterogeneous populations, and the question of the critical vaccination coverage needed for the eradication of a disease, or prevention of major outbreaks, in communities in which there is a heterogeneous mixing structure. [9,14--16]

In terms of stochastic spatio-temporal modelling, there are connections with current research on interacting particle systems and probabilistic cellular automata that need further exploration. [Durrett in 4; 17] In terms of statistical modelling and data analysis, there are issues in common with many other areas in which spatio-temporal processes are observed. One area for discussion will be the collection and analysis of complex spatial data, and the efficient estimation of parameters of interest. At present, there is much interest in fitting models to such data by a variety of techniques, amongst which the use of Markov chain Monte Carlo methods is prominent. [18] There is substantial scope for exploring the use of computer-intensive methods in the context of infection/disease data.

Genetic variations and resistance, in both the host and parasite populations, are becoming an important focus of attention. Ecological and evolutionary dynamics are essential for understanding infectious diseases. Population dynamics models of infectious disease typically ignore genetic variation while co-evolutionary models usually ignore population dynamics. We need to study models incorporating both effects.

There is concern over the evolution of resistance to the available limited repertoire of control measures (such as pesticides for controlling vector populations or the use of antibiotics in hosts). It is essential to maximise the useful lifetime of such measures before widespread resistance occurs. How can drugs be best used to minimise resistance? What are the selective consequences of intervention strategies on pathogen life histories? For example, does the use of chloroquine in malaria select for greater infectiousness? For infectious diseases, resistance management is an important topic for future study, which can benefit from the substantial body of theoretical and practical experience available in the agricultural sciences. [19--22]

Molecular biology is beginning to look at the diversity of infectious disease agents, which can be regarded as an evolutionary strategy to avoid immune reactions. Such diversity is being put forward as a possible explanation for the long incubation period between infection with HIV and full AIDS. On the other hand there is the question of the co-evolution of resistance of a host to its parasites and the development by the immune system of cross-immunity to `similar' antigens. [23,24]

Immuno-epidemiology is concerned with the implications of infection and disease dynamics within the host (immunology) for population epidemic dynamics, and is a major growth area in the study of infectious diseases. Work here involves bringing together models for the workings of the immune system and those for the infection process in the population. For example, for an epidemic model we need to allow for the (heterogeneous) susceptibility to infection and infectivity of each individual. Thus we need to be able to determine the effect on the immune system of exposure to infection and the effect of the immune system on the infectiousness of the individual. The interactions between these are crucial in diseases with agents varying from viruses (dengue, HIV), through bacteria (TB) and protozoa (malaria), to helminths (schistosomiasis, onchocerciasis).

The workshop will bring together experts from the relevant
applied fields and mathematical modellers to review progress and to
coordinate future approaches. In all three of the key workshop
areas, the relation of
models to empirical observations is of paramount importance, and there
will be substantial emphasis in the workshop on the development and
application of appropriate statistical methodology.
In particular, the
modelling and analysis of spatio-temporal processes is currently a
major concern in a variety of applied fields, and is
receiving substantial attention from the statistical community.
[* e.g.* 25--27]
It is of particular interest to explore the extent to which advances, for
example in the use of Markov chain Monte Carlo methods, can be exploited
in the analysis of data from epidemic processes.
[18,28]

Another area in which important statistical advances have been made in the last few years concerns nonlinear time series. [11--13] The workshop will be able to benefit from, and provide additional impetus to, current work in this area. In particular, there is the opportunity for cross-fertilisation with the activities of the TIMSAC (Time Series and Chaos) Study Group of the Royal Statistical Society. One obvious problem that needs to be addressed is the question of predicting major outbreaks of infection from an unstable steady state.

Studies involving data collection need careful design to enable the best use to be made of available resources. In the past, sometimes little attention seems to have been given to the most appropriate choice of the data that are to be collected to test a particular research hypothesis. In particular, there is considerable scope for the development of statistical designs suitable for the collection of spatio-temporal data. Techniques need to be developed to deal with the problems caused by missing data and although the use of covariate information and surrogate markers has been the subject of recent research activity (for example, with regard to the use of CD4 counts and other markers as predictors of progression to AIDS [29]) there remains much to be done.

Too often in the past, epidemic processes have been modelled exclusively using a deterministic approach, and little or no emphasis has been placed on providing standard errors or confidence intervals for estimates. We regard it as imperative that due allowances for uncertainty in both model structure and parameter values are incorporated, particularly when predictions are to be made.

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Please send any comments or corrections to
* Denis Mollison*

*22nd March 1997*