Lecture notes, Supplementary material, Mathematica nb
Single
population dynamics (Ch. 1)
Discrete
population growth
Discrete dynamics: stability,
bifurcation diagram & chaos
Mathematica nb and links: Cobwebs; stability; power spectrum; Hassel map;
Basic
DE: logistic equation (data -calibration US population).
Derivation of logistic and its modifications
Bifurcations: Budworm infestation, (nb); Ludvig model
Biological delays
Differential-delay
equations; stability analysis.nb; nonlinear DDE.nb. Metapopulations
Structured populations
Age
structure (Leslie matrix, Euler-Lotka; McKendric approach)
Discrete age + continuous time: notes, nb
Notes on Laplace transform
Stochastic populations: nb
Working with population data: xls and nb (data for nb)
Population
dynamics of interacting species (Ch.2)
Host-parasitoid
interactions: notes, nb
Volterra - Lotka
predator-prey (nb) and its extensions: notes, nb (phase-plane, equilibria, stability, bifurcations)
Analysis of competition
Infectious
diseases (Ch. 3)
General intro (INTH 301/401, R. Blanton)
Modeling (SEIR methodology): ppt, pdf . Notes on extended SIR
Notebooks: Basic SIR; calibration, Contact pattern SIR
Vector-borne
diseases and macro-parasites: notes, nb
In-host
models (HIV and malaria)
Evolutionary aspects ("virulent-bening" competition)
Population genetics and evolution (Ch.4)
Mendelian genetics and selection (Hardy-Weinberg and FHW): nb.
The
balance between selection and mutation
Evolution
of genetic systems
Additional topics: DNA and nucleotides. Lectures on population genetics
Biological
motion (Ch. 5)
Macroscopic
theory of motion and Chemotaxis: Advection-diffusion, nb
Biological
invasion: plankton sedimentation. Transit time for diffusion
Reaction-diffusion and FK traveling wave analysis; nb
Basic bio-chemistry; Michaelis-Menten approach; nb
Additional notes on (i) Basic M-M as singular perturbation ; (ii) Cooperative and suiside substrate;
Neural
modeling (Hodgkin-Huxley and Fitzhugh-Nagumo): nb. Other examples (autocatalator.nb)
Basic
immunology and HIV/AIDS
Pattern
formation in reacting systems (Ch.7)
Turing
instability in double-diffusive systems;
LRA-SRI, bifurcations, color patterns; nb
Autocatalytic reactions and chemical oscillators:
Simple autocatalyzis, Volterra-Lotka, Brusselator (Turing patterns; nb)
Belousosv-Zhabotinsky: theory and patterns; cellular automata BZ
Chemotaxis (reaction with biological movement)
patterns from J.D. Murray; analysis (notes); nb
Mathematics, CWRU, Cleveland, OH 44106
E-mail: dxg5@case.edu
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