`a`

Dynamically consistent discrete-time SI and SIS epidemic models

Pages: 653 - 662, Issue special, November 2013

 Abstract        References        Full Text (349.2K)          

Lih-Ing W. Roeger - Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042, United States (email)

1 L.J.S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Math. Biosci., 124 (1994), 83-105.
2 L.J.S. Allen, "An Introduction to Mathematical Biology," Prentice Hall, New Jersey, 2007.
3 R. Anguelov and J.M.S. Lubuma, Contribution to the mathematics of the nonstandard finite difference method and applications, Numer. Methods Par. Diff. Equ., 17 (2001), 518-543.       
4 M. Chapwanya, Jean M.-S. Lubuma, and R.E. Mickens, From enzyme kinetics to epidemilogical models with Michaelis-Menten contact rate: Design of nonstandard finite difference schemes, Computers and Mathematics with Applications, (2012), xxx-yyy.       
5 S. Elaydi, "An Introduction to Difference Equations," $3^{rd}$ edition, Springer, New York, 2005.       
6 H.W. Hethcote, Qualitative analyses of communicable disease models, Math. Biosci., 28 (1976), 335-356.       
7 H.W. Hethcote, The Mathematics of Infectious Diseases, SIAM Review, 42 (2000), 599-653.       
8 S.R.J. Jang, Nonstandard finite difference methods and biological models, in "Advances in the applications of nonstandard finite diffference schemes," edited by R.E. Mickens, World Scientific, New Jersey, 2005.       
9 P. Liu and S.N. Elaydi, Discrete Competitive and Cooperative Models of Lotka-Volterra Type, Journal of Computational Analysis and Applications, 3 (2001), 53-73.       
10 R.E. Mickens, "Nonstandard Finite Difference Models of Differential Equations," World Scientific, New Jersey, 1994.       
11 R.E. Mickens, "Advances in the applications of nonstandard finite difference schemes," World Scientific, New Jersey, 2005.       
12 R.E. Mickens, Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition, Numerical Methods for Partial Differential Equations, 23 (2006), 672-691.       
13 R.E. Mickens, Numerical integration of population models satisfying conservation laws: NSF methods, Journal of Biological Dynamics, 1 (2007), 427-436.       
14 R.E. Mickens, A SIR-model with square-root dynamics: An NSFD scheme, Journal of Difference Equations and Applications, 16 (2010), 209-216.       
15 R.E. Mickens and T.M. Washington, A note on and NSFD scheme for a mathematical model of respiratory virus transmission, J. Difference Equations and Appl., 18 (2012), 525-529.       
16 L.-I.W. Roeger, Nonstandard finite difference schemes for differential equations with $n+1$ distinct fixed-points, Journal of Difference Equations and Applications, 15 (2009), 133-151.       
17 L.-I.W. Roeger, Dynamically consistent finite difference schemes for the differential equation $dy/dt=b_ny^n+b_{n-1}y^{n-1}+\cdots+b_1 y+b_0$, Journal of Difference Equations and Applications, 18 (2012), 305-312.       
18 L.-I. W. Roeger and G. Lahodny, Jr., Dynamically consistent discrete Lotka-Volterra competition systems, Journal of Difference Equations and Applications, 19 (2013), 191-200.       

Go to top