`a`
Mathematical Biosciences and Engineering (MBE)
 

Epidemic models for complex networks with demographics
Pages: 1295 - 1317, Issue 6, December 2014

doi:10.3934/mbe.2014.11.1295      Abstract        References        Full text (717.7K)           Related Articles

Zhen Jin - Complex Systems Research Center, Shanxi University, Taiyuan, Shan'xi 030006, China (email)
Guiquan Sun - Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051, China (email)
Huaiping Zhu - LAMPS and CDM, Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3, Canada (email)

1 R. M. Anderson and R. M. May, Infectious Diseases of Humans, Oxford University Press, Oxford, 1992.
2 A.-L. Barabasi and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), 509-511.       
3 M. Barthelemy, A. Barrat, R. Pastor-Satorras and A. Vespignani, Dynamical patterns of epidemic outbreaks in complex heterogeneous networks, Journal of Theoretical Biology, 235 (2005), 275-288.       
4 E. Ben-Naim and P. L. Krapivsky, Addition-deletion networks, J. Phys. A: Math. Theor., 40 (2007), 8607-8619.       
5 M. Boguna, R. Pastor-Satorras and A. Vespignani, Epidemic spreading in complex networks with degree correlations, e-print cond-mat/0301149, (2003).
6 S. Busenberg and P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 28 (1990), 257-270.       
7 C. Castillo-Chavez and H. R. Thieme, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity (eds. O. Arino, D. Axelrod, M. Kimmel and M. Langlais), Theory of Epidemics, 1, Wuerz, Winnipeg, 1993, 33-50.
8 K. Emrah, Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions, Applied Mathematics and Computation, 197 (2008), 345-357.       
9 L. Q. Gao and H. W. Hethcote, Disease transmission models with density-dependent demographics, J. Math. Biol., 30 (1992), 717-731.       
10 L. Hufnagel, D. Brockmann and T. Geisel, Forecast and control of epidemics in a globalized world, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 15124.
11 Y. Jin and W. Wang, The effect of population dispersal on the spread of a disease, J. Math. Anal. Appl., 308 (2005), 343-364.       
12 J. Joo and J. L. Lebowitz, Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation, Phys. Rev. E, 69 (2004), 066105.
13 M. J. Keeling and K. T. D. Eames, Networks and epidemic models, J. R. Soc. Interface, 2 (2005), 295-307.
14 M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007.       
15 W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. A, 115 (1927), 700-711.
16 I. Z. Kiss, D. M. Green and R. R. Kao, Heterogeneity and multiple of transmission on final epidemic size, Mathematical Biosciences, 203 (2006), 124-136.       
17 I. Z. Kiss, P. L. Simon and R. R. Kao, A contact-network-based formulation of a preferential mixing model, Bulletin of Mathematical Biology, 71 (2009), 888-905.       
18 J. Lindquist, J. Ma, P. van den Driessche and F. H. Willeboords, Network evolution by different rewiring schemes, Physica D, 238 (2009), 370-378.       
19 Z. Ma and J. Li, Dynamical Modeling and Anaylsis of Epidemics, World Scientific, 2009.
20 R. M. May and A. L. Lloyd, Infection dynamics on scale-free networks, Phys. Rev. E, 64 (2001), 066112.
21 Y. Moreno, R. Pastor-Satorras and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, Eur. Phys. J. B, 26 (2002), 521-529.
22 R. Olinky and L. Stone, Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission, Phys. Rev. E, 70 (2004), 030902.
23 R. Pastor-Satorras and A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E, 63 (2001), 066117.
24 R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Let., 86 (2001), 3200.
25 M. G. Roberta, An SEI model with density-dependent demographics and epidemiology, IMA Journal of Mathematics Applied in Medicine & Biology, 13 (1996), 245-257.
26 L. B. Shaw and I. B. Schwartz, Fluctuating epidemics on adaptive networks, Phys. Rev. E, 77 (2008), 066101.       
27 H. L. Smith, On the asymptotic behavior of a class of deterministic models of cooperating species, SIAM J. Appl. Math., 46 (1986), 368-375.       
28 H. R. Thieme, Asymptotically autonomous differential equations in the plane, Rocky Mountain J. Math., 24 (1994), 351-380.       
29 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.       
30 L. Wang and G. Z. Dai, Global stability of virus spreading in complex heterogeneous networks, Siam J. Appl. Math., 68 (2008), 1495-1502.       
31 W. Wang and X.-Q. Zhao, An epidemic model in a patchy environment, Mathematical Biosciences, 190 (2004), 97-112.       
32 X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.       
33 X.-Q. Zhao and Z.-J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations, Canad. Appl. Math. Quart., 4 (1996), 421-444.       

Go to top