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Abstract and Applied Analysis
Volume 2014, Article ID 234509, 11 pages
http://dx.doi.org/10.1155/2014/234509
Research Article

A Hand-Foot-and-Mouth Disease Model with Periodic Transmission Rate in Wenzhou, China

1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
2Wenzhou Center for Disease Control and Prevention, Wenzhou 325000, China

Received 11 January 2014; Revised 18 February 2014; Accepted 20 February 2014; Published 25 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Yeting Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish an SEIQRS epidemic model with periodic transmission rate to investigate the spread of seasonal HFMD in Wenzhou. The value of this study lies in two aspects. Mathematically, we show that the global dynamics of the HFMD model can be governed by its reproduction number ; if , the disease-free equilibrium of the model is globally asymptotically stable, which means that the disease will vanish after some period of time; while if , the model has at least one positive periodic solution and is uniformly persistent, which indicates that HFMD becomes an endemic disease. Epidemiologically, based on the statistical data of HFMD in Wenzhou, we find that the HFMD becomes an endemic disease and will break out in Wenzhou. One of the most interesting findings is that, for controlling the HFMD spread, we must increase the quarantined rate or decrease the treatment cycle.