# American Institute of Mathematical Sciences

2007, 2007(Special): 506-519. doi: 10.3934/proc.2007.2007.506

## Multi-compartment models

 1 Laboratoire de Mathématiques et Applications, UMR CNRS 7122, University of Metz and INRIA Lorraine, Metz, France, France 2 University of Yaoundé I, Cameroon, Cameroon

Received  September 2006 Revised  June 2007 Published  September 2007

We consider models with a general structure which, for example, encompasses the so-called DI, SP or DISP models with mass action incidence. We give a very simple formule for the basic reproduction ratio $R_0$. If $R_0 \<= 1$ we prove that the disease free equilibrium is globally asymptotically stable on the nonnegative orthant. If $R_0$ > 1, we prove the existence of a unique endemic equilibrium in the positive orthant and give an explicit formula. We prove the global asymptotic stability of the endemic equilibrium, when $R_0$ > 1 for SP model.
Citation: Abderrahman Iggidr, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa. Multi-compartment models. Conference Publications, 2007, 2007 (Special) : 506-519. doi: 10.3934/proc.2007.2007.506
 [1] 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 [2] 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 [3] 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 [4] 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 [5] Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267 [6] 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 [7] 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 [8] Shouying Huang, Jifa Jiang. Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723-739. doi: 10.3934/mbe.2016016 [9] 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 [10] Attila Dénes, Gergely Röst. Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1101-1117. doi: 10.3934/dcdsb.2016.21.1101 [11] Jianquan Li, Zhien Ma. Stability analysis for SIS epidemic models with vaccination and constant population size. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 635-642. doi: 10.3934/dcdsb.2004.4.635 [12] Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discrete-time SI and SIS epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (4) : 699-710. doi: 10.3934/mbe.2007.4.699 [13] Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021144 [14] Jing Hui, Lansun Chen. Impulsive vaccination of sir epidemic models with nonlinear incidence rates. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 595-605. doi: 10.3934/dcdsb.2004.4.595 [15] 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 [16] 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 [17] 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 [18] Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 999-1025. doi: 10.3934/dcdsb.2014.19.999 [19] Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi. Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences & Engineering, 2012, 9 (2) : 297-312. doi: 10.3934/mbe.2012.9.297 [20] 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

Impact Factor:

## Metrics

• HTML views (0)
• Cited by (0)

• on AIMS