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Dynamics of a networked connectivity model of epidemics
1. | Health Science Center at Houston, University of Texas, Houston, TX 77030, United States |
2. | Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, United States |
3. | Cystic Fibrosis Foundation Therapeutics Lab, Bethesda, MD 20814, United States |
4. | Department of Mathematics, Missouri State University, Springfield, MO 65897 |
References:
[1] |
F. Albertini and D. D'Alessandro, Asymptotic stability of continuous-time systems with saturation nonlinearities,, Systems & Control Letters, 29 (1996), 175.
doi: 10.1016/S0167-6911(96)00052-7. |
[2] |
A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences,, Classics in Applied Mathematics, (1994).
doi: 10.1137/1.9781611971262. |
[3] |
C. Castillo-Chavez, Z. Feng and W. Huang, On the computation of $R_0$ and its role on global stability,, Math. Appr. for Emerg. and Reemerg. Infect. Dis, 125 (2002), 229.
|
[4] |
H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set,, J. Dynamics & Diff. Equations, 6 (1994), 583.
doi: 10.1007/BF02218848. |
[5] |
M. Gatto, L. Mari, E. Bertuzzo, R. Casagrandi, L. Righetto, I. Rodriguez-Iturbe and A. Rinaldo, Generalized reproduction numbers and the prediction of patterns in waterborne disease,, Proceed. Nat. Acad. of Scienc., 109 (2012), 19703.
doi: 10.1073/pnas.1217567109. |
[6] |
Z. Hu, Z. Teng and L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model,, Mathematics & Computers in Simulation, 97 (2014), 80.
doi: 10.1016/j.matcom.2013.08.008. |
[7] |
J. P. LaSalle, The Stability of Dynamical Systems,, SIAM, (1976).
doi: 10.1137/1.9781611970432. |
[8] |
M. Li, J. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size,, Mathematical Biosciences, 160 (1999), 191.
doi: 10.1016/S0025-5564(99)00030-9. |
[9] |
J. Rebaza, Dynamics of prey threshold harvesting and refuge,, Computational & Applied Mathematics, 236 (2012), 1743.
doi: 10.1016/j.cam.2011.10.005. |
[10] |
E. Seneta, Nonnegative Matrices and Markov Chains,, Springer-Verlag, (1981).
doi: 10.1007/0-387-32792-4. |
[11] |
Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions,, SIAM J. of Applied Mathematics, 73 (2013), 1513.
doi: 10.1137/120876642. |
[12] |
J. R. Silvester, Determinants of block matrices,, Mathematical Gazette, 84 (2000), 460.
doi: 10.2307/3620776. |
[13] |
H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[14] |
J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera,, Discr. Cont. Dynam. Syst. 2013, (2013), 747.
|
[15] |
C. Torres Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir,, BMC Infectious Diseases, 1 (2001), 1.
doi: 10.1186/1471-2334-1-1. |
show all references
References:
[1] |
F. Albertini and D. D'Alessandro, Asymptotic stability of continuous-time systems with saturation nonlinearities,, Systems & Control Letters, 29 (1996), 175.
doi: 10.1016/S0167-6911(96)00052-7. |
[2] |
A. Berman and R. Plemmons, Nonnegative Matrices in the Mathematical Sciences,, Classics in Applied Mathematics, (1994).
doi: 10.1137/1.9781611971262. |
[3] |
C. Castillo-Chavez, Z. Feng and W. Huang, On the computation of $R_0$ and its role on global stability,, Math. Appr. for Emerg. and Reemerg. Infect. Dis, 125 (2002), 229.
|
[4] |
H. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set,, J. Dynamics & Diff. Equations, 6 (1994), 583.
doi: 10.1007/BF02218848. |
[5] |
M. Gatto, L. Mari, E. Bertuzzo, R. Casagrandi, L. Righetto, I. Rodriguez-Iturbe and A. Rinaldo, Generalized reproduction numbers and the prediction of patterns in waterborne disease,, Proceed. Nat. Acad. of Scienc., 109 (2012), 19703.
doi: 10.1073/pnas.1217567109. |
[6] |
Z. Hu, Z. Teng and L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model,, Mathematics & Computers in Simulation, 97 (2014), 80.
doi: 10.1016/j.matcom.2013.08.008. |
[7] |
J. P. LaSalle, The Stability of Dynamical Systems,, SIAM, (1976).
doi: 10.1137/1.9781611970432. |
[8] |
M. Li, J. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size,, Mathematical Biosciences, 160 (1999), 191.
doi: 10.1016/S0025-5564(99)00030-9. |
[9] |
J. Rebaza, Dynamics of prey threshold harvesting and refuge,, Computational & Applied Mathematics, 236 (2012), 1743.
doi: 10.1016/j.cam.2011.10.005. |
[10] |
E. Seneta, Nonnegative Matrices and Markov Chains,, Springer-Verlag, (1981).
doi: 10.1007/0-387-32792-4. |
[11] |
Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions,, SIAM J. of Applied Mathematics, 73 (2013), 1513.
doi: 10.1137/120876642. |
[12] |
J. R. Silvester, Determinants of block matrices,, Mathematical Gazette, 84 (2000), 460.
doi: 10.2307/3620776. |
[13] |
H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[14] |
J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera,, Discr. Cont. Dynam. Syst. 2013, (2013), 747.
|
[15] |
C. Torres Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir,, BMC Infectious Diseases, 1 (2001), 1.
doi: 10.1186/1471-2334-1-1. |
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