A note on dynamics of an age-of-infection cholera model

Mathematical Biosciences and Engineering : MBE
Jinliang WangToshikazu Kuniya

Abstract

A recent paper [F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10, 2013, 1335--1349.] presented a model for the dynamics of cholera transmission. The model is incorporated with both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is proved to be a sharp threshold determining whether or not cholera dies out. The global stability for disease-free equilibrium and endemic equilibrium is proved by constructing suitable Lyapunov functionals. However, for the proof of the global stability of endemic equilibrium, we have to show first the relative compactness of the orbit generated by model in order to make use of the invariance principle. Furthermore, uniform persistence of system must be shown since the Lyapunov functional is possible to be infinite if i(a,t)/i*(a)=0 on some age interval. In this note, we give a supplement to above paper with necessary mathematical arguments.

References

May 1, 1980·Archives of Disease in Childhood·J A Walker-Smith
Apr 18, 2003·Frontiers in Bioscience : a Journal and Virtual Library·Ann Louise Olson, John B Knight
Jan 15, 2013·Mathematical Biosciences and Engineering : MBE·C Connell McCluskey
Nov 20, 2013·Mathematical Biosciences and Engineering : MBE·Fred BrauerP van den Driessche
Feb 11, 2014·Mathematical Biosciences and Engineering : MBE·Jianxin YangXue-Zhi Li
Feb 18, 2015·Journal of Biological Dynamics·Jinliang WangToshikazu Kuniya

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Citations

Sep 7, 2016·Journal of Biological Dynamics·Jinliang WangYuming Chen
Jan 18, 2017·Mathematical Biosciences and Engineering : MBE·Shaoli WangLibin Rong
Nov 23, 2017·Mathematical Biosciences and Engineering : MBE·Shanjing Ren

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