Skip to main content Skip to navigation

Sam Brand

A bit about me...

I am Sam Brand.

Academic Career:

  • Bsc Mathematics at King's College, University of London
  • Msc Information Processing and Neural Networks at King's College, University of London
  • Msc Complexity Science at University of Warwick

My Phd research area is in the Mathematical Epidemiology of infectious diseases, the treatment of epidemic spread as a problem in the theory of stochastic dynamical systems.

Supervisors: Prof. Matthew J. Keeling, Mathematics and Life Sciences University of Warwick and Prof. Robert S. MacKay, Complexity Science and Mathematics University of Warwick.

Short Overview of Mathematical Epidemiology


An idealised representation of disease transmission and recovery

Mathematically orientated models of the spread of a infectious disease have a long pedigree, dating back to Bernoulli. The complex underlying dynamics of intra-host infection, immune response and inter-host transmission are coarse-grained into a limited number of disease states for host individuals. The simplest common choices for disease state are 'susceptible to infection' (S), 'currently infected' (I), and if recovery imparts long-term future immunity 'Removed from infection' (R). Epidemic spread can then be modelled as a stochastic dynamical system on the space of possible population disease states.

Classical homogeneity assumptions on the of host population and their location/interactions in space lead, in the limit of large numbers of possible hosts, to the well-known SIR model of epidemic dynamics. The possible relaxations away from this classical picture are too numerous to include in their entirety, but some major areas of active and interconnected research are:

  • Stochastic vs deterministic models. Characterising the negative correlation between susceptibles and infecteds. Role of stochastic forcing.
  • Spatial spread. Introducing appropriate sense of locality. Understanding and quantifying Human and Animal behaviour and mixing patterns.
  • Biological realism and non-Markovian dependence on history. Incorporating variation between host immuno-responses and during the life-cycle of the pathogen. Understanding interaction between seperate pathogen strains.
  • Vector-bourne Disease. The role on intermediary vector hosts.

Ongoing Research areas

Some areas of interest for me in mathematical epidemiology:

Fast simulation of spatial epidemics: Getting significant speed gains on force of infection calculations by treating spatial epidemic state as a single 'image' rather than a large ensemble of degrees of freedom.

Interplay between Space and Stochasticity: For epidemics where spread is governed by spatial separation the 'typical' length scale of transmission governs how many habitats are 'local' to one another. I use perturbative methods to characterise deviation away from the well understood mean-field epidemic where typical scale of transmission is infinite.

Optimal Control: Solving the dynamic programming equations (DPE) that arise from considerations of optimal action for a sensible formulation of control problem, e.g. optimal vaccination targeting. I use a variety of solution methods, in particular I am interested in the non-linear Feynman-Kac approach to solving nonlinear DPEs and forwards-backwards Stochastic differential equations.


A snapshot of epidemic intensity spreading over 10,000 simulated farms


A simple control problem for individuals stratified into two locations. What is the optimal Vaccination policy?

 epidemic curve

Radical change in epidemic curve as typical transmission distance becomes shorter

Previous Work - Granular Rheology

I studied through computer simulation the rheology of granular suspensions as they are forced down channels via a pressure gradient in the suspending fluid, making connections to experimental results in colloids. In particular I investigated transitions between 'fluid-like' regimes of granular flow and the formation of "solid-like" cluster that could lead to dynamically absorbing states of either high ordering and rapid flow (granular crystalisation) or low ordering and kinetic arrest (jamming).

granular flow

A schematic of forcing a suspension of particles down a channel


- "Complex Flow in Granular Media" (2010) Brand, S., Pica-Ciamarra, M., Nicodemi, M., Advances in Complex Systems

- "Stochastic Transitions and Jamming in Granular Pipe Flow" (2011) Brand, S., Ball, R. C., Nicodemi, M., Physics Review E

Selected Bibliography

- Anderson, R. and May, R. (1991), “Infectious Diseases of Humans: Dynamics and Control” OUP
- Fleming, W. H., Soner, H. M. (1993), "Controlled Markov Processes and Viscosity Solutions" Springer-Verlag
- Tildesley, M.J., Savill, N.J.,Shaw, D.J., Deardon, R., Brooks, S.P., Woolhouse, M.E.J., Grenfell, B.T. and Keeling, M.J. (2006) “Optimal reactive vaccination strategies for a foot-and-mouth outbreak in the UK” Nature
- MacKay, R. S. (2007) “Parameter Dependence of Markov Processes on Large Networks” Proc. ECCS
- Grassly, N. C. and Fraser, C. (2008) “Mathematical models of infectious disease transmission” Nature Review Microbiology

Sam Brand

Sam Brand

Contact details:

phriap AT live DOT warwick DOT ac DOT uk

Complexity Science Doctoral Training Centre
Zeeman Building
University of Warwick
CV4 7AL, UK.