The researchers found that in the combined derivation and validation cohorts, there were 3,709 cardiovascular events and 818,478 person-years of follow-up (five-year cumulative

incidence function, 0.026 and 0.018 for men and women, respectively).

The model proposed by Fine-Gray models the cumulative

incidence function, considered by other authors as appropriate to estimate the death probabilities.

However, an alternative method, which is the cumulative probability of failure from a specific cause over time, was suggested and labeled the cumulative

incidence function (CIF) that accounted for the competing risks and has a reasonable interpretation.

[7] explored the role of the choice of

incidence function in HIV models formulated in [6] and obtained that the phenomenon of backward bifurcation can be removed by substituting the standard

incidence function with a mass action incidence.

[8] proposed a nonlinear saturated

incidence function g(I)S = [[beta]SI.sup.p]/(1 + [[alpha]I.sup.q]) to model the effect of behavioral changes to certain communicable disease, where [[beta]SI.sup.p] describes the infection force of the disease and 1/(1 + [[alpha]I.sup.P]) measures the inhibition effect from the behavioral change of the susceptible individuals when the number of infectious individuals increases.

One of the more widely-used techniques in modelling metapopulation dynamics within real landscapes is the

incidence function model (IFM; Hanski et al.

Petri-Net model consists of a 7-tuple such as a finite set P of place, a finite set T of transition, backward

incidence function B, forward

incidence function F, initial marking [[mu].sub.0], time function [tau], state function [epsilon].

In Part I, the chapters begin with relatively simple two-population and Levins metapopulation models, and then to

incidence function, state transition, and n-population models.

We analyze how z should vary with trophic rank, using a generalization of the

incidence function model of Holt (1993, 1996a).

To avoid the use of a single

incidence function, the use of a general incidence rate that includes a family of particular functions with similar properties has become a topic of interest by several authors (see, e.g., [4-8]).

This study presents an efficient parameter estimation method for SPOMs, which is applied to a well-defined SPOM, the

incidence function model (IFM; Hanski 1994a).

Recently, we have studied metapopulation processes with a stochastic patch occupancy model called the

incidence function model (Hanski 1994a, 1997, Hanski et al.