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A semi-hybrid model for malaria with limited superinfection

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Philippe Picard
Philippe Picard*
Affiliation:
Université de Lyon 1
*
∗ Postal address: Mathématiques Appliquées, Université de Lyon 1, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France. Email address: isfa@univ_lyon1.fr
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Abstract

Modelling malaria with consistency necessitates the introduction of at least two families of interconnected processes. Even in a Markovian context the simplest fully stochastic model is intractable and is usually transformed into a hybrid model, by supposing that these two families are stochastically independent and linked only through two deterministic connections. A model closer to the fully stochastic model is presented here, where one of the two families is subordinated to the other and just a unique deterministic connection is required. For this model a threshold theorem can be proved but the threshold level is not the one obtained in a hybrid model. The difference disappears only when the human population size approaches infinity.

Keywords

Nåsell-Hirsch modelhybrid modelthreshold conditionasymptotic eradicationsaturation levelstwo-state Markov processsubordinated process

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1027 - 1057
Copyright
Copyright © Applied Probability Trust 1998 

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