Mathematical Biosciences and Engineering (MBE)

An SIRS model with differential susceptibility and infectivity on uncorrelated networks
Pages: 415 - 429, Issue 3, June 2015

doi:10.3934/mbe.2015.12.415      Abstract        References        Full text (481.0K)           Related Articles

Maoxing Liu - Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China (email)
Yuming Chen - Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China (email)

1 M. Artzrouni, Transmission probabilities and reproductive numbers for sexually transmitted infections with variable infectivity: Application to the spread of HIV between low- and high-activity populations, Mathematical Population Studies, 16 (2009), 266-287.       
2 A.-L. Barabási and R. Alberta, Emergence of scaling in random networks, Science, 286 (1999), 509-512.       
3 B. Bonzi, A. A. Fall, A. Iggidr and G. Sallet, Stability of differential susceptibility and infectivity epidemic models, J. Math. Biol., 62 (2011), 39-64.       
4 S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys., 80 (2008), 1275-1335.
5 X. Fu, M. Small, D. M. Walker and H. Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys. Rev. E, 77 (2008), 036113, 8pp.       
6 W.-P. Guo, X. Li and X.-F. Wang, Epidemics and immunization on Euclidean distance preferred small-world networks, Physica A, 380 (2007), 684-690.
7 J. M. Hyman and J. Li, Differential susceptibility epidemic models, J. Math. Biol., 50 (2005), 626-644.       
8 J. M. Hyman and J. Li, Differential susceptibility and infectivity epidemic models, Math. Biosci. Engrg., 3 (2006), 89-100.       
9 J. M. Hyman and J. Li, Epidemic models with differential susceptibility and staged progression and their dynamics, Math. Biosci. Engrg., 6 (2009), 321-332.       
10 A. Lajmanovich and J. A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28 (1976), 221-236.       
11 P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.       
12 F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley and Y. Åberg, The web of human sexual contacts, Nature, 411 (2001), 907-908.
13 J. Lou and T. Ruggeri, The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network, J. Math. Anal. Appl., 365 (2010), 210-219.       
14 Z. Ma, J. Liu and J. Li, Stability analysis for differential infectivity epidemic models, Nonlinear Anal.: RWA, 4 (2003), 841-856.       
15 J. D. May, Mathematical Biology I: An Introduction, 3rd Ed., Springer-Verlag, New York, 2002.       
16 R. M. May and A. L. Lloyd, Infection dynamics on scale-free networks, Phys. Rev. E, 64 (2001), 066112.
17 M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167-256.       
18 R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200-3203.
19 R. Pastor-Satorras and A. Vespignani, Epidemic dynamics in finite size scale-free networks, Phys. Rev. E, 65 (2002), 035108.
20 R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Phys. Rev. E, 65 (2002), 036104.
21 W. J. Reed, A stochastic model for the spread of a sexually transmitted disease which results in a scale-free network, Math. Biosci., 201 (2006), 3-14.       
22 A. Schneeberger, C. H. Mercer, S. A. J. Gregson, N. M. Ferguson, C. A. Nyamukapa, R. M. Anderson, A. M. Johmson and G. P. Garnett, Scale-free networks and sexually transmitted diseases: A description of observed patterns of sexual contacts in Britain and Zimbabwe, Sex. Transm. Dis., 31 (2004), 380-387.
23 A. Smed-Sörensen et al., Differential susceptibility to human immunodeficiency virus type 1 infection of myeloid and Plasmacytoid dendritic cells, J. Virology, 79 (2005), 8861-8869.
24 N. Sugimine and K. Aihara, Stability of an equilibrium state in a multiinfectious-type SIS model on a truncated network, Artif. Life Robotics, 11 (2007), 157-161.
25 H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.       
26 R. Yang et al., Epidemic spreading on heterogeneous networks with identical infectivity, Phys. Lett. A, 364 (2007), 189-193.
27 H. Zhang, L. Chen and J. J. Nieto, A delayed epidemic model with stage-structure and pulses for pest management strategy, Nonlinear Anal. Real World Appl., 9 (2008), 1714-1726.       
28 Z. Zhang and J. Peng, A SIRS epidemic model with infection-age dependence, J. Math. Anal. Appl., 331 (2007), 1396-1414.       
29 Z. Zhang, J. Peng and J. Zhang, Analysis of a bacteria-immunity model with delay quorum sensing, J. Math. Anal. Appl., 340 (2008), 102-115.       
30 S. Zou, J. Wu and Y. Chen, Multiple epidemic waves in delayed susceptible-infected-recovered models on complex networks, Phys. Rev. E, 83 (2011), 056121.

Go to top