### Heterogeneous network epidemics: real-time growth, variance and extinction of infection

Authors: Thomas House, Frank Ball

Journal: Journal of Mathematical Biology

Publication Date: 17 January, 2017

Department of: Mathematics

### In Abstract

#### Heterogeneity in number of contacts amplifies variability in the spread of disease

People can interact with highly variable numbers of contacts over the course of an illness – a lecturer who ”soldiers on” with the ′flu has many more opportunities to create new infections than one who stays at home!

Now, mathematicians at the Universities of Manchester and Nottingham have demonstrated the implications for such variability on the population-level spread of disease. They have calculated the precise way that the probability of a large oubreak, and the speed and variability with which such an outbreak spreads if it happens, depend on the distribution of the numbers of contacts in the population. The main new finding is that contact heterogeneity creates more variability in the spreading process than one might expect: precisely speaking, the variance in the former affects the mean in the latter and so on for other moments.

The researchers also considered what inferences can be made on the basis of early data on the growth of an outbreak. The results shows that it is important to know exactly how people are interacting with each other if we are to plan for infectious disease outbreaks appropriately, and also to understand phenomena like the spread of ideas and social attitudes.