# American Institute of Mathematical Sciences

2005, 2(3): 437-443. doi: 10.3934/mbe.2005.2.437

## Internal eradicability for an epidemiological model with diffusion

 1 Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506, Romania 2 Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, case 26, Université Bordeaux 2, 33076 Bordeaux Cedex, France

Received  January 2005 Revised  August 2005 Published  August 2005

This work is concerned with the analysis of the possibility for eradicating a disease in an infected population. The epidemiological model under study is of SI type with diffusion. We assume the policy strategy acting on the infected individuals over a subset of the whole spatial territory. Using the framework of nonlinear reaction-diffusion equations, and spectral theory of linear differential operators, we give necessary conditions and sufficient conditions of eradicability.
Citation: Sebastian Aniţa, Bedreddine Ainseba. Internal eradicability for an epidemiological model with diffusion. Mathematical Biosciences & Engineering, 2005, 2 (3) : 437-443. doi: 10.3934/mbe.2005.2.437
 [1] Arnaud Ducrot, Michel Langlais, Pierre Magal. Multiple travelling waves for an $SI$-epidemic model. Networks and Heterogeneous Media, 2013, 8 (1) : 171-190. doi: 10.3934/nhm.2013.8.171 [2] Yoshiaki Muroya. A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model). Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 999-1008. doi: 10.3934/dcdss.2015.8.999 [3] Shuang-Ming Wang, Zhaosheng Feng, Zhi-Cheng Wang, Liang Zhang. Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure. Communications on Pure and Applied Analysis, 2022, 21 (6) : 2005-2034. doi: 10.3934/cpaa.2021145 [4] Elisabeth Logak, Isabelle Passat. An epidemic model with nonlocal diffusion on networks. Networks and Heterogeneous Media, 2016, 11 (4) : 693-719. doi: 10.3934/nhm.2016014 [5] Mudassar Imran, Mohamed Ben-Romdhane, Ali R. Ansari, Helmi Temimi. Numerical study of an influenza epidemic dynamical model with diffusion. Discrete and Continuous Dynamical Systems - S, 2020, 13 (10) : 2761-2787. doi: 10.3934/dcdss.2020168 [6] Yaru Hu, Jinfeng Wang. Dynamics of an SIRS epidemic model with cross-diffusion. Communications on Pure and Applied Analysis, 2022, 21 (1) : 315-336. doi: 10.3934/cpaa.2021179 [7] Lih-Ing W. Roeger. Dynamically consistent discrete-time SI and SIS epidemic models. Conference Publications, 2013, 2013 (special) : 653-662. doi: 10.3934/proc.2013.2013.653 [8] 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 [9] Fred Brauer. A model for an SI disease in an age - structured population. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257 [10] Linda J. S. Allen, B. M. Bolker, Yuan Lou, A. L. Nevai. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1 [11] Haomin Huang, Mingxin Wang. The reaction-diffusion system for an SIR epidemic model with a free boundary. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2039-2050. doi: 10.3934/dcdsb.2015.20.2039 [12] Wenzhang Huang, Maoan Han, Kaiyu Liu. Dynamics of an SIS reaction-diffusion epidemic model for disease transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 51-66. doi: 10.3934/mbe.2010.7.51 [13] Meng Zhao, Wantong Li, Yihong Du. The effect of nonlocal reaction in an epidemic model with nonlocal diffusion and free boundaries. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4599-4620. doi: 10.3934/cpaa.2020208 [14] Liang Zhang, Zhi-Cheng Wang. Threshold dynamics of a reaction-diffusion epidemic model with stage structure. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3797-3820. doi: 10.3934/dcdsb.2017191 [15] Yachun Tong, Inkyung Ahn, Zhigui Lin. Effect of diffusion in a spatial SIS epidemic model with spontaneous infection. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4045-4057. doi: 10.3934/dcdsb.2020273 [16] Arnaud Ducrot, Michel Langlais, Pierre Magal. Qualitative analysis and travelling wave solutions for the SI model with vertical transmission. Communications on Pure and Applied Analysis, 2012, 11 (1) : 97-113. doi: 10.3934/cpaa.2012.11.97 [17] Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217 [18] Chengxia Lei, Jie Xiong, Xinhui Zhou. Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 81-98. doi: 10.3934/dcdsb.2019173 [19] Danhua Jiang, Zhi-Cheng Wang, Liang Zhang. A reaction-diffusion-advection SIS epidemic model in a spatially-temporally heterogeneous environment. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4557-4578. doi: 10.3934/dcdsb.2018176 [20] Kazuo Yamazaki, Xueying Wang. Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1297-1316. doi: 10.3934/dcdsb.2016.21.1297

2018 Impact Factor: 1.313