A bit about me...
I am Sam Brand.
- 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
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:
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?
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).||
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 http://www.worldscinet.com/acs/13/1303/S021952591000261X.html
- "Stochastic Transitions and Jamming in Granular Pipe Flow" (2011) Brand, S., Ball, R. C., Nicodemi, M., Physics Review E http://pre.aps.org/abstract/PRE/v83/i3/e031309
- 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