Abstract
We consider a model of a branching stochastic process that takes into account the incubation period of the life of individuals. We demonstrate that such processes may be treated as a two-type age-dependent branching process with a periodic mean matrix. Based on this we derive the extinction probability and the asymptotic behavior of the mean number of individuals, when the Malthusian parameter exists. Exact formulas for the expected extinction time and for the distribution of the number of generations to extinction will be obtained. Possible applications in determining the optimal vaccination rate in epidemics will also be discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 71-88 |
| Number of pages | 18 |
| Journal | Stochastic Models |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2008 |
Bibliographical note
Funding Information:These results are part of the project No FT-2006/03 funded by King Fahd University of Petroleum and Minerals. We are indebted to KFUPM for the excellent research facilities. The first author thanks Ch. Jacob and E. Vergu, from INRA-Jouy en Josas, for useful discussions during the Workshop on Stochastic Modelling in Population Dynamics, April, 2007, CIRM, France. We are also grateful to both referees and the editors for their valuable comments on the first version of the paper.
Keywords
- Branching process
- Incubation period
- Malthusian parameter
- SIR epidemic
- Time to extinction
- Ultimate extinction
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics
