A model for ovine brucellosis incorporating direct and indirect transmission

In this work, we construct and analyse an ovine brucellosis mathematical model. In this model, the population is divided into susceptible and infected subclasses. Susceptible individuals can contract the disease in two ways: (i) direct mode – caused by contact with infected individuals; (ii) indirect mode – related to the presence of virulent organisms in the environment. We derive a net reproductive number and analyse the global asymptotic behaviour of the model. We also perform some numerical simulations, and investigate the effect of a slaughtering policy.

[1]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[2]  A. Zients.  Andy , 2003 .

[3]  N. Toft,et al.  Evaluation of three serological tests for brucellosis in naturally infected cattle using latent class analysis. , 2007, Veterinary microbiology.

[4]  S. Lafi,et al.  Epidemiology of ovine brucellosis in Awassi sheep in Northern Jordan. , 2003, Preventive veterinary medicine.

[5]  M. Ranjbar,et al.  Osteoarticular complications of brucellosis in Hamedan, an endemic area in the west of Iran. , 2007, International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases.

[6]  R. Bowers,et al.  A semi-stochastic model for Salmonella infection in a multi-group herd. , 2006, Mathematical biosciences.

[7]  J. McGiven,et al.  The improved specificity of bovine brucellosis testing in Great Britain. , 2008, Research in veterinary science.

[8]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[9]  G. Carrin,et al.  Human health benefits from livestock vaccination for brucellosis: case study. , 2003, Bulletin of the World Health Organization.

[10]  P. Magal,et al.  Asymptotic Behavior in a Salmonella Infection Model , 2007 .

[11]  Chris Cosner,et al.  Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction , 2001, Journal of mathematical biology.

[12]  Pierre Magal,et al.  Effect of genetic resistance of the hen to Salmonella carrier-state on incidence of bacterial contamination: synergy with vaccination. , 2008, Veterinary research.

[13]  H. Erdem.  Brucellosis , 1954, The Lancet.

[14]  B. Mantur,et al.  Brucellosis in India — a review , 2008, Journal of Biosciences.

[15]  M. Minas,et al.  The "effects" of Rev-1 vaccination of sheep and goats on human brucellosis in Greece. , 2004, Preventive veterinary medicine.

[16]  R. Naulin,et al.  Analysis of a model of bovine brucellosis using singular perturbations , 1994, Journal of mathematical biology.

[17]  A. Roddam.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation O Diekmann and JAP Heesterbeek, 2000, Chichester: John Wiley pp. 303, £39.95. ISBN 0-471-49241-8 , 2001 .

[18]  P Vounatsou,et al.  A model of animal-human brucellosis transmission in Mongolia. , 2005, Preventive veterinary medicine.

[19]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[20]  P. Magal,et al.  A model of Salmonella infection within industrial house hens. , 2006, Journal of theoretical biology.

[21]  M. Refai.  Incidence and control of brucellosis in the Near East region. , 2002, Veterinary microbiology.

[22]  H. Mao,et al.  Pathogenic and molecular characterization of the H5N1 avian influenza virus isolated from the first human case in Zhejiang province, China. , 2007, Diagnostic microbiology and infectious disease.

[23]  A. Benkirane.  Ovine and caprine brucellosis: World distribution and control/eradication strategies in West Asia/North Africa region , 2006 .

[24]  Michel Langlais,et al.  A reaction-diffusion system modeling direct and indirect transmission of diseases , 2004 .

[25]  R. Bowers,et al.  Understanding the dynamics of Salmonella infections in dairy herds: a modelling approach. , 2005, Journal of theoretical biology.

[26]  W. Fitzgibbon,et al.  An age-dependent model describing the spread of panleucopenia virus within feline populations , 2003 .

[27]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[28]  Horst R. Thieme,et al.  Mathematics in Population Biology , 2003 .

[29]  W. Fitzgibbon,et al.  A mathematical model for indirectly transmitted diseases. , 2007, Mathematical biosciences.