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
Math. Comput. Appl. 2017, 22(2), 29; https://doi.org/10.3390/mca22020029
Received: 8 February 2017 / Revised: 2 April 2017 / Accepted: 4 April 2017 / Published: 8 April 2017
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
▼
Show Figures
Figure 1
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
MDPI and ACS Style
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. https://doi.org/10.3390/mca22020029
AMA Style
Wu C. Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number. Mathematical and Computational Applications. 2017; 22(2):29. https://doi.org/10.3390/mca22020029
Chicago/Turabian StyleWu, Chunqing. 2017. "Analysis of a Hand-Foot-Mouth Disease Model with Standard Incidence Rate and Estimation for Basic Reproduction Number" Math. Comput. Appl. 22, no. 2: 29. https://doi.org/10.3390/mca22020029
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
