Header

UZH-Logo

Maintenance Infos

Approximating the long-term behaviour of a model for parasitic infection


Luchsinger, C J (2001). Approximating the long-term behaviour of a model for parasitic infection. Journal of Mathematical Biology, 42(6):555-581.

Abstract

In a companion paper two stochastic models, useful for the initial behaviour of a parasitic infection, were introduced. Now we analyse the long term behaviour. First a law of large numbers is proved which allows us to analyse the deterministic analogues of the stochastic models. The behaviour of the deterministic models is analogous to the stochastic models in that again three basic reproduction ratios are necessary to fully describe the information needed to separate growth from extinction. The existence of stationary solutions is shown in the deterministic models, which can be used as a justification for simulation of quasi-equilibria in the stochastic models. Host-mortality is included in all models. The proofs involve martingale and coupling methods.

Abstract

In a companion paper two stochastic models, useful for the initial behaviour of a parasitic infection, were introduced. Now we analyse the long term behaviour. First a law of large numbers is proved which allows us to analyse the deterministic analogues of the stochastic models. The behaviour of the deterministic models is analogous to the stochastic models in that again three basic reproduction ratios are necessary to fully describe the information needed to separate growth from extinction. The existence of stationary solutions is shown in the deterministic models, which can be used as a justification for simulation of quasi-equilibria in the stochastic models. Host-mortality is included in all models. The proofs involve martingale and coupling methods.

Statistics

Citations

7 citations in Web of Science®
8 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

0 downloads since deposited on 23 Apr 2009
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:June 2001
Deposited On:23 Apr 2009 06:40
Last Modified:06 Dec 2017 19:33
Publisher:Springer
ISSN:0303-6812
Publisher DOI:https://doi.org/10.1007/s002850100083
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1845592

Download