Mathematical Biology
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TOC
1 Population Growth
1.1 A deterministic model of population growth
1.2 A stochastic model of population growth
1.3 Asymptotics of large initial populations
1.3.1 Derivation of the deterministic model
1.3.2 Derivation of the normal probability distribution
1.4 Simulation of population growth
2 Age-structured populations
2.1 Fibonacci’s rabbits
2.1.1 The golden ratio
2.2 Rabbits are an age-structured population
2.3 Discrete age-structured populations
2.4 Continuous age-structured populations
2.5 The brood size of a hermaphroditic worm
3 Population Dynamics
3.1 Logistic equation for population growth
3.2 A model of species competition
3.3 The Lotka-Volterra predator-prey model
4 Infectious Disease Modeling
4.1 The SI model
4.2 The SIS model
4.3 The SIR epidemic disease model
4.4 The SIR endemic disease model
4.5 Vaccination
4.6 Evolution of virulence
5 Population Genetics
5.1 Haploid genetics
5.1.1 Spread of a favored allele
5.1.2 Mutation-selection balance
5.2 Diploid genetics
5.2.1 Sexual reproduction
5.2.2 Spread of a favored allele
5.2.3 Mutation-selection balance
5.2.4 Heterosis
5.3 Frequency-dependent selection
5.4 Linkage equilibrium
5.5 Random genetic drift
6 Biochemical Reactions
6.1 The law of mass action
6.2 Enzyme kinetics
6.3 Competitive inhibition
6.4 Allosteric inhibition
6.5 Cooperativity
7 Sequence Alignment
7.1 DNA
7.2 Brute force alignment
7.3 Dynamic programming
7.4 Gaps
7.5 Local alignments
7.6 Software
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