A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

✍ Scribed by K. G. Janardan

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 367 KB
• Volume: 39
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710390712

✦ Synopsis

This paper considers a generalized birth process {X,,,(r), t > 0) and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese. weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to mode1 such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.