## Sammanfattning

We consider stochastic population processes (Markov jump processes)

that develop as consequence of the occurrence of randon events at

random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously

proposed, higher-order approximations are completely new. Further, we

analyse a model for insect development as a sequence of E developmental

stages regulated by rates that are linear in the implied subpopulations. Transitions to the next stage compete with death at all times. The process ends at a predetermined stage, for example pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.

that develop as consequence of the occurrence of randon events at

random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously

proposed, higher-order approximations are completely new. Further, we

analyse a model for insect development as a sequence of E developmental

stages regulated by rates that are linear in the implied subpopulations. Transitions to the next stage compete with death at all times. The process ends at a predetermined stage, for example pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.

Originalspråk | engelska |
---|---|

Artikelnummer | 873624 |

Tidskrift | The Scientific World Journal |

Volym | 2014 |

DOI | |

Status | Published - 2014 |

## Ämnesklassifikation (UKÄ)

- Matematik