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VOL. 53 | 2009 A discrete-time rodent-hantavirus model structured by infection and developmental stages
Curtis L. Wesley, Linda J. S. Allen, Colleen B. Jonsson, Yong-Kyu Chu, Robert D. Owen

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

Abstract

Hantaviruses are a group of viruses that infect wild rodents without causing any apparent illness or disease. New discrete-time models for the spread of hantavirus in a rodent population are formulated and analyzed. The models are structured by the stages of the infection, the stages of development, and the sex of the rodent. The basic reproduction number $\mathcal{R}_0$ is computed for the deterministic model and a condition is given for a simplified model with males only to be permanent. A stochastic model is also formulated. Numerical simulations illustrate the differences between the deterministic and stochastic models and the dynamics in the male and female rodents. It is shown, in the numerical examples, that a transcritical bifurcation occurs at $\mathcal{R}_0 = 1$ and a unique enzootic equilibrium exists when $\mathcal{R}_0 \gt 1$. The sensitivity of the equilibrium values to changes in the parameters is also investigated.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1177.92023
MathSciNet: MR2582435

Digital Object Identifier: 10.2969/aspm/05310387

Rights: Copyright © 2009 Mathematical Society of Japan

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