Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality

[1]  Hassan Fathabadi,et al.  On Stability Analysis of Nonlinear Systems , 2012 .

[2]  Auda Fares,et al.  Seasonality of Tuberculosis , 2011, Journal of global infectious diseases.

[3]  Samuel Bowong,et al.  Optimal control of the transmission dynamics of tuberculosis , 2010 .

[4]  Xiao-Qiang Zhao,et al.  A Tuberculosis Model with Seasonality , 2010, Bulletin of mathematical biology.

[5]  Samuel Bowong,et al.  Mathematical analysis of a tuberculosis model with differential infectivity , 2009 .

[6]  Carmen Chicone,et al.  Stability Theory of Ordinary Differential Equations , 2009, Encyclopedia of Complexity and Systems Science.

[7]  Xiao-Qiang Zhao,et al.  Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments , 2008 .

[8]  Rachid Ouifki,et al.  Modeling the joint epidemics of TB and HIV in a South African township , 2008, Journal of mathematical biology.

[9]  C. Bhunu,et al.  Tuberculosis Transmission Model with Chemoprophylaxis and Treatment , 2008, Bulletin of mathematical biology.

[10]  S. Akhtar,et al.  Seasonality in pulmonary tuberculosis among migrant workers entering Kuwait , 2008, BMC infectious diseases.

[11]  Samuel Bowong,et al.  Global stability analysis for SEIS models with n latent classes. , 2008, Mathematical biosciences and engineering : MBE.

[12]  James Watmough,et al.  Role of incidence function in vaccine-induced backward bifurcation in some HIV models. , 2007, Mathematical biosciences.

[13]  G. Sallet,et al.  General models of host-parasite systems. Global analysis , 2007 .

[14]  Jean-Claude Kamgang,et al.  Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle , 2011, SIAM J. Appl. Math..

[15]  N. Grassly,et al.  Seasonal infectious disease epidemiology , 2006, Proceedings of the Royal Society B: Biological Sciences.

[16]  Naohiro Nagayama,et al.  Seasonality in various forms of tuberculosis. , 2006, The international journal of tuberculosis and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease.

[17]  C. McCluskey,et al.  Lyapunov functions for tuberculosis models with fast and slow progression. , 2006, Mathematical biosciences and engineering : MBE.

[18]  P. Hosseini,et al.  Seasonality and the dynamics of infectious diseases. , 2006, Ecology letters.

[19]  Kwok Chiu Chang,et al.  Seasonal pattern of tuberculosis in Hong Kong. , 2005, International Journal of Epidemiology.

[20]  Thomas R Frieden,et al.  Seasonality of tuberculosis in India: is it real and what does it tell us? , 2004, The Lancet.

[21]  Fred Brauer,et al.  Backward bifurcations in simple vaccination models , 2004 .

[22]  Carlos Castillo-Chavez,et al.  Dynamical models of tuberculosis and their applications. , 2004, Mathematical biosciences and engineering : MBE.

[23]  Masashi Kamo,et al.  External forcing of ecological and epidemiological systems: a resonance approach , 2004 .

[24]  Philip K Maini,et al.  A lyapunov function and global properties for sir and seir epidemiological models with nonlinear incidence. , 2004, Mathematical biosciences and engineering : MBE.

[25]  J. M. García,et al.  A statistical analysis of the seasonality in pulmonary tuberculosis , 2000, European Journal of Epidemiology.

[26]  Denise Kirschner,et al.  On treatment of tuberculosis in heterogeneous populations. , 2003, Journal of theoretical biology.

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

[28]  Thomas R Frieden,et al.  Tuberculosis control: past 10 years and future progress. , 2003, Tuberculosis.

[29]  C. Dye,et al.  Global tuberculosis control: surveillance planning financing. WHO report 2003. , 2003 .

[30]  Julien Arino,et al.  Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation , 2003, SIAM J. Appl. Math..

[31]  Denise Kirschner,et al.  Comparing epidemic tuberculosis in demographically distinct heterogeneous populations. , 2002, Mathematical biosciences.

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

[33]  MC Raviglione,et al.  Evolution of WHO policies for tuberculosis control, 1948–2001 , 2002, The Lancet.

[34]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[35]  C. Castillo-Chavez,et al.  A model for tuberculosis with exogenous reinfection. , 2000, Theoretical population biology.

[36]  C. Dye,et al.  Consensus statement. Global burden of tuberculosis: estimated incidence, prevalence, and mortality by country. WHO Global Surveillance and Monitoring Project. , 1999, JAMA.

[37]  C. Chintu,et al.  An African perspective on the threat of tuberculosis and HIV/AIDS—can despair be turned to hope? , 1999, The Lancet.

[38]  Carlos Castillo-Chavez,et al.  Backwards bifurcations and catastrophe in simple models of fatal diseases , 1998, Journal of mathematical biology.

[39]  Gieri Simonett,et al.  Mathematical models in medical and health science , 1998 .

[40]  Christopher Dye,et al.  Assessment of worldwide tuberculosis control , 1997, The Lancet.

[41]  C. Castillo-Chavez,et al.  To treat or not to treat: the case of tuberculosis , 1997, Journal of mathematical biology.

[42]  D. Strachan,et al.  Seasonality of tuberculosis: the reverse of other respiratory diseases in the UK. , 1996, Thorax.

[43]  S. Blower,et al.  Control Strategies for Tuberculosis Epidemics: New Models for Old Problems , 1996, Science.

[44]  R. Gie,et al.  A decade of experience with Mycobacterium tuberculosis culture from children: a seasonal influence on incidence of childhood tuberculosis. , 1996, Tubercle and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease.

[45]  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 .

[46]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[47]  V. Capasso Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.

[48]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[49]  I B Schwartz,et al.  Seasonality and period-doubling bifurcations in an epidemic model. , 1984, Journal of theoretical biology.

[50]  J. Yorke,et al.  Gonorrhea Transmission Dynamics and Control , 1984 .

[51]  S. Levin Lectu re Notes in Biomathematics , 1983 .

[52]  R. May,et al.  Population Biology of Infectious Diseases , 1982, Dahlem Workshop Reports.

[53]  R. May,et al.  Population biology of infectious diseases: Part I , 1979, Nature.

[54]  R. May,et al.  Population biology of infectious diseases: Part II , 1979, Nature.

[55]  J. P. Lasalle The stability of dynamical systems , 1976 .

[56]  G. P. Szegö,et al.  Stability theory of dynamical systems , 1970 .

[57]  J A Romeyn,et al.  Exogenous reinfection in tuberculosis. , 1970, The American review of respiratory disease.

[58]  E O Powell,et al.  Theory of the chemostat. , 1965, Laboratory practice.