Literature DB >> 25424418

Influence of diffusion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic.

Florinda Capone1, Valentina De Cataldis2, Roberta De Luca3.   

Abstract

A reaction-diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed.

Entities:  

Keywords:  Cholera; Epidemic models; Lyapunov direct method; Reaction–diffusion systems; Stability

Mesh：

Year:  2014        PMID： 25424418     DOI： 10.1007/s00285-014-0849-9

Source DB:  PubMed          Journal:  J Math Biol        ISSN： 0303-6812            Impact factor:   2.259


  13 in total

1.  Global stability for cholera epidemic models.

Authors:  Jianjun Paul Tian; Jin Wang
Journal:  Math Biosci       Date:  2011-04-12       Impact factor: 2.144

2.  Epidemic models with nonlinear infection forces.

Authors:  Wendi Wang
Journal:  Math Biosci Eng       Date:  2006-01       Impact factor: 2.080

3.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

Authors:  O Diekmann; J A Heesterbeek; J A Metz
Journal:  J Math Biol       Date:  1990       Impact factor: 2.259

4.  The role of immunity and seasonality in cholera epidemics.

Authors:  Rosângela P Sanches; Claudia P Ferreira; Roberto A Kraenkel
Journal:  Bull Math Biol       Date:  2011-04-06       Impact factor: 1.758

5.  Backwards bifurcations and catastrophe in simple models of fatal diseases.

Authors:  J Dushoff; W Huang; C Castillo-Chavez
Journal:  J Math Biol       Date:  1998-02       Impact factor: 2.259

6.  Impact of heterogeneity on the dynamics of an SEIR epidemic model.

Authors:  Zhisheng Shuai; P van den Driessche
Journal:  Math Biosci Eng       Date:  2012-04       Impact factor: 2.080

Review 7.  Environmental reservoir of Vibrio cholerae. The causative agent of cholera.

Authors:  R R Colwell; A Huq
Journal:  Ann N Y Acad Sci       Date:  1994-12-15       Impact factor: 5.691

8.  Detection of non-culturable Vibrio cholerae O1 associated with a cyanobacterium from an aquatic environment in Bangladesh.

Authors:  M S Islam; M A Miah; M K Hasan; R B Sack; M J Albert
Journal:  Trans R Soc Trop Med Hyg       Date:  1994 May-Jun       Impact factor: 2.184

9.  Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases.

Authors:  V Capasso; L Maddalena
Journal:  J Math Biol       Date:  1981       Impact factor: 2.259

10.  Characterization of a 20-kDa pilus protein expressed by a diarrheogenic strain of non-O1/non-O139 Vibrio cholerae.

Authors:  T K Sengupta; R K Nandy; S Mukhopadhyay; R H Hall; V Sathyamoorthy; A C Ghose
Journal:  FEMS Microbiol Lett       Date:  1998-03-15       Impact factor: 2.742
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  2 in total

1.  A priori L∞ estimates for solutions of a class of reaction-diffusion systems.

Authors:  Zengji Du; Rui Peng
Journal:  J Math Biol       Date:  2015-07-04       Impact factor: 2.259

2.  Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti.

Authors:  William E Fitzgibbon; Jeffrey J Morgan; Glenn F Webb; Yixiang Wu
Journal:  J R Soc Interface       Date:  2020-08-05       Impact factor: 4.118
  2 in total

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