mathematics

Mathematical Biology & Population Dynamics

Mathematical models of living systems — predator-prey dynamics, epidemic spreading, morphogenesis patterns, traveling wavefronts in populations, and stochastic branching processes in cell lineages.

mathematical biologypopulation dynamicsepidemiologyreaction-diffusionLotka-VolterraSIR modelTuring patternsbranching process

Mathematical biology applies differential equations, stochastic processes, and dynamical systems theory to understand living organisms. From the oscillating populations of lynx and hare to the self-organized stripes on a zebrafish, mathematics reveals the hidden engines driving biological complexity. These models are not mere abstractions — they predict real outbreak trajectories, guide conservation strategies, and explain embryonic development.

These five simulations let you explore Lotka-Volterra predator-prey cycles, SIR epidemic compartment dynamics, Turing reaction-diffusion patterns, Fisher-KPP traveling waves, and Galton-Watson branching processes — each with real-time interactive parameters and scientifically accurate computations.

5 interactive simulations

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Galton-Watson Branching Process

Simulate stochastic branching processes — explore how offspring distribution determines extinction probability, population growth, and genealogical tree structure

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Fisher-KPP Traveling Wave Equation

Simulate Fisher-KPP traveling wavefronts — explore how diffusion and logistic growth combine to produce advancing population fronts at a minimum speed

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Lotka-Volterra Predator-Prey Dynamics

Simulate classic predator-prey oscillations — explore how birth rates, predation efficiency, and mortality shape population cycles in ecological systems

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SIR Compartment Epidemic Model

Simulate epidemic dynamics with the SIR model — explore how transmission rate, recovery rate, and population size determine outbreak size and herd immunity thresholds

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Turing Reaction-Diffusion Patterns

Simulate Turing morphogenesis — explore how activator-inhibitor diffusion ratios generate spots, stripes, and labyrinthine patterns from uniform initial conditions