Vardayani Ratti
My research interest is in Mathematical Biology, in particular applications in ecology, infectious diseases, pollination biology and agriculture.
Recent invited talks
- Rochester Institute of Technology, Rochester, USA, 2018
- Arizona State University, Arizona, USA, 2018
- AMS Special Session at Spring Eastern Sectional Meetin, Northeastern University, Boston, 2018
- Sonia Kovalevsky Day, Dartmouth College, USA, 2018
- Bowdoin College, Maine, USA, 2018
- Fields Institute's Workshop on Pollinators and Pollination Modeling, Toronto, 2018
- Joint Mathematics Meeting, San Diego, USA, 2018
- Minisymposium on Mathematical Biology, Dartmouth College, 2017
- Joint Mathematics Meetings, Atlanta, USA, 2017
- Society of Mathematical Biology (SMB) Annual Meeting and Conference, Nottingham, UK, 2016
Contact
| John Wesley Young Research Instructor |
| Dartmouth College |
| Department of Mathematics |
| 27 N. Main Street |
| Hanover, NH 03755 |
Research
Manuscripts (undergraduate co-authors are in bold)
- Dorothy Wallace, Vardayani Ratti, Anita Kodali, Jonathan M. Winter, Matthew P. Ayres, Jonathan W. Chipman, Carissa F. Aoki, Erich C. Osterberg, Clara Silvanic, Trevor F. Partridge, Mariana J. Webb. The Effect of Rising Temperature on Lyme disease: Ixodes scapularis population dynamics and Borrelia burgdorferi transmission and prevalence. Submitted.
- Ratti, V.; Wallace, D.I. A malaria transmission model predicts holoendemic, hyperendemic, and hypoendemic transmission patterns under varied seasonal vector dynamics. Submitted.
- Wallace, D.I.; Kachalia, A.A.; Ratti, V. Effect of habitat diversity on the population dynamics of Anopheles gambiae. In preparation.
- Ratti, V.; Nanda, S.; Eszterhas, S. K.; Howell, A.; Wallace, D.I.(2018) A Mathematical Model of HIV dynamics Treated with a Population of Gene Edited Hematopoietic Progenitor Cells Exhibiting Threshold Phenomenon. Mathematical Medicine and Biology. DOI: 10.1093/imammb/dqz011 Pre-print
- Ratti, V.; Rheingold, E.; Wallace, D.I. (2018) Reduction of Mosquito Abundance Via Indoor Wall Treatments: A Mathematical Model. Journal of Medical Entomology, 55(4), 833-845.
- Ratti, V.; Kevan, P.G.; Eberl, H.J. (2017) A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus. Bulletin of Mathematical Biology. 79(6): 1218-1253.
- Ratti, V.; Kevan, P.G.; Eberl, H.J. (2016) A discrete-continuous modeling framework to study the role of swarming in a honeybee colony infested with Varroa destructor and Acute Bee Paralysis Virus. The 2015 AMMCS-CAIMS Congress. DOI: 10.1007/978-3-319-30379-6_28. In book: Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pp.299-308.
- Ratti, V.; Kevan, P.G.; Eberl, H.J.(2015) A mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex with seasonal effects. Bulletin of Mathematical Biology. 77(8):1493-1520.
- Ratti, V.; Kevan, P.G.; Eberl, H.J.(2013) A mathematical model of the honeybee-varroa destructor-acute bee paralysis virus complex. Canadian Applied Math Quarterly, 21(1):63-93.
Book Chapter
- Eberl, H.J.; Kevan, P.G.; Ratti, V.(2014) Infectious disease modeling for honeybee colonies in J. Dellivers(ed). “In Silico Bees”, p.87-134, CRC, Press Boca Raton.
Theses
- Ratti, V. Predictive Modeling of the Disease Dynamics of Honeybee-Varroa destructor-Virus Systems. Ph.D. Thesis
- Ratti, V. Local Stability Analysis of the Honeybee-Varroa destructor-Acute Bee Paralysis Virus. M.Sc. Thesis
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Teaching
Spring 2019
This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.
Textbook: Linear Algebra and Its Applications by Otto Breschler, Pearson 2013
Previous courses
This course involves collaborative learning. It is an introduction to single variable calculus aimed at students who have seen some calculus before, either before matriculation or in introductory calculus course (Math 1). Math 3 begins by revisiting the core topics in Math 1 - convergence, limits, and derivatives - in greater depth before moving to applications of differentiation such as related rates, finding extreme values, and optimization. The course then turns to integration theory, introducing the integral via Riemann sums, the fundamental theorem of calculus, and basic techniques of integration.
Textbook: ``Calculus'' by Herman and Strang's, Volume 1. (open access PDF)
This course is a sequel to Math 3 and provides an introduction to Taylor series and functions of several variables. The first third of the course is devoted to approximation of functions by Taylor polynomials and representing functions by Taylor series. The second third of the course introduces vector-valued functions. It begins with the study of vector geometry, equations of lines and planes, and space curves. The last third of the course is devoted to studying differential calculus of functions of several variables.
Textbook: ``Calculus", by James Stewart, 8th Edition, ISBN: 978-1-285-74062-1
This course is designed to provide students with the basic tools for building and analyzing mathematical models in Biology primarily using ordinary differential equations. In addition, you will learn how to analyze and simulate the models. You will also learn to interpret and communicate the results in the context of biology.
Textbooks:
- ``Classics in Applied Mathematics'' by Leah Edelstein-Keshet
- ``Essential Mathematical Biology'' by Nicholas F. Britton
- ``Mathematical Biology'' by James D. Murray
This course presents the fundamental concepts and applications of linear algebra with emphasis on Euclidean space. Significant goals of the course are that the student develop the ability to perform meaningful computations and to write accurate proofs. Topics include bases, subspaces, dimension, determinants, characteristic polynomials, eigenvalues, eigenvectors, and especially matrix representations of linear transformations and change of basis. Applications may be drawn from areas such as optimization, statistics, biology, physics, and signal processing.
Textbook: Linear Algebra and Its Applications (5th Edition) by David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson 2015
This course is a sequel to Math 8 and provides an introduction to calculus of vector-valued functions. The course starts with iterated, double, triple, and surface integrals including change of coordinates. The remainder of the course is devoted to vector fields, line integrals, Green’s theorem, curl and divergence, and Stokes’ theorem.
Textbook: ``Calculus Early Transcendentals Multivariable", by Rogawski & Adams, 3rd Edition, ISBN: 978-1464171758
This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations using eigenvectors and eigenvalues, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series.
Textbook: Elementary Differential Equations and Boundary Value Problems (10th Edition) by Boyce & DiPrima, Wiley 2012
Graduate Teaching Assistant (2009 - 2015)
- Partial Differential Equations, Winter 2015
- Biomathematics I, Winter 2014
- Matrix Algebra, Winter 2014
- Linear Algebra, Winter 2013
- Integrated Math Physics I, Fall 2012
- Elements of Calculus II, Winter 2010, Fall 2010, Fall 2011
- Differential Equations I, Winter 2010, Fall 2010
- Applied Differential Equations II, Winter 2011, Winter 2010
- Biomathematics, Winter 2011
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