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Biomathematics
Explore growth and populations; epidemics and reactions; space, evolution and inference. Concepts and connections are available independently of video coverage.
Prerequisites and connections
Ordinary differential equations
An ODE relates an unknown function of one variable to its derivatives.
Video explanations to be added
Growth and populations
Exponential growth
A constant per-capita growth rate yields exponential population change.
Video explanations to be addedLogistic growth
Density-dependent growth slows toward a carrying capacity in the basic logistic model.
Video explanations to be addedLotka–Volterra models
Coupled equations represent predator–prey or competition interactions under simplified assumptions.
Video explanations to be addedPopulation matrix models
Age or stage structure produces matrix updates of population counts.
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Epidemics and reactions
SIR models
Susceptible, infectious and recovered compartments evolve through transmission and recovery rules.
Video explanations to be addedReproduction number
A reproduction number summarizes secondary infections in a specified epidemic setting.
Video explanations to be addedReaction kinetics
Reaction rates determine concentration changes through stoichiometry and kinetic assumptions.
Video explanations to be addedMichaelis–Menten kinetics
A saturating enzyme-rate law arises under appropriate kinetic and approximation assumptions.
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Space, evolution and inference
Reaction–diffusion systems
Local reactions and spatial diffusion jointly evolve concentrations or populations.
Video explanations to be addedTuring patterns
Diffusion can destabilize a reaction equilibrium and create spatial patterns under suitable parameter conditions.
Video explanations to be addedEvolutionary dynamics
Selection, mutation and interaction change trait or strategy frequencies.
Video explanations to be addedBiological parameter inference
Data constrain model parameters, with identifiability and uncertainty affecting interpretation.
Video explanations to be added