Mathematics of Life and Social Sciences Group

Our group applies mathematical, computational, and statistical techniques to address research questions in the life and social sciences.

Our research

Much of our research is interdisciplinary and group members typically collaborate closely with researchers in biology, ecology, medicine from a range of universities, research institutes and industries. We use an exceptionally broad range of mathematical techniques, encompassing the full range of current applied mathematics.


The group's research interests fall into five themes:

At Surrey, in recent years mathematicians have worked on some particularly novel projects in both ecology, epidemiology and population genetics. Some of these projects highlight the importance of the overlaps of the three areas.

Invasive species

Stephen Gourley

Work has been proceeding on the modelling of invasive species, with particular emphasis on the Asian longhorned beetle and the invasive plant, Japanese knotweed {\em Fallopia japonica}. Simple classical models do not describe the spread of invasive species well because the species are not kept in check by co-evolved natural predators. Accurate models for invasive species can have features usually considered unrealistic in classic models, such as the possibility of a biomass variable increasing without bound, as in the case of Japanese knotweed. On the other hand, Allee effects can often become important and result in an introduced species failing to spread. This can be a problem where a species has been deliberately introduced as a biocontrol agent.

Ecological competition

Stephen Gourley

Competition in age structured models has been an area of recent interest, with particular emphasis to stage-structured models of insect species in which there is intra-specific competition among larvae, or inter-specific competition between the larvae of different strains. Competition may also occur among adults. Mathematical modelling of such scenarios can result in a particular type of differential equation in which the nonlinearities of the differential equation can only be defined implicitly (i.e. the differential equation cannot even be written down explicitly). These types of equations generate particular challenges to both analytic and numerical study.

Plant-herbivore interactions

Stephen Gourley

Collaborative work with ecologists has resulted in a possible new mechanism for the generation of  population cycles of  snowshoe hares in boreal ecosystems. Such cycles are often considered to be a consequence of predation by predators such as the lynx. However, our work shows that, if careful attention is paid to the precise feeding behaviour of hares, particularly their tendency to seek out older, less toxic, parts of twigs and reject younger more toxic twig segments that are attached to those older segments, this type of feeding behaviour is itself more than sufficient to generate population cycles, even in the total absence of predation. 

Insect-borne diseases and insecticide resistance

Stephen Gourley

In epidemiology work has focussed mainly on diseases carried by flying insects such as mosquitoes and midges. We have worked particularly on bluetongue disease and malaria. Our work on malaria has emphasized possible new approaches to mosquito control that could delay the onset of resistance to insecticides. Delayed action insecticides work by targeting only older mosquitoes. These are the most dangerous, since the malaria parasite has a long latency time in the mosquito. An insecticide that selectively targets only older adults would exert less selection pressure for resistance, since old individuals have already laid most of their eggs, with no loss of malaria control. We are using mathematical modelling to try to predict the long term effects of the use of such an insecticide. We are also trying to make predictions concerning the use of larvicides, which are insecticides that target insect larvae. Again, mosquitoes acquire resistance to such insecticides over time. However, resistance is sometimes acquired at an evolutionary cost (for example, resistant mutants may have a shorter adult life expectancy). Since the adult mosquito life-span is one of the most important parameters in mosquito and malaria control,  driving the population to resistance has the potential, in principle, to benefit malaria control.

Anti-microbial resistance in time and space

Gianne Derks

This project focuses on Animal-human-environment ESBL transfers (initiated via the EPSRC funded Collaborative Hub for Advancing Interdisciplinary Research (CHAIR)). Extended Spectrum Beta-Lactamases (ESBLs) are enzymes produced by bacteria such as Escherichia coli (E.coli) and Klebsiella. ESBLs can be found in humans, animals and the environment and have been extensively researched in each field. ESBLs can be resistant to a range o frequently used antibiotics. This proof of concept study aims to use readily available data from various fields, e.g. GP data, vet practice data, climate data, geographical data, and combine this to answer the main question: How do ESBLs transfer between animals-human and environment. This project will advance towards high level model construction for the modelling to identify significant contributing drivers for ESBL transfer. Follow up studies are planned to investigate specific drivers in more detail.

Genetics of rapidly growing populations

Mark Roberts

Mathematical models for the change of allele frequencies over time have played a central role in the development of population genetics over the last century and continue to be of critical importance in the genomic era. However, analysis of these models has rarely ventured beyond the case of populations of constant size, despite the obvious relevance of exponential growth to human genetics. This project is revealing that properties of allele frequencies predicted by constant population models, and which are often regarded as fundamental by geneticists, do not hold for populations that are growing exponentially. Potential areas of applications include genetic diversity, genetic epidemiology, genetic archaeology, and evolution. Current collaborators include Patricia Lund (Coventry) and Peter Nabutanyi (Dar Es Salaam, Bielefeld).       

Epidemiology of albinism

Mark Roberts

‘Albinism’ is a group of conditions that are caused by mutations to genes that are involved in the production of melanin. People with albinism are found throughout the world, but with frequencies that vary significantly between continents and countries. Data from large samples and censuses in Zimbabwe, Namibia and Tanzania also show very significant, unexpected, and sometimes potentially worrying differences between groups within countries.  These observed differences are likely to have a variety of causes including genetic processes, socio-economic factors and data collection methodologies. The aim of this project, which is being developed with Patricia Lund (Coventry), is to establish methods and collect data that will make it possible to determine the most significant causes in a particular context, and to impact health, social and human rights policy.

Cellular systems are highly complex with feedback mechanisms typically operating over multiple time and length scales. This complexity makes mathematical approaches ideal for investigating a range of cellular processes.

We consider both fundamental biological processes such as tissue development and cell signalling as well as doing more applications base research in pharmacokinetics and pharmacodynamics.

We work closely with experimental collaborators and industrial partners (which include Syngenta, AstraZeneca and Pfizer). We are have representatives in the UK Quantitative Systems Pharmacology (UK-QSP) and Predictive modelling for healthcare through Maths (POEMS) networks.

Drug delivery in tissues and tumours

Carina Dunlop

The spatial distribution of drugs within tissues is a major factor in determining their efficacy and the dynamics of treatment. Determining correct dosages and treatment protocols all depend crucially on understanding how the drug will reach the tissue and at what concentration. Equally, it is becoming increasingly clear that biological tissues are highly heterogenous with multiple cell types and vessels affecting diffusive processes. This research strand focuses on developing spatial descriptions of drug distribution in both healthy and disregulated tissues. This is a cross-cutting theme interfacing with PKPD research and tissue modelling research throughout MoLSS.

Drug-receptor interaction modelling

Gianne DerksPhilip Aston

Drugs  like antibodies aim to bind with receptors (antigens) to be effective. Sometimes a receptor has more binding positions. This project looks at the case when there are one or two binding possibilities. Central to the analysis is the target mediated drug disposition model (TMDD), in which a receptor binds with only one antibody, and its extension to binding with one or two antibodies (dimerisation model). It is assumed that the binding is the fastest process. This gives a separation of time scales, which allows us to use geometric singular perturbation theory to analyse these models. In both models, the slow manifold consists of two components, which intersect transversely in the origin. The dimerisation model leads to a degenerate intersection. To analyse such intersection, we consider a general two parameter slow-fast system in which the critical set consists of a one dimensional manifold and a two dimensional manifold, intersecting at the origin. Using geometric desingularisation, we determine the fate of the incoming one-dimensional manifold, which can be a jump away from the critical set or an exchange of stability between the attracting components of the critical set. The ultimate goal is to return to the dimerisation model and give the approximation of the full dynamics in the dimerisation model.


Carina Dunlop

This area of research focuses on the cell as a physical object, incorporating an understanding of the role of mechanical forces into models of biological processes. It draws on a diverse range of concepts in pursuing this research ranging from population modelling to the theories of fluid dynamics and elasticity theory. In particular, mechanotransduction and tissue self-organisation and morphogenesis.


Cells are observed to respond directly to changes in the mechanical properties of their environments with e.g. type specification, growth and death all being found to be sensitive to changes in substrate stiffness. Importantly this mechanotransduction must be carefully coordinated within tissues to account not just for cell-substrate but also cell-cell interactions.

Tissue self-organisation and morphogenesis

Tissues grow and shape themselves through the physical actions of individual cells, which include moving, adhering, and contracting. Crucially these behaviours must be carefully controlled through cell-cell and cell-matrix signalling to ensure the regulation of tissue size and shape. To model this process of tissue growth and shape control a range of approaches is used including agent-based simulations and continuum modelling.

Our lives have an approximately daily (circadian) rhythm of wake and sleep, feeding and fasting. These rhythms are part of a complex, hierarchical, coupled oscillator system with rhythmicity generated within nearly every cell of our bodies and coordinated by the so-called `master’ clock in the suprachiasmatic nucleus of the brain. 

There is increasing evidence that disrupting our biological rhythms is bad for our health and a contributory factor to obesity, cardiovascular disease, mood disorders and cognitive decline.

We are using mathematical models at many different scales to help understand the structure of this complex system – from detailed models of gene transcription/translation cycles at the molecular level through to human scale models of the sleep/wake cycle.

The impact of the modern light environment on sleep

Anne Skeldon with Derk-Jan Dijk (Surrey Sleep Research Centre)

We are interested in mathematical modelling the impact of the modern light environment on sleep and the consequent impact on health and wellbeing. Traditionally, humans experienced bright light during the day and very low levels of light after sunset. The use of bright artificial lighting has had a profound effect on our light environment, giving us much greater choice over when we work and socialise. But with what impact? Light pollution at night disrupts the behaviour of wildlife and is correlated with poor sleep quality and reduced sleep duration in humans.

During waking hours, our lifestyles mean that we spend the majority of time indoors and expose ourselves to artificial light long after sunset. The net effect is that we have a greatly reduced exposure to the natural cycle of light and dark, resulting in delayed circadian rhythms, later sleep timing, social jet-lag and difficulties maintaining 24 hour rhythmicity. All of which are further exacerbated by the increased use of lighting in the evening with an enhanced-blue component. Read a recent paper with one of our collaborators, Andrew Phillips (Harvard Medical School). This uses mathematical modelling to understand how light, individual physiological differences and social constraints such as getting up for work or school interact.  

Analysis of mathematical models of sleep/wake regulation: nonsmooth dynamics and bifurcations

Anne SkeldonGianne Derks

The most influential model of sleep/wake regulation is the two process model. This model postulates that sleep and wake occur as a result of the interaction of two oscillators, one describing circadian rhythmicity (the body clock) and one describing sleep homeostasis (sleep need). This model has formed the theoretical framework for sleep researchers for the last 30 years, and forms the backbone of recent `physiological' models of sleep. The two process model is an interesting example of a nonsmooth dynamical system. With our PhD student, Matt Bailey, we have been investigating the bifurcations and dynamics of the two process model.

The two process model can be represented as a circle map. With Paul Glendinning (Manchester), we have been analysing a broader class of `threshold models' of which the two process model is an example.

Crime is rarely spatially or temporally constant and often occurs in spikes (in time) or hotspots (in space).

The development of mechanistic dynamical models that can predict these spikes and hotspots is an emerging area in the field of mathematical criminology, where we develop a range of agent-based and partial-differential equations-based models to analyse the qualitative behaviour of crime and combine with data.

This work requires an interesting combination of mathematical modelling, dynamical systems analysis and Bayesian statistics.

The simplest type of crime is urban burglary and provides an excellent `testbed’ to explore the mathematical problems that one encounters when trying forecast crime. Interesting problems in this area look at how to model police response, neighbourhood effects and uncertainty in the data.

Development of fast, efficient data assimilation methods

David LloydNaratip Santitissadeekorn

We are developing novel methods to combine data and models to make medium to long-term forecasts. This work is in collaboration with Martin Short (Georgia Tech).

Riots in urban crime

David Lloyd

Analysis of invading riot fronts in urban crime partial differential models with nonlocal effects.

Data analysis and statistical techniques are an essential element in many cross-disciplinary projects. Within MoLSS, we have expertise in the design of experiments, the development of new data assimilation methods and novel methods for the analysis of physiological time series.

Design of experiments

Janet Godolphin

Design of experiments concerns the planning of a task to describe or explain the relationship between factors affecting a process and the output of that process. That is, it is used to find cause-and-effect relationships and to obtain comparisons between treatments. Experimental design has a role in many areas of research including: drug development; horticultural research; improvement of industrial processes.

Current research areas include robustness against design breakdown and construction of fractional and factorial designs with runs in blocks.

Robustness against design breakdown

Nuisance factors are design factors, such as batches of raw material in a manufacturing process, that affect the response but which are of no interest. Blocking is a technique used to eliminate the effect of nuisance factors on treatment comparisons. It is generally straightforward to obtain a blocked design with "good" properties. However, observations can be lost during experimentation so the eventual design is different from the planned design and may have less desirable properties. In the most extreme situation, an eventual design can be disconnected and it will not be possible to make comparisons between all treatments. Understanding the causes of design breakdown for different design types leads to a design selection approach that incorporates robustness against breakdown through observation loss.

Construction of fractional and factorial designs with runs in blocks

Manufacturing and other industrial processes can involve a large number of factors and factorial designs and fractional factorial designs play an important role in optimising such processes. A current problem concerns the construction of designs providing estimates of all main effects and two factor interactions when the treatment structure is factorial but, due to practical constraints, runs are arranged in blocks.

Data assimilation for urban crime models

Naratip Santitissadeekorn

Recent mathematical research has developed several crime models such as agent-based model (ABM) for the urban burglary that incorporate well-known interactions between individual criminals and environment at the neighborhood level. These models provide an important tool to establish the links between hypothesized criminal behaviors embedded in the models and observed crime data. I have been developing a nonlinear filtering algorithm technique that can statistically merge the model predictions with the crime data, mathematically modeled a point process, in order to make better projections of future crime patterns such as crime hot spots. It will also provide a noninvasive tool to quantify some well-known criminal behaviors (e.g. near-repeat victimization).

Data assimilation in the neighbourhood of bifurcations

Anne Skeldon

Data assimilation involves fusing models and data either to estimate model parameters or to predict state variables, or both. In order to develop robust algorithms, it is important to understand both the data and the model structure. Motivated by models of the carbon cycle in forests, we have been analysing and evaluating the performance of data assimilation schemes in the neighbourhood of tipping points.

Our people

Academic staff

Gianne Derks profile image

Professor Gianne Derks

Head of Department of Mathematics

Carina Dunlop profile image

Dr Carina Dunlop

Senior Lecturer

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Professor David Lloyd

Professor in Mathematics

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Professor Mark Roberts

Professor (Emeritus)

Naratip Santitissadeekorn profile image

Dr Naratip Santitissadeekorn

Senior Lecturer in Data Assimilation

Research staff

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Dr Sylvain Delahaies

Visiting Research Fellow

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Peter Williams

Statistics Consultant

Postgraduate research students

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Jane Lyle

Postgraduate Research Student

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Adam Nasim

Postgraduate Research Student

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Dr Josephine Solowiej-Wedderburn

Postgraduate Research Student

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Dr Imran Usmani

Postgraduate Research Student

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Department of Mathematics
Thomas Telford building (AA), floor 4
University of Surrey