A model for the trapping of animals with a circular pitfall is formulated. The model's assumptions are: The animals move independently according to the same Brownian motions. The boundary of the pitfall acts as an absorbing or elastic barrier. Initially a fixed number of animals is independently homogeneously distributed over a finite study area, or the initial positions follow a homogeneous planar Poisson process. The model depends on three free parameters: the motility of the animals, their reaction to the pitfall, (...) the initial density.It appears that the catches in disjoint time intervals are multinomially or independently Poisson distributed. The parameters of these distributions are obtained by solving certain partial differential equations. (shrink)

Kendall's (1956) approach to the general epidemic is generalized by dropping the assumptions of constant infectivity and random recovery or death of ill individuals. A great deal of attention is paid to the biological background and the heuristics of the model formulation. Some new results are: (l) the derivation of Kermack's and McKendrick's integral equation from what seems to be the most general set of assumptions in section 2.2, (2) the use of Kermack's and McKendrick's final value equation to arrive (...) at a finite time version of the threshold theorem for the general case, comparable to that for the case of only one Markovian state of illness in section 2.5, (3) the analysis of the behaviour of the solutions of the integral equation when the starting infection approaches zero in section 2.7, (4) the derivation of the probability structure of a general branching process, after conditioning on extinction in section 3.6, (5) the statement of the generalized versions of Kendall's ideas in the form of precise limit conjectures in section 4, (6) the derivation of a closed expression for the limit epidemic resulting from (3) in appendix 4. (shrink)