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Parameter dependent stability/instability in a human respiratory control system model
Dynamically consistent discretetime SI and SIS epidemic models
1.  Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 794091042, United States 
References:
[1] 
L.J.S. Allen, Some discretetime SI, SIR, and SIS epidemic models,, Math. Biosci., 124 (1994), 83. Google Scholar 
[2] 
L.J.S. Allen, "An Introduction to Mathematical Biology,", Prentice Hall, (2007). Google Scholar 
[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. Google Scholar 
[4] 
M. Chapwanya, Jean M.S. Lubuma, and R.E. Mickens, From enzyme kinetics to epidemilogical models with MichaelisMenten contact rate: Design of nonstandard finite difference schemes,, Computers and Mathematics with Applications, (2012). Google Scholar 
[5] 
S. Elaydi, "An Introduction to Difference Equations,", $3^{rd}$ edition, (2005). Google Scholar 
[6] 
H.W. Hethcote, Qualitative analyses of communicable disease models,, Math. Biosci., 28 (1976), 335. Google Scholar 
[7] 
H.W. Hethcote, The Mathematics of Infectious Diseases,, SIAM Review, 42 (2000), 599. Google Scholar 
[8] 
S.R.J. Jang, Nonstandard finite difference methods and biological models,, in, (2005). Google Scholar 
[9] 
P. Liu and S.N. Elaydi, Discrete Competitive and Cooperative Models of LotkaVolterra Type,, Journal of Computational Analysis and Applications, 3 (2001), 53. Google Scholar 
[10] 
R.E. Mickens, "Nonstandard Finite Difference Models of Differential Equations,", World Scientific, (1994). Google Scholar 
[11] 
R.E. Mickens, "Advances in the applications of nonstandard finite difference schemes,", World Scientific, (2005). Google Scholar 
[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. Google Scholar 
[13] 
R.E. Mickens, Numerical integration of population models satisfying conservation laws: NSF methods,, Journal of Biological Dynamics, 1 (2007), 427. Google Scholar 
[14] 
R.E. Mickens, A SIRmodel with squareroot dynamics: An NSFD scheme,, Journal of Difference Equations and Applications, 16 (2010), 209. Google Scholar 
[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. Google Scholar 
[16] 
L.I.W. Roeger, Nonstandard finite difference schemes for differential equations with $n+1$ distinct fixedpoints,, Journal of Difference Equations and Applications, 15 (2009), 133. Google Scholar 
[17] 
L.I.W. Roeger, Dynamically consistent finite difference schemes for the differential equation $dy/dt=b_ny^n+b_{n1}y^{n1}+\cdots+b_1 y+b_0$,, Journal of Difference Equations and Applications, 18 (2012), 305. Google Scholar 
[18] 
L.I. W. Roeger and G. Lahodny, Jr., Dynamically consistent discrete LotkaVolterra competition systems,, Journal of Difference Equations and Applications, 19 (2013), 191. Google Scholar 
show all references
References:
[1] 
L.J.S. Allen, Some discretetime SI, SIR, and SIS epidemic models,, Math. Biosci., 124 (1994), 83. Google Scholar 
[2] 
L.J.S. Allen, "An Introduction to Mathematical Biology,", Prentice Hall, (2007). Google Scholar 
[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. Google Scholar 
[4] 
M. Chapwanya, Jean M.S. Lubuma, and R.E. Mickens, From enzyme kinetics to epidemilogical models with MichaelisMenten contact rate: Design of nonstandard finite difference schemes,, Computers and Mathematics with Applications, (2012). Google Scholar 
[5] 
S. Elaydi, "An Introduction to Difference Equations,", $3^{rd}$ edition, (2005). Google Scholar 
[6] 
H.W. Hethcote, Qualitative analyses of communicable disease models,, Math. Biosci., 28 (1976), 335. Google Scholar 
[7] 
H.W. Hethcote, The Mathematics of Infectious Diseases,, SIAM Review, 42 (2000), 599. Google Scholar 
[8] 
S.R.J. Jang, Nonstandard finite difference methods and biological models,, in, (2005). Google Scholar 
[9] 
P. Liu and S.N. Elaydi, Discrete Competitive and Cooperative Models of LotkaVolterra Type,, Journal of Computational Analysis and Applications, 3 (2001), 53. Google Scholar 
[10] 
R.E. Mickens, "Nonstandard Finite Difference Models of Differential Equations,", World Scientific, (1994). Google Scholar 
[11] 
R.E. Mickens, "Advances in the applications of nonstandard finite difference schemes,", World Scientific, (2005). Google Scholar 
[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. Google Scholar 
[13] 
R.E. Mickens, Numerical integration of population models satisfying conservation laws: NSF methods,, Journal of Biological Dynamics, 1 (2007), 427. Google Scholar 
[14] 
R.E. Mickens, A SIRmodel with squareroot dynamics: An NSFD scheme,, Journal of Difference Equations and Applications, 16 (2010), 209. Google Scholar 
[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. Google Scholar 
[16] 
L.I.W. Roeger, Nonstandard finite difference schemes for differential equations with $n+1$ distinct fixedpoints,, Journal of Difference Equations and Applications, 15 (2009), 133. Google Scholar 
[17] 
L.I.W. Roeger, Dynamically consistent finite difference schemes for the differential equation $dy/dt=b_ny^n+b_{n1}y^{n1}+\cdots+b_1 y+b_0$,, Journal of Difference Equations and Applications, 18 (2012), 305. Google Scholar 
[18] 
L.I. W. Roeger and G. Lahodny, Jr., Dynamically consistent discrete LotkaVolterra competition systems,, Journal of Difference Equations and Applications, 19 (2013), 191. Google Scholar 
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