biology

Population Dynamics

Model how populations grow, age, and collapse — from epidemic spreading and demographic transitions to Malthusian limits and age-structured pyramids.

populationepidemicSIR modeldemographyMalthuslogistic growthpopulation pyramid

Population dynamics studies how and why populations change over time. Whether tracking the spread of a disease through a city, forecasting demographic shifts across generations, or understanding why some populations crash while others explode, the same mathematical frameworks apply — differential equations, matrix models, and feedback loops.

These simulations let you run SIR epidemic models, build age-structured populations, watch demographic transitions unfold over centuries, compare Malthusian versus logistic growth, and construct animated population pyramids. Tweak birth rates, mortality, and contact rates to see how small parameter changes produce dramatically different futures.

5 interactive simulations

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Age-Structured Population Model

Model how age-specific birth and death rates shape a population's age distribution over generations using Leslie matrix dynamics

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Demographic Transition Stages

Simulate the four stages of demographic transition — from high birth/death rates to low rates — and watch population explode then stabilize

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Malthusian vs Logistic Growth

Compare unlimited exponential growth against resource-limited logistic growth — see why Malthus was right about the math but wrong about the outcome

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Population Pyramid Dynamics

Build animated population pyramids — watch how birth rates, mortality, and migration reshape the age-sex distribution over decades

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SIR Epidemic Model Simulator

Simulate how infectious diseases spread through populations using the SIR model — adjust transmission and recovery rates to flatten the curve