Kasvumudel

Kasvumudel, or growth model, is a mathematical framework used to describe how the size of a system changes over time. In Estonian-language literature, kasvumudel is applied across disciplines such as biology, demography, economics and information diffusion to analyze how quantities grow or saturate.

A typical model defines a dependent variable N(t) that represents size at time t, and includes parameters such as the intrinsic growth rate r and, in capacity-limited formulations, carrying capacity K. Common forms include the exponential model, the logistic model and the Gompertz model. Exponential growth is described by dN/dt = rN, yielding unbounded increase in a constant environment. Logistic growth uses dN/dt = rN(1 − N/K), introducing a saturation effect as N approaches K. The Gompertz model has dN/dt = rN ln(K/N), producing a slower approach to carrying capacity. Extensions such as the Richards model and the von Bertalanffy model offer additional flexibility in the shape of the growth curve.

Applications of kasvumudel span population dynamics, tumor growth, spread of innovations, urban development and market adoption. Parameter estimation involves fitting the model to data, often through nonlinear least squares or maximum likelihood, using initial conditions and observed time points.

Limitations include assumptions of homogeneity, constant parameters and a closed system, which may not hold in real settings. External drivers, stochasticity and spatial structure can reduce predictive accuracy. Model selection commonly uses criteria like AIC or BIC to compare alternatives. Kasvumudel provides a concise, interpretable framework for describing growth processes, while acknowledging its simplifications.