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.
 explored the role of the choice of incidence function
in HIV models formulated in  and obtained that the phenomenon of backward bifurcation can be removed by substituting the standard incidence function
with a mass action incidence.
 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.