Research interests

I am a Professor of Applied Mathematics at University of Sussex, with my research at the interface between network sciences, dynamical systems and stochastic processes. In particular, I focus on dynamical processes on static and dynamic networks, using mainly epidemic, and more recently, neuronal network models. I work on developing paradigms / theoretical models that capture complexities arising in real networks, such as heterogeneity in the characteristics, behaviour and interaction of individuals, as well as higher-order network structure. Recently, I have significantly contributed to: (a) identifying links between approximate models and their rigorous mathematical counterpart, (b) proving the exactness of certain epidemic models on tree-like networks, (c) highlighting linkages between various modern epidemic models, and (d) extending modelling to more realistic networks exhibiting clustering and motifs.

Research key words

  1. Mathematical areas and techniques: Network or Graph Theory; Stochastic Processes; Markov Chains; Simulations; Dynamical Systems; Bifurcation Theory; Delay Differential Equations; Control.
  2. Network-modelling specific: Exact and Approximate Models on Networks; Closures; Sub-graphs; Motifs; Adaptive/Dynamic/Time-evolving Networks, Non-Markovian Network Processes.
  3. Applications: Mathematical Biology; Mathematical Epidemiology; Computaional Neuroscience; Neuronal Networks; Information Transmission and Human Behaviour; Contact Tracing; Livestock Disease; Digital Marketing; Spread of Innovations.

Key words grouped by collaborators

  1. Prof Péter L. Simon (Institute of Mathematics, Eötvös Loránd University, Budapest): Networks; Graph Theory; Stochastic Processes; Markov Chains; Dynamical Systems; Bifurcation Theory; Exact and Approximate Models on Networks; Closures; Adaptive Networks; Dynamic Networks, Control, Hyper-graphs.
  2. Dr Luc Berthouze (University of Sussex): Computational Neuroscience; Neuronal Networks; Self-organised Critical Systems; Sub-graphs; Motifs; Higher-order Structure.
  3. Dr Konstantin Blyuss (University of Sussex): Pairwsie Models; Weighted Networks; Non-Markovian Network Processes; Delay Differential Equations.
  4. Prof Jackie Cassell (Brighton and Sussex Medical School): Sexually Transmitted Infections; Information Transmission; Human Behaviour.
  5. Dr Joel C. Miller (Monash University): Edge-based Models; Weighted Networks, Network-based Epidemic Models.
  6. Dr Thomas House (University of Warwick): Pairwise models; Closures; Sub-graphs; Motifs; Clustering.
  7. Prof Joan Saldana and Dr David Juher (Universitat de Girona): Information Transmission; Multiplex Networks.
  8. Dr Kieran Sharkey (The University of Liverpool): Individual-based Exact Network Models.
  9. Prof Mark Broom (City University, London): Game Theoretical Models on Structured Populations.
  10. Dr Gergely Röst (University of Szeged): Delay Differential Equations; Non-Markovian processes; PDEs.

Various research projects (past and present)

  1. Exact and approximate epidemic models on networks: theory and applications
  2. Model development and analysis techniques for epidemiological and neurobiological dynamics on networks
  3. Uncovering higher-order structure in clustered networks
  4. Bifurcations in system behaviour and network structure for a class of dynamic network models
  5. Modelling the spread/diffusion of research idea/innovations and information
  6. Approximate and exact models in computational neuroscience: a unifying mathematical approach
  7. The role of resource constraints and optimal allocation of limited control resources in various scenarios of disease control

Past/latent collaborators

  1. Prof Rowland R. Kao (Faculty of Veterinary Medicine, Glasgow University)
  2. Dr Darren M. Green (Institute of Aquaculture, University of Sterling)
  3. Dr Mario Recker (College of Engineering, Mathematics and Physical Sciences, University of Exeter)