# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology

8-12 July 2018
Australia/Sydney timezone

## Ecological stability, epidemiological stability and reservoirs of infection

11 Jul 2018, 16:30
30m
New Law School/--106 (University of Sydney)

### New Law School/--106

#### University of Sydney

100
Oral Presentation Minisymposium: Reproduction Numbers

### Speaker

Prof. Mick Roberts (Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand)

### Description

The structure of an ecosystem and the interaction of the species within it can determine whether a pathogen can persist. We have described a model for interacting species that are hosts and non-hosts of a pathogen. The population densities of the ecosystem species can determine the value of the basic reproduction number, $\mathcal{R}_0$. We have defined concepts of ecological and epidemiological stability, shown how changes in the ecosystem can change the dynamics of the pathogen, and how the introduction or removal of a pathogen can lead to changes in the ecosystem structure. In particular, the so-called dilution effect, where an increase in biodiversity leads to a reduction in the prevalence of an infectious disease, has been the subject of speculation and controversy. We have found criteria for when the dilution effect is present, or when the opposite (amplification) effect may occur. Another concept often used informally in the literature is that of a reservoir of infection. Finding a robust definition of a reservoir is not straightforward, particularly as the presence of other species in an ecosystem, even non-host species, can change the value of $\mathcal{R}_0$.

Collaborative research with Hans Heesterbeek.

### Primary author

Prof. Mick Roberts (Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand)

### Presentation Materials

There are no materials yet.