| Carlos Braumann, Patrícia Filipe, Clara Carlos, Nuno Brites | Carlos J. Roquete |
| CIMA/U Evora | ICAAM/U Évora |
| Portugal | Portugal |
Abstract
Many of the deterministic models proposed in the literature for the growth of an individual animal (or plant) from birth to maturity can be written in the form dY(t)=β(α-Y(t))dt, where Y(t)=h(X(t)), with h a strictly increasing continuously differentiable function and X(t) the size of the individual at age t. Different models have specific functional forms for h (e.g., the Gompertz model has h(x)=ln x, and the Bertalanffy-Richards model has h(x)=xc). Of course, α=h(A), where A is the asymptotic (maturity) size. In a randomly fluctuating environment, we propose stochastic differential equation (SDE) models of the type dY(t)=β(α-Y(t))dt+σ dW(t), where σ is an environmental noise intensity parameter and W(t) is a standard Wiener process.
Properties of the model are deduced, including studying the time required for an animal to reach a given size. Statistical issues concerning parameter estimation and prediction will also be tackled and an real life application to cattle data will be shown. Optimization issues in livestock management will be considered and applied to the same data (applications in forestry are also possible). Of course, when a livestock producer has several animals, it is likely that the average asymptotic size A varies from animal to animal according to some distribution. This generalization is also considered here.
Jornada Matemática SPM/CIM "Mathematical Biology"