Date
Sections
Lecture notes
Homework
Other readings
Programs
10/18(R)
Exam 1
1 2 3
10/23(T)
6.6
Lecture14
Homework 6 (due 10/26)
10/25(R)
8.3, 8.6
Lecture15
Lecture16 (summarizing
12-15)
competition
and mutualism
10/30(T)
6.6
Lecture17
Homework
7 (due 11/2)
infectious
disease
epidemic
pandemic
epidemic
models
CDC
outbreak page
sir.m
predatorprey.m
hopf.m
hiv.m
11/1(R)
6.6
Lecture18
Lecture18a
R0
e
is for Ebola
How
memes go viral
Math
of zombies
Spread
of epidemic disease on networks
11/6(T)
7.1-7.5, 8.8
Lecture19
Lecture19a
Homework
8 (due 11/9)
Enzyme rate
equation
autocatalytic
reaction
sigmoid
function Hill
function
11/8(R)
8.1-8.2, 8.5
Lecture20
action
potential
Hodgkin–Huxley
model
FitzHugh-Nagumo
model
Morris-Lecar
model
oscillating
chemical reaction (video)
11/13(T)
9.1-9.5
Lecture21
Lecture21a
Homework 9 (due 11/16)
Diffusion
Molecular
diffusion
diffusion
coefficient
random
walk
Brownian
motion Binomial
distribution
Normal
Distribution
Einstein
1905 (Brownian)
How
sneeze particles travel inside an airplane (video)
Molecular
diffusion (video)
random
walk
random
walk 2d
random
walk 3d
Brownian
motion
Binomial
dis
Normal
dis
heat
eq 1
heat
eq 2
11/15(R)
10.5-10.6
Lecture22
Invasive
species
Fisher's
equation
11/20(T)
6.4, 9.8
Lecture23
Lecture23a
Routh–Hurwitz
stability criterion
11/22(R)
Thanksgiving
no class
11/27(T)
11.4-11.7
Lecture24
animal
coat
Lecture24a
Homework
10 (due 11/30)
Alan
Turing pattern
formation
Gierer-Meinhardt
model
The
Imitation Game (trailer) (video)
pattern
formation (video) more
Gierer-Meinhardt
model spot (video)
Gierer-Meinhardt
labyrinth (video)
schnakenberg
model simulation
11/29(R)
Berry, Briggs(Wong), Gaines, Gizaw, Hauk,
Hwang, James,
12/4(T)
Kean,Larson(Stevenson), Lin, Liu, McKay,
Miller, Noll, Raj,
12/6(R)
Roy, Shang, Song, Stevenson(Larson),
Stolting, Tseng, Wong(Briggs), Zhang
12/12(F)
12/16(T)
General Articles in
Mathematical biology
Modeling
of
Biological Systems , A Workshop at the
National Science Foundation in 1996
Mathematical Biology is Good for Mathematics Michael C. Reed, Notices of
American Mathematical Society, October 2015.
When
Does Compromise Prevent More Pollution? C.
Clemons, J. Cossey, M. Ferrara, S. Forcey, T. Norfolk, G.
Obeng, D. Ricciardi, and G. Young. Notices
of American Mathematical Society, October 2012.
Why
Are There No 3-Headed Monsters? Mathematical Modeling in
Biology J. D. Murray. Notices
of American Mathematical Society, June/July 2012.
What
Is Mathematical Biology and How Useful Is It? by
Avner Friedman, August 2010.
Climate
Change and the Mathematics of Transport in Sea Ice
by Kenneth Golden. May 2009
Mathematics, Biology, and Physics:
Interactions and Interdependence Michael C. Mackey
and Moisés Santillán, Notices of
American Mathematical Society, Sept, 2005.
Why
Is Mathematical Biology So Hard?
Michael C. Reed, Notices of American Mathematical Society,
March, 2004.
Uses
and Abuses of Mathematics in Biology Robert M. May, Science, February 6, 2004.
Mathematical Challenges from Genomics and
Molecular Biology Richard M. Karp, Notices of American Mathematical Society, May, 2002.
Mathematical Challenges in Spatial Ecology Claudia
Neuhauser, Notices of American
Mathematical Society, Dec. 2001.
Linking Mind to Brain: The Mathematics of
Biological Intelligence Stephen Grossberg, Notices of American Mathematical Society, Dec.
2000.
We Got Rhythm: Dynamical Systems of the
Nervous System Nancy Kopell, Notices
of American Mathematical Society, Jan. 2000.
Getting
Started
in Mathematical Biology Frank Hoppensteadt , Notices
of American Mathematical Society, Sept. 1995.
Some
Advice
to Young Mathematical Biologists
Kenneth Lange, (from internet), date unknown.
How
the leopard gets its spots? James
Murray, Scientific American, 258(3): 80-87, 1988.
Some Classical Papers of Mathematical Biology
G. H. Hardy, 1908. Mendelian
proportions
in a mixed population , Science , N. S. Vol. XXVIII: 49-50.
A. J. Lotka , 1920. Analytical
Note on Certain Rhythmic Relations in Organic Systems . PNAS , 6 :410-415.
R. Pearl and L.J. Reed, 1920. On
the rate of growth of the population of the United States
since 1790 and its mathematical representation . PNAS ,
6:275-288.
W. O. Kermack and A. G. McKendrick, 1927. A
Contribution to the Mathematical Theory of Epidemics .
Pro. Royal Soc. London. Series A, Vol. 115, No. 772,
700-721.
V. Volterra, 1926. Variazioni e fluttuazioni del numero
d'individui in specie animali conviventi," Mem. R.
Accad. Naz. dei Lincei 2: 31-113. (Variations and fluctuations of the number of
individuals in animal species living together ).
V. Volterra, 1926. Fluctuations in the
abundance of a species considered mathematically. Nature
118: 558-60.
G.F. Gause, 1934. The Struggle for
Existence , Baltimore: Williams & Wilkins.
R.A. Fisher, 1937. The
wave of advance of advantageous gene , Ann. Eugen . 7 : 355-369.
C. Elton and M. Nicholson, 1942. The
Ten-Year Cycle in Numbers of the Lynx in Canada . Jour.
Anim. Ecol. , Vol. 11, No. 2, 215-244.
P.H. Leslie, 1945. On
the use of matrices in certain population mathematics .
Biometrica , Vol. 33,183-212.
A. L. Hodgkin and A. F. Huxley, 1952. A
quantitative description of membrane current and its
application to conduction and excitation in nerve , J Physiol. 117 (4) : 500–544.
A. Turing, 1952. The
chemical basis of morphogenesis , Phil. Tran. Royal
Soc. London, Series B, No.641, Vol. 237, 37-72.
C.B. Huffaker, C.B. 1958, Experimental
Studies
on Predation: Dispersion factors and predator-prey
oscillations , Hilgardia 27 343-383.
P.H. Leslie, J.C. Gower, 1960. The
properties of a stochastic model for the predator-prey
type of interaction between two species . Biometrica ,
47, 219-234.
M.L. Rosenzweig, 1971. Paradox
of
enrichment: destabilization of exploitation ecosystems in
ecological time , Science
29 , 385-387.
A. Gierer, H. Meinhardt, 1972. A
theory of biological pattern formation . Biological
Cybernetics, Vol. 12, 30-39.
R.M. May, 1976. Simple
mathematical models with very complicated dynamics , Nature ,
Vol. 261, 459-467.
R.M. May, 1977. Thresholds
and breakpoints in ecosystems with a multiplicity of
stable states , Nature , Vol. 269, 471-477.
R. M Anderson and R.M. May, 1979. Population biology of
infectious diseases: Part
I , Nature , Vol. 280, 361-367. Part
II , Nature Vol. 280, 455-461.
Project topics:
Mackey-Glass model of physiological control systems.
paper
1 , paper 2 (see page 37 of textbook), web
(physiology, differential equations)
Backward
bifurcation in epidemic model (epidemiology,
differential equations ) Yuxin Shang
FitzHugh-Nagumo
model
in neural science (original
paper in 1961) (neuron science,differential
equations )
Killer whale population model. Paper
(ecology, difference equations) Hannah
Stevenson -Anders Larson
Flour beetle model. paper
1 , paper
2 (ecology , difference equations)
Spotted owl model. paper (ecology, difference
equations) Alec Miller
Cannibalism model paper
(ecology , difference equations) Hannah
Stevenson -Anders Larson
Feedback control in biochemical pathways paper
(biochemistry,differential equations)
Chaos in food chain model paper
(ecology, differential equations)
Oyster model paper
(marine sci, differential equations)
Reproduction and distribution rates of T-cells in
syphilis paper (disease)
HIV model paper
(disease, differential equations) Tiffany Tseng,
Elizabeth McKay
Fishery management paper
(fishery, differential equations) Harrison McGuire
Fairy rings paper
paper
paper
(plant)
Quorum sensing model paper
(bacteria)
Hypercycle model paper
(origin of life)
Mathematics of Darwin’s theory of evolution paper
(evolution) Abby Berry
Yellowstone wolf population model paper
(ecology) Teddy Noll
Ebola epidemics (epidemiology, differential
equations)
1918 influenza paper paper paper (epidemiology,
differential equations)
Lead in the human body paper
(biochemistry, differential equations) also see
textbook page 160 (problem 29)
Glucose-insulin model (medical application,
differential equations) (see Chapter 4, page 158-159,
problems 26-28) Lulu Zhang
Genetics model for breast cancer
Chaos in simple food web models with Omnivory paper
(ecology, differential equations) Phillip Hwang
Cooperativity effects on Ligand Fluctuations in mGluR
A Computational Study of Neurexin Mutations Leading to
Dynamic Neuronal Network Activity Martha Gizaw
The Effect of the Grey Squirrel Invasion on Red Squirrel
Population in the United Kingdom Kathryn Kean
Mathematical Model to Account for Relative Abundance
Factor in the Success of Batesian Mimicry Lindsay
Stolting
Demographic and genetic consequences of environmental
heterogeneity for biological control Xi Lin
Detecting the Spatial Scale Limit of Lacunarity for
Grey-Scale Raster and/or Point Data from a Moving Window
Analysis using Differential Equations Mollie Gaines
Modeling Phage Growth in Relation to Bacterial Population
Dynamics Autumn Liu
Panda population model Jingzheng Song
Pharmacokinetic/pharmacodynamic model for aspirin Ban
Hauk
SIR Differential Equations Model to study Influenza Roy
Rudraksh
Michael James
Stabilizing Fish Populations Through Pollution Tax
Michael Briggs-Evan Wong
Optimization of Crop Biomass Growth Through Regulating
Water Supply Michael Briggs-Evan Wong