Tuberculosis with relapse: A model

ABSTRACT In a model of tuberculosis with relapse, the basic reproduction number R0 includes new and relapse infections. Lyapunov functions help to prove that the global dynamic is completely determined by R0. Replicated Latin hypercube sampling shows that early diagnosis and treatment are more efficient when relapse cases are considered.

[1]  M Gabriela M Gomes,et al.  Drug resistance in tuberculosis--a reinfection model. , 2007, Theoretical population biology.

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

[3]  C. Dye,et al.  The Population Dynamics and Control of Tuberculosis , 2010, Science.

[4]  Brigitte Gicquel,et al.  Is Adipose Tissue a Place for Mycobacterium tuberculosis Persistence? , 2006, PloS one.

[5]  Ted Cohen,et al.  Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness , 2004, Nature Medicine.

[6]  S. Blower,et al.  Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. , 1997, American journal of epidemiology.

[7]  Hadi Dowlatabadi,et al.  Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example , 1994 .

[8]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[9]  Jianquan Li,et al.  Global stability of two tuberculosis models with treatment and self-cure , 2012 .

[10]  C. Dolea,et al.  World Health Organization , 1949, International Organization.

[11]  R. Ruth,et al.  Stability of dynamical systems , 1988 .

[12]  Jürgen Kurths,et al.  Two-Patch Transmission of Tuberculosis , 2011 .

[13]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[14]  S. Blower,et al.  The intrinsic transmission dynamics of tuberculosis epidemics , 1995, Nature Medicine.

[15]  Carlos Castillo-Chavez,et al.  Modeling TB and HIV co-infections. , 2009, Mathematical biosciences and engineering : MBE.

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

[17]  M. Borgdorff,et al.  New Measurable Indicator for Tuberculosis Case Detection , 2004, Emerging infectious diseases.

[18]  Xingfu Zou,et al.  Modeling diseases with latency and relapse. , 2007, Mathematical biosciences and engineering : MBE.