Mathematical Biosciences and Engineering (MBE)

An SEIR epidemic model with constant latency time and infectious period
Pages: 931 - 952, Issue 4, October 2011

doi:10.3934/mbe.2011.8.931      Abstract        References        Full text (433.6K)           Related Articles

Edoardo Beretta - CIMAB, University of Milano, via C. Saldini 50, I20133 Milano, Italy (email)
Dimitri Breda - Department of Mathematics and Computer Science, University of Udine, via delle Scienze 206, I33100 Udine, Italy (email)

1 E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 1144-1165.       
2 V. Capasso and G. Serio, A generalization of the Kermack-McKendric deterministic epidemic model, Math. Biosci., 42 (1978), 43-61.       
3 M. Giaquinta and G. Modica, "Mathematical Analysis. An Introduction to Functions of Several Variables," Birkhauser Boston, Inc., Boston, MA, 2009.       
4 G. Huang and Y. Takeuchi, Global analysis on delay epidemiological dynamic models with nonlinear incidence, J. Math. Biol., 63 (2011), 125-139.
5 G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infection, SIAM J. Appl. Math., 70 (2010), 2693-2708.       
6 G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207.
7 A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
8 Y. Kuang, "Delay Differential Equations with Application in Population Dynamics," Dynamics in Science and Engineering, Academic Press, New York, 1993.
9 M. A. Safi and A. B. Gumel, Global asymptotic dynamics of a model of quarantine and isolation, Discrete Contin. Dyn. S., 14 (2010), 209-231.       
10 H. L. Smith, "An Introduction to Delay Differential Equations with Applications to the Life Sciences," Texts in Applied Mathematics, Springer, New York, 2011.       
11 R. Xu and Y. Du, \ A delayed SIR epidemic model with saturation incidence and constant infectious period, J. Appl. Math. Comp., 35 (2010), 229-250.
12 R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence rate, Nonlinear Dynam., 61 (2010), 229-239.       
13 F. Zhang, Z. Li and F. Zhang, Global stability of an SIR epidemic model with constant infectious period, Appl. Math. Comput, 199 (2008), 285-291.

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