-
Previous Article
Impulsive SICNNs with chaotic postsynaptic currents
- DCDS-B Home
- This Issue
-
Next Article
On the spectral stability of standing waves of the one-dimensional $M^5$-model
Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions
1. | Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., H-6720 Szeged,, Hungary |
2. | Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1. |
References:
[1] |
M. E. Alexander and S. M. Moghadas, Periodicity in an epidemic model with a generalized non-linear incidence,, Math. Biosci., 189 (2004), 75.
doi: 10.1016/j.mbs.2004.01.003. |
[2] |
N. P. Bhatia and G. P. Szegö, Dynamical Systems: Stability Theory and Applications,, Lecture Notes in Mathematics, (1967).
|
[3] |
V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model,, Math. Biosci., 42 (1978), 43.
doi: 10.1016/0025-5564(78)90006-8. |
[4] |
H. Dulac, Recherche des cycles limites,, C. R. Acad. Sci. Paris, 204 (1937), 1703. Google Scholar |
[5] |
L. Edelstein-Keshet, Mathematical Models in Biology,, The Random House/Birkhäuser Mathematics Series, (1988).
|
[6] |
H. W. Hethcote, The mathematics of infectious diseases,, SIAM Rev., 42 (2000), 599.
doi: 10.1137/S0036144500371907. |
[7] |
A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission,, Bull. Math. Biol., 68 (2006), 615.
doi: 10.1007/s11538-005-9037-9. |
[8] |
D. H. Knipl and G. Röst, Backward bifurcation in SIVS model with immigration of non-infectives,, Biomath, 2 (2013).
doi: 10.11145/j.biomath.2013.12.051. |
[9] |
M. A. Krasnoselskii, Positive Solutions of Operator Equations,, P. Noordhoff Ltd. Groningen, (1964).
doi: 10.11145/j.biomath.2013.12.051. |
[10] |
W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models,, J. Math. Biol., 23 (1986), 187.
doi: 10.1007/BF00276956. |
[11] |
T. C. Reluga and J. Medlock, Resistance mechanisms matter in SIR models,, Math. Biosci. Eng., 4 (2007), 553.
doi: 10.3934/mbe.2007.4.553. |
[12] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[13] |
W. Wang, Backward bifurcation of an epidemic model with treatment,, Math. Biosci., 201 (2006), 58.
doi: 10.1016/j.mbs.2005.12.022. |
[14] |
D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate,, Math. Biosci., 208 (2007), 419.
doi: 10.1016/j.mbs.2006.09.025. |
show all references
References:
[1] |
M. E. Alexander and S. M. Moghadas, Periodicity in an epidemic model with a generalized non-linear incidence,, Math. Biosci., 189 (2004), 75.
doi: 10.1016/j.mbs.2004.01.003. |
[2] |
N. P. Bhatia and G. P. Szegö, Dynamical Systems: Stability Theory and Applications,, Lecture Notes in Mathematics, (1967).
|
[3] |
V. Capasso and G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model,, Math. Biosci., 42 (1978), 43.
doi: 10.1016/0025-5564(78)90006-8. |
[4] |
H. Dulac, Recherche des cycles limites,, C. R. Acad. Sci. Paris, 204 (1937), 1703. Google Scholar |
[5] |
L. Edelstein-Keshet, Mathematical Models in Biology,, The Random House/Birkhäuser Mathematics Series, (1988).
|
[6] |
H. W. Hethcote, The mathematics of infectious diseases,, SIAM Rev., 42 (2000), 599.
doi: 10.1137/S0036144500371907. |
[7] |
A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission,, Bull. Math. Biol., 68 (2006), 615.
doi: 10.1007/s11538-005-9037-9. |
[8] |
D. H. Knipl and G. Röst, Backward bifurcation in SIVS model with immigration of non-infectives,, Biomath, 2 (2013).
doi: 10.11145/j.biomath.2013.12.051. |
[9] |
M. A. Krasnoselskii, Positive Solutions of Operator Equations,, P. Noordhoff Ltd. Groningen, (1964).
doi: 10.11145/j.biomath.2013.12.051. |
[10] |
W. M. Liu, S. A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models,, J. Math. Biol., 23 (1986), 187.
doi: 10.1007/BF00276956. |
[11] |
T. C. Reluga and J. Medlock, Resistance mechanisms matter in SIR models,, Math. Biosci. Eng., 4 (2007), 553.
doi: 10.3934/mbe.2007.4.553. |
[12] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[13] |
W. Wang, Backward bifurcation of an epidemic model with treatment,, Math. Biosci., 201 (2006), 58.
doi: 10.1016/j.mbs.2005.12.022. |
[14] |
D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate,, Math. Biosci., 208 (2007), 419.
doi: 10.1016/j.mbs.2006.09.025. |
[1] |
Marc Chamberland, Anna Cima, Armengol Gasull, Francesc Mañosas. Characterizing asymptotic stability with Dulac functions. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 59-76. doi: 10.3934/dcds.2007.17.59 |
[2] |
Andrey V. Melnik, Andrei Korobeinikov. Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Mathematical Biosciences & Engineering, 2013, 10 (2) : 369-378. doi: 10.3934/mbe.2013.10.369 |
[3] |
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability for a class of discrete SIR epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (2) : 347-361. doi: 10.3934/mbe.2010.7.347 |
[4] |
Deqiong Ding, Wendi Qin, Xiaohua Ding. Lyapunov functions and global stability for a discretized multigroup SIR epidemic model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1971-1981. doi: 10.3934/dcdsb.2015.20.1971 |
[5] |
Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 1119-1128. doi: 10.3934/proc.2011.2011.1119 |
[6] |
Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449 |
[7] |
Jinliang Wang, Xianning Liu, Toshikazu Kuniya, Jingmei Pang. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2795-2812. doi: 10.3934/dcdsb.2017151 |
[8] |
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 61-74. doi: 10.3934/dcdsb.2011.15.61 |
[9] |
Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643 |
[10] |
Andrei Korobeinikov, Philip K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences & Engineering, 2004, 1 (1) : 57-60. doi: 10.3934/mbe.2004.1.57 |
[11] |
C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837-850. doi: 10.3934/mbe.2010.7.837 |
[12] |
Qingming Gou, Wendi Wang. Global stability of two epidemic models. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 333-345. doi: 10.3934/dcdsb.2007.8.333 |
[13] |
Shui-Nee Chow, Yongfeng Li. Model reference control for SIRS models. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 675-697. doi: 10.3934/dcds.2009.24.675 |
[14] |
Yoshiaki Muroya, Toshikazu Kuniya, Yoichi Enatsu. Global stability of a delayed multi-group SIRS epidemic model with nonlinear incidence rates and relapse of infection. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3057-3091. doi: 10.3934/dcdsb.2015.20.3057 |
[15] |
Hiroshi Ito. Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020338 |
[16] |
Jing-Jing Xiang, Juan Wang, Li-Ming Cai. Global stability of the dengue disease transmission models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2217-2232. doi: 10.3934/dcdsb.2015.20.2217 |
[17] |
Zhanyuan Hou. Geometric method for global stability of discrete population models. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3305-3334. doi: 10.3934/dcdsb.2020063 |
[18] |
Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101 |
[19] |
Timothy C. Reluga, Jan Medlock. Resistance mechanisms matter in SIR models. Mathematical Biosciences & Engineering, 2007, 4 (3) : 553-563. doi: 10.3934/mbe.2007.4.553 |
[20] |
Qingshan Yang, Xuerong Mao. Stochastic dynamics of SIRS epidemic models with random perturbation. Mathematical Biosciences & Engineering, 2014, 11 (4) : 1003-1025. doi: 10.3934/mbe.2014.11.1003 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]