2010, 7(2): 455-477. doi: 10.3934/mbe.2010.7.455

Pulse vaccination strategies in a metapopulation SIR model


Division of Mathematics, University of Dundee, Dundee, Scotland, DD1 4HN, United Kingdom

Received  March 2009 Revised  September 2009 Published  April 2010

We examine a model for a disease with SIR-type dynamics circulating in a population living on two or more patches between any pair of which migration is allowed. We suppose that a pulse vaccination strategy (PVS) is carried out on each patch. Conditions are derived on each PVS such that the disease will be eradicated on all patches. The PVS on one patch is assumed to be essentially independent of the PVS on the other patches except in so far as they are all performed simultaneously. This independence is of practical value when we bear in mind that the patches may represent regions or countries with autonomous public health authorities, which may make individual decisions about the days appropriate for a vaccination pulse to occur in their own region or country. Simulations corroborate our theoretical results.
Citation: Alan J. Terry. Pulse vaccination strategies in a metapopulation SIR model. Mathematical Biosciences & Engineering, 2010, 7 (2) : 455-477. doi: 10.3934/mbe.2010.7.455

Shujing Gao, Dehui Xie, Lansun Chen. Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 77-86. doi: 10.3934/dcdsb.2007.7.77


Qianqian Cui, Zhipeng Qiu, Ling Ding. An SIR epidemic model with vaccination in a patchy environment. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1141-1157. doi: 10.3934/mbe.2017059


Jinyan Wang, Yanni Xiao, Robert A. Cheke. Modelling the effects of contaminated environments in mainland China on seasonal HFMD infections and the potential benefit of a pulse vaccination strategy. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5849-5870. doi: 10.3934/dcdsb.2019109


Urszula Ledzewicz, Heinz Schättler. On optimal singular controls for a general SIR-model with vaccination and treatment. Conference Publications, 2011, 2011 (Special) : 981-990. doi: 10.3934/proc.2011.2011.981


Aili Wang, Yanni Xiao, Robert A. Cheke. Global dynamics of a piece-wise epidemic model with switching vaccination strategy. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2915-2940. doi: 10.3934/dcdsb.2014.19.2915


Dashun Xu, Z. Feng. A metapopulation model with local competitions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 495-510. doi: 10.3934/dcdsb.2009.12.495


Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real. Optimal control of vaccine distribution in a rabies metapopulation model. Mathematical Biosciences & Engineering, 2008, 5 (2) : 219-238. doi: 10.3934/mbe.2008.5.219


Zhilan Feng, Robert Swihart, Yingfei Yi, Huaiping Zhu. Coexistence in a metapopulation model with explicit local dynamics. Mathematical Biosciences & Engineering, 2004, 1 (1) : 131-145. doi: 10.3934/mbe.2004.1.131


Luca Bolzoni, Rossella Della Marca, Maria Groppi, Alessandra Gragnani. Dynamics of a metapopulation epidemic model with localized culling. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2307-2330. doi: 10.3934/dcdsb.2020036


Mehdi Badra. Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1169-1208. doi: 10.3934/dcds.2012.32.1169


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


Siyu Liu, Xue Yang, Yingjie Bi, Yong Li. Dynamic behavior and optimal scheduling for mixed vaccination strategy with temporary immunity. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1469-1483. doi: 10.3934/dcdsb.2018216


Siyu Liu, Yong Li, Yingjie Bi, Qingdao Huang. Mixed vaccination strategy for the control of tuberculosis: A case study in China. Mathematical Biosciences & Engineering, 2017, 14 (3) : 695-708. doi: 10.3934/mbe.2017039


Suman Ganguli, David Gammack, Denise E. Kirschner. A Metapopulation Model Of Granuloma Formation In The Lung During Infection With Mycobacterium Tuberculosis. Mathematical Biosciences & Engineering, 2005, 2 (3) : 535-560. doi: 10.3934/mbe.2005.2.535


Britnee Crawford, Christopher Kribs-Zaleta. A metapopulation model for sylvatic T. cruzi transmission with vector migration. Mathematical Biosciences & Engineering, 2014, 11 (3) : 471-509. doi: 10.3934/mbe.2014.11.471


Panagiotes A. Voltairas, Antonios Charalambopoulos, Dimitrios I. Fotiadis, Lambros K. Michalis. A quasi-lumped model for the peripheral distortion of the arterial pulse. Mathematical Biosciences & Engineering, 2012, 9 (1) : 175-198. doi: 10.3934/mbe.2012.9.175


Islam A. Moneim, David Greenhalgh. Use Of A Periodic Vaccination Strategy To Control The Spread Of Epidemics With Seasonally Varying Contact Rate. Mathematical Biosciences & Engineering, 2005, 2 (3) : 591-611. doi: 10.3934/mbe.2005.2.591


Sun-Ho Choi, Hyowon Seo, Minha Yoo. A multi-stage SIR model for rumor spreading. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2351-2372. doi: 10.3934/dcdsb.2020124


Bum Il Hong, Nahmwoo Hahm, Sun-Ho Choi. SIR Rumor spreading model with trust rate distribution. Networks & Heterogeneous Media, 2018, 13 (3) : 515-530. doi: 10.3934/nhm.2018023


Tao Feng, Zhipeng Qiu. Global analysis of a stochastic TB model with vaccination and treatment. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2923-2939. doi: 10.3934/dcdsb.2018292

2018 Impact Factor: 1.313


  • PDF downloads (53)
  • HTML views (0)
  • Cited by (15)

Other articles
by authors

[Back to Top]