Spreading processes on (multilayer and multiplex) networks

Understanding how the outcomes of spreading processes on real-world networks are affected by the multilayer and multiplex network structures and by different network topologies.

The need and impact

There is growing understanding that spreading processes on real-world networks are typically moderated or influenced by additional factors, which themselves occur on networks and with feedback loops between the processes on the two networks. These dual spreading processes can occur either across a single node set with multiple edge types (multiplex networks), or multiple distinct node sets, with different edge types within and between the node sets (multilayer networks).

This project aims to understand how the outcomes of spreading processes are affected by the multilayer and multiplex network structures and by different network topologies arising in different applications, for example, by considering demographic factors in networks of epidemic spread. Developing new knowledge related to network science and complex systems – namely spreading processes on multilayer and multiplex networks – and the modelling and simulation thereof, directly addresses the roles that demographics and social processes play in mediating spreading on networks. This enables us to understand how outcomes for groups and individuals are affected.

The combination of mathematical modelling and practical applications using concrete data proposed offers a unique chance to understand the role of social factors in epidemic spread. Accurate models of contagion are essential for formulating public health strategy and epidemic response, and are particularly necessary as rates of immunisation fall in Aotearoa New Zealand and in the Pacific. Application to wilding conifers will inform strategy for biological control of pest species, a critical issue for Aotearoa New Zealand.

The approach

In this project we consider spreading on multidimensional networks: that is, networks which contain more than one node type and/or more than one edge type. In particular, we are considering spreading processes which are mediated by a second, parallel processes within the same network.

We will use a combination of mathematical models and simulations, together with concrete real-world data from applications. One example we will consider is the spread of seasonal influenza on a contact network mediated by individual’s vaccination status, where the vaccination status is itself influenced by information and attitudes spreading on a social network with feedback from individuals’ experiences of influenza. A second application we will address is the spreading of wilding conifers on a geographically embedded network mediated by land-owner behaviour and attitudes on a social network.

Research aims

  • Develop mathematical models for spreading on multilayer & multiplex networks, including an understanding of the effects of network topology.
  • Co-develop data on topological properties of contact and social networks in different demographies, particularly those of interest to New Zealand.
  • Use empirical data from applications to characterize the models.


  • Dr Dion O’Neale (Project Co-Lead)
  • Associate Professor Claire Postlethwaite (Project Co-Lead)
  • Dr Emily Harvey