Curriculum Vitae: Alun L. Lloyd
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and interests, publication list, educational
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||Professor, Graduate Program in Biomathematics,
Department of Mathematics, North Carolina State University.
||Graduate Program in Biomathematics
Department of Mathematics
North Carolina State University
|Phone (work): ||(919) 515-1910
|FAX (work):||(919) 515-1909
Research Experience and Interests
My research involves the use of mathematical models and statistical techniques to
address important biomedical questions.
The Impact of Spatial Heterogeneity, Stochasticity and Seasonality on the Dynamics of Populations
Few biological systems are well-mixed: interactions are usually spatially localized to some degree. Many biological systems are subject to randomness (stochasticity) and seasonality (due, for instance, to environmental or behavioral factors that vary over the course of a year). I have developed analytic techniques which help to understand the often complex interaction between spatial, stochastic and seasonal effects. Moment equations can be used to estimate the variability of stochastic processes, and can indicate when randomness is likely to play a major role in the behavior of a system. The study of certain spatial systems can be simplified by the use of a transformation technique, which decouples behavior in the vicinity of a spatially homogeneous state into separate modes. These techniques have been applied to the study of childhood diseases, such as measles, which provide an ideal model system within which the population-level impact of such factors can be studied. An example of an epidemiological question that can then be addressed is the degree to which epidemics in different regions are synchronized. This has important implications for understanding the persistence of such diseases despite relatively high vaccine usage in recent years.
Network Dynamics in Biology
Many biological processes can be described in terms of network models, in which nodes represent individuals (such as people, animal species, or genes and proteins) and edges between nodes represent possible interactions between individuals (social contact, species interactions or gene/protein interactions). Given this description, a natural question to ask is how network topology impacts upon the dynamics of the biological system. I have been examining this question, using an epidemiological system as a model, looking closely at the effect of detailed spatial structure on disease transmission and persistence. Hierarchical network structures are of particular interest, reflecting the different levels (cities, schools, families) on which disease transmission occurs. Research in this area is currently of particular interest to anti-bioterrorism planners, as it can inform the design of disease control measures which account for population structure.
Dynamics of Childhood Diseases in the United States
Detailed studies of historical incidence records of childhood diseases, together with modelling studies, have shed much light on the transmission dynamics and population-level behaviour of childhood diseases such as measles and chickenpox. I have computerized the available incidence data for measles, mumps, rubella and chickenpox for the United States, and this gives a monthly (or even weekly) account of cases in each of the fifty states since the fifties or sixties. Using this detailed data set I am addressing a range of questions, including basic phenomenological issues (such as disease periodicity and inter-epidemic intervals), effects of the introduction of vaccination programs and the spatial patterns of disease incidence.
Dynamics of Multistrain Viral Infections: Vaccination, Drug Treatment and Drug Resistance
Since many viruses evolve rapidly, infection-considered either at the individual or population level-often consists of a collection of co-circulating viral strains. In this project, the implications of multiple strain structure for the outcome of treatment (e.g. drug therapy) or control measures (such as mass vaccination or prophylactic drug use) on the spread of a disease are considered. An issue of particular interest is the potential for the emergence and spread of mutant virus strains which are resistant to drug therapy. A particular setting of interest is human rhinovirus infection: these viruses are responsible for roughly half of all common colds. Newly developed drugs have the potential for reducing the surprisingly large economic burden of cold infections, but with accompanying risks in terms of drug resistance.
Genetic Control of HAM/TSP Disease
Infection with human T lymphotropic virus type I (HTLV-I) can lead to one of several different outcomes: life-long asymptomatic infection, a neurological disorder (HTLV-I-associated myelopathy/tropical spastic parparesis: HAM/TSP), or rapidly fatal leukemia. Using data from a population in an area of southern Japan where HTLV-I is endemic, statistical techniques were used to study the host genetic and viral factors which influence an individual's viral load and outcome of HTLV-I infection. One particularly interesting result to emerge from this study was the finding that HLA class I alleles influence both virus load and infection outcome, arguing that a strong cytotoxic T lymphocyte (CTL) response can prevent disease in persistent virus infections.
Viral Dynamics of HIV and SIV Infection
uses statistical techniques and mathematical models to analyse
data on viral load in HIV and SIV infection. Previous work has lead to several important
results, including the estimation of the basic reproductive ratio (R0) of SIV and the
demonstration that virus load in the very early stages of infection (before the full onset
of specific immune responses) is critical in establishing the viral replication pattern
and the associated clinical course of SIV infection. Ongoing work is examining the role of
specific immune responses over the course of infection. Data obtained during initial
infection and subsequent drug treatment in macaques should reveal much about the formation
of specific immune responses and their impact on viral load during the post-acute
Rhythmic Phenomena in Biology
Rhythmic phenomena are seen throughout biology and on timescales from milliseconds to
years. In recent years, much has been learned about the molecular mechanisms underpinning
many of these rhythms, such as the circadian clock, allowing the formulation of detailed
kinetic models for such phenomena. I am interested in developing both detailed models and
more conceptual models which explain how such behaviour might be maintained and the
interactions which occur between oscillations on different timescales. I have also used
and developed statistical techniques which analyse time series data generated by such
systems, attempting to characterise the behaviour in dynamical terms (do any
irregularities arise from chaotic or random effects?) and to reveal the underlying
mechanisms which generate the data.
I am interested in addressing issues of model robustness; many approximations are made
when formulating mathematical models, often for mathematical convenience rather than on
biological grounds. In order to trust predictions made by models, it is necessary to have
a thorough understanding of the implications of such approximations and which properties
of models remain unaltered when they are made.
Educational and Employment History
- August 2003 to present
Associate Professor, North Carolina State University.
- October 1999 to August 2003
Long Term Member, Institute for Advanced Study, Princeton.
- October 1996 to September 1999
MRC Research Fellow, Department of Zoology, University of Oxford
and Lecturer in Statistics and Computer Packages in the Biological Sciences, St Hilda's
College, Oxford (from October 1997).
- October 1992 to September 1996
Studied for D.Phil. degree, Department of Zoology, University of Oxford.
Thesis title Mathematical Models for Spatial Heterogeneity in Population Dynamics and
Epidemiology, supervisor Professor Sir Robert May, FRS.
Supported by a four-year Wellcome Trust Mathematical Biology Scholarship.
- October 1988 to June 1992
Read mathematics at Trinity College, Cambridge.
First Class in Parts IA, IB and II of Mathematical Tripos.
Awarded Certificate of Advanced Mathematical Study (Mathematical Tripos Part III).
Prizes and Awards
||Institute of Physics Prize for best performance in Nuffield physics O level.
||Royal Society of Chemistry Prize for best performance in WJEC chemistry A level.
Awarded Ministry of Defence Student Scientist Sponsorship.
||Elected to Junior Scholarship, Trinity College, Cambridge.
||Elected to Senior Scholarship, Trinity College, Cambridge.
||Awarded Wellcome Trust Mathematical Biology Scholarship.
||Awarded Medical Research Council Non-Clinical Research Training Fellowship.
||Elected to a Stipendary Lectureship, St. Hilda's College, Oxford.
I have wide-ranging teaching experience. I was heavily involved in the teaching of the
Quantitative Methods (statistics and modelling) course in the Oxford departments of
Zoology and Plant Sciences. I have given numerous tutorials, demonstrated in practical
classes and advised several students on statistical issues arising from their final year
projects. For two years, I was responsible for teaching statistics to biology
undergraduates at St. Hilda's College, which involved the supervision of approximately
forty students in their second and third years. I have given several graduate level
lectures on subjects including epidemiology (Epidemiology Short Course, Depts. of Zoology
and Continuing Education, Oxford) and the use of statistical techniques in the analysis of
epidemiological data (Summer School on Nonlinear Dynamics in Biology, University of
I have been involved in several projects which have increased the public's
understanding of science, taking ideas from mathematical biology to a wider public
audience. I was involved in the National Theatre's (London, U.K.) production of Tom
Stoppard's play Arcadia, explaning scientific ideas and methodology to members of
the cast in addition to helping design the programme notes. I was an advisor on the Chaos
Box exhibition at the Science Museum, London. An article I wrote for Scientific
American described a computer implementation of the Prisoner's Dilemma, encouraging
readers to experiment with the model.
Last updated, August 2003.
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