CV CV Institute for Mathematics and Its Application Home: (612) 346-8397 University of Minnesota Work: (612) 626-0779 400 Lind Hall, 207 Church st. S.E. Fax: (612) 626-7370 Minneapolis, MN 55455 E-mail: pnelson@ima.umn.edu
Ph.D. 1998 University of Washington, Seattle, Washington
Dissertation: Mathematical Models in Immunology and
HIV Pathogenesis.
Advisor: Professor J.D. Murray, FRS
M.S. 1997 University of Washington, Seattle, Washington
Applied Mathematics
B.S. 1994 Arizona State University, Tempe, Arizona
Applied Mathematics
Mathematical Biology (the application of mathematics to
medicine, immunology, cancer, and cellular dynamics),
Differential Equations, Perturbations Methods, and
Non-Linear Dynamics.
1999-present Book reviewer for the Society of Mathematical Biology.1998-present Research reviewer for numerous journals.
1998-1999 Post-doctoral Associate, University of Minnesota Institute for Mathematics and Its Applications
1994 Teaching and Research Assistant, Arizona State University
1992-1994 Test Manager, at Arizona State University, Department of Mathematics. I was responsible for the development and preparation of undergraduate exams in Intermediate Algebra, Algebra, Pre-Calculus, and Business Math. Supervisor: Professor Floyd Downs, Director of Undergraduate Mathematics. (602) 965 - 3951.
1997/1998 Research Associate, Department of Applied Mathematics,
Univeristy of Washington. Development of a model and
numerical code to study a mechanochemical system of biological
pattern formation.
1997/1998 NSF Training Grant, Department of Zoology, University of
Washington. Traineeship in Mathematical Biology to develop
mathematical models to use in understanding the dynamics of the
immune system.
1995/1996 Teaching Assistant, University of Washington
Assistant in graduate level Numerical Analysis sequence,
Responsible for teaching several lectures each term.
1994 Teaching Assistant, University of Washington, Department of
Astronomy. Responsible for teaching two lab sessions each week.
1993 Teaching Assistant, Arizona State University
Responsible for teaching introductory algebra and trigonometry.
* Study of delay differential equations and their application to
theoretical immunology. Currently, I am examining a system of
differential difference equations and the effects of including
a delay on the estimates for certain crucial parameters in
HIV pathogenesis.
* Analysis of receptor aggregation during an immune response to
allergies.
* Development of mathematical models used to study the dynamics of
HIV infection. Using delay differential equations to capture
the essential delays associated with drug therapy and cellular
replication. This work is in collaboration with Dr. Alan
S. Perelson at the Los Alamos National Laboratory.
* Developing a set of non-linear differential equations to model
the immune system, particularly in response to specific pathogens
such as measles, TB, and Herpes. I am looking at interactions
between macrophages, cytokines, and T-cells infected with bacteria,
parasite, or fungus and the systems' response to an invasion by a
virus. This work is motivated by the severity of secondary infections
in children with the measles virus.
* Obtained numerical solutions for singularly perturbed initial
value problems for simple ordinary differential equations. These
results were then compared with the analytical results obtained
by Professor Robert O'Malley, University of Washington, Department
of Applied Mathematics. My work is cited in his paper
"Stiff Differential Equations and Singular Problems".
* Developed a set of PDE equations for modeling prostate tumor
growth and androgen independent relapse. Work was in collaboration
with Dr. Larry True, a pathologist in the medical school, who
performed clinical experiments using nude mice to determine the
levels of a prostate specific antigen and other proteins in response
to the growth of prostate tumors before and after castration. As
well as working on developing the model equations, I was
responsible for doing numerical simulations analyzing competition
between two different types of cancer cells.
* Studying the effects of drug resistant pneumonia in day care
centers. Using a set of differential equations to examine the
effects of drug treatment in children and the effects of drug
resistance in day care. Working with Dr. Tao Sheng Kwan-gett,
MD, School of Public Health, University of Washington.
* Analyzing nonlinear oscillators and the deterioration of the
limit cycles in response to forcing. An application will deal
with biological systems with limit cycle dynamics and forcing
in response to seasonality. Work is in collaboration with
Professor William O Criminale, Department of Applied
Mathematics.
1999 * Duke University, May (invited).
Workshop on Mathematical Biology for Undergraduates,
Department of Mathematics.
Title: Mathematical models and the Immune System.
1999 * Arizona State University, April (invited).
Mathematical Biology Seminar Series, Department of
Mathematics,
Title: Analysis of an intracellur delay model used to
study HIV pathogenesis.
1998 * Institute for Mathematics and Its Applications. University of
Minnesota, Nov. Drug Therapy Models of HIV Infection.
1998 * Univeristy of Washington, May.
Thesis Defense: Mathematical Models of HIV and Immunology.
1998 * Pacific Northwest Workshop in Mathematical Biology, March
(Invited).
Title: The effects of variable drug efficacy on the dynamics of
HIV-1 in vivo.
1998 * Washington State University, January (Invited).
Mathematics Colloquium, Department of Pure and Applied Mathematics,
Title: Examining HIV-1 Dynamics using Delay Differential
Equations and Variable Drug Efficacy.
1998 * Washington State University, January (Invited).
Microbiology Colloquium, Department of Microbiology,
Title: Understanding the Innate and Cell-mediated Immune
Responses to Infections.
1997 * Vanderbilt University, May.
Mathematical Models in Medicine and Health Sciences.(Conference)
Title: Interaction between Macrophages, Cytokines and the
Measles virus.
1997 * University of Washington, October.
Mathematical Biology Training Program, Department of Zoology,
Title: Using mathematical models to better understand the
dynamics of HIV progression in vivo.
1997 * University of Washington, March.
Graduate Student Seminar Series, Department of Applied Mathematics.
* Perelson, A.S and Nelson, P.W. Mathematical Models of HIV-1
Dynamics in vivo.
SIAM Review V41 1, pgs3-44
* Nelson, P.W. Mathematical Models in Immunology and HIV
Ph.D. Thesis (University of Washington)
* Nelson, P.W., Murray, J.D., and Perelson, A.S. Analysis of a
system of delay differential equations; How does the delay
change the model's prediction of kinetic parameters.
(submitted Mathematical Biosciences)
* Nelson, P.W., Mittler, J. and Perelson, A.S.
Estimating kinetic parameters in HIV pathogenesis with
models incorporating intracellular delays. (In Prepartation)
* Nelson, P.W. Models of Macrophage Activation in
Response to Pathogens (submitted Bulletin of
Mathematical Biology)
* Kwan-Gett, T.S., Nelson, P.W. and Hughes, J. Emergence of Drug
Resistance Pneumonia in Children in Daycare
Centers. (submitted Emerging Infectious Diseases)
* Criminale, W.O., Jackson, T.L. and Nelson, P.W. Analysis of
Coupled Non-linear Oscillators. (In preparation)
* Nelson, P.W., Weinberger, H.F. and Perelson, A.S.
Determining a closed region in 3 dimensional space and
its implication to the biology for a general model used
to study infectious diseases. (In preparation)
1999 * Visiting Scientist, Los Alamos National Laboratory.1998 * Research Associate at Los Alamos National Laboratory.
1997/98 * Research Assistant, University of Washington, Department of Applied Mathematics.
1997/98 * NSF Training Grant, University of Washington, Department of Zoology. Fellowship to develop and analyze mathematical models applied to biology.
1997 * Staff Research Assistantship at Los Alamos National Laboratory. Supervisor: Dr. Alan Perelson
1994 * Nominated for outstanding graduating senior in the College of Liberal Arts and Sciences at Arizona State University
* SMB, Society of Mathematical Biologists (1997)
* SIAM, Society of Industrial and Applied Mathematics (1997).
* EID, Emerging Infectious Diseases (Center for Disease
Control) (1997).
* MAA, The Mathematical Association of America (1998)
1998 * Co-Organizer of a tutorial on HIV Pathogenesis to be given
at the Institute for Mathematics and Its Application in
preparation for the workshop on HIV Modeling.
1998 * Co-Organizer of the sixth annual Pacific Northwest Workshop
in Mathematical Biology. This year the conference was held
on the San Juan Islands on the last weekend of March.
1997/98 * Organizer of the Graduate Student Seminar Series in Applied
Mathematics at the University of Washington.
1996/98 * Volunteer Scientist for the Department of BioTechnology, University
of Washington. Working with local high schools and grade schools
to improve the methods in which science is taught and enjoyed in
school.
1996/98 * Organizer for the journal club in Mathematical Biology. Set up
projects for new students to work on to get a feel for
mathematical biology.
1995/96 * Graduate Student Representative for the Department of Applied
Mathematics. Selected by the students to represent their views
and comments to the faculty.
Hardware: Unix workstations, Linux, IBM.
O/S: Unix, Linux, Dos and Windows.
Languages: Fortran, Basic.
Software: Matlab, Mathematica, Maple, LaTex, Tex and many
differential equation solvers.
Applied Linear Algebra, Complex Analysis, Ordinary and Partial Differential Equations, Mathematical Biology I, II, Calculus of Variations, Probability and Stochastic Modeling, Fluid Dynamics, Advanced Methods in Partial Differential Equations I, II, Nonlinear Dynamics and Chaos, Advanced Topics in Numerical Analysis I, Mathematical Modeling, and Advanced Immunology I, II
Hiking, climbing, fishing, sports, reading, cooking
and collecting baseball cards.
Professor J.D. Murray FRS Dr. Alan S. Perelson
Department of Applied Mathematics Group Leader
University of Washington Theoretical Biology & Biophysics
Seattle, WA 98195 MS-K710, T-10
Tel: (206) 685 - 2841 Los Alamos National Laboratory
E-mail: murrayjd@amath.washington.edu E-mail: asp@t10.lanl.gov
Professor Jerry Kevorkian Professor William Criminale
Department of Applied Mathematics Department of Applied Mathematics
University of Washington University of Washington
Seattle, WA 98195 Seattle, WA 98195
Tel: (206) 543 - 5493 Tel: (206) 543 - 5493
E-mail: kevork@amath.washington.edu E-mail: lascala@amath.washington.edu