Syllabus
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Course Code: Elective 6 MMATH21 -413 Course Name: Bio-Mathematics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Population Dynamics: The Malthusian growth ; The Logistic equation; A model of species
competition; The Lotka-Volterra predator-prey model; Age-structured Populations : Fibonacci’s rabbits; The golden ratio Φ; The Fibonacci numbers in a sunflower; Rabbits are an age-structured population; Discrete age-structured populations; Continuous age-structured populations; The brood size of a hermaphroditic worm. |
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| 2 | Stochastic Population Growth : A stochastic model of population growth; Asymptotics of large
initial populations; Derivation of the deterministic model; Derivation of the normal probability
distribution; Simulation of population growth. Infectious Disease Modeling: The SI model; The SIS model; The SIR epidemic disease model; Vaccination ; The SIR endemic disease model ; Evolution of virulence. |
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| 3 | Population Genetics: Haploid genetics; Spread of a favored allele; Mutation-selection balance ; Diploid genetics; Sexual reproduction; Spread of a favored allele; Mutation-selection balance; Heterosis; Frequency-dependent selection; Linkage equilibrium; Random genetic drift. | |
| 4 | Biochemical Reactions: The law of mass action; Enzyme kinetics; Competitive inhibition; Allosteric inhibition; Cooperativity. Sequence Alignment: DNA ; Brute force alignment; Dynamic programming; Gaps; Local alignments; Software. | |
