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Math. Comput. Appl. 2017, 22(2), 29; doi:10.3390/mca22020029

Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number

School of Mathematics and Physics, Changzhou University, Changzhou 213164, Jiangsu, China
Academic Editor: Fazal M. Mahomed
Received: 8 February 2017 / Revised: 2 April 2017 / Accepted: 4 April 2017 / Published: 8 April 2017
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Abstract

Firstly, an SEIR mathematical model with standard incidence rate is established to describe the transmission of Hand-Foot-Mouth disease (HFMD). The equilibrium of the nondimensionalized model is calculated and the basic reproduction number of the model is defined. In addition, the local stability of the equilibrium is analyzed via the characteristic roots of the Jacobian matrix at the equilibrium, respectively. Numerical simulations are given to confirm the theoretical results. Secondly, a formula aimed to estimate the basic reproduction number of the transmission of HFMD is deduced. As examples to make use of the formula, the basic reproduction number of the HFMD transmission of Singapore of years 2015 and 2016 is estimated based on the newly infected cases notified by the surveillance organizations, respectively. The formula can realize real time estimation for the basic reproduction number and does not need to estimate the transmission efficiency of HFMD between individuals. View Full-Text
Keywords: Hand-Foot-Mouth disease; mathematical model; basic reproduction number; local asymptotical stability; estimation Hand-Foot-Mouth disease; mathematical model; basic reproduction number; local asymptotical stability; estimation
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Wu, C. Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number. Math. Comput. Appl. 2017, 22, 29.

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