A Two-Strain Tuberculosis Model with Age of Infection

Long periods of latency and the emergence of antibiotic resistance due to incomplete treatment are very important features of tuberculosis (TB) dynamics. Previous studies of two-strain TB have been performed by ODE models. In this article, we formulate a two-strain TB model with an arbitrarily distributed delay in the latent stage of individuals infected with the drug-sensitive strain and look at the effects of variable periods of latency on the disease dynamics.

[1]  Richard K Miller,et al.  Nonlinear Volterra Integral Equations , 1970 .

[2]  J. Gerberding,et al.  Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework , 1998, Journal of Molecular Medicine.

[3]  P. Hopewell,et al.  Overview of Clinical Tuberculosis , 1994 .

[4]  G. Webb Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

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

[6]  Miller Bess,et al.  Preventive therapy for tuberculosis. , 1993, The Medical clinics of North America.

[7]  B G Williams,et al.  Criteria for the control of drug-resistant tuberculosis. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[8]  C. Dye,et al.  Will tuberculosis become resistant to all antibiotics? , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  Horst R. Thieme,et al.  Endemic Models with Arbitrarily Distributed Periods of Infection II: Fast Disease Dynamics and Permanent Recovery , 2000, SIAM J. Appl. Math..

[10]  B. Miller Preventive therapy for tuberculosis. , 1993, The Medical clinics of North America.

[11]  Carlos Castillo-Chavez,et al.  On the Role of Variable Latent Periods in Mathematical Models for Tuberculosis , 2001 .

[12]  S. Blower,et al.  Quantifying the intrinsic transmission dynamics of tuberculosis. , 1998, Theoretical population biology.

[13]  Mimmo Iannelli,et al.  Mathematical Theory of Age-Structured Population Dynamics , 1995 .

[14]  Carlos Castillo-Chavez,et al.  A model for TB with exogenous reinfection , 1999 .

[15]  A. Kochi,et al.  The global tuberculosis situation and the new control strategy of the World Health Organization. , 1991, Tubercle.

[16]  Horst R. Thieme,et al.  Persistence under relaxed point-dissipativity (with application to an endemic model) , 1993 .

[17]  D. Hartfiel,et al.  Understanding , 2003 .

[18]  Global Tuberculosis Programme Global tuberculosis control : WHO report , 1997 .

[19]  Horst R. Thieme,et al.  Endemic Models with Arbitrarily Distributed Periods of Infection I: Fundamental Properties of the Model , 2000, SIAM J. Appl. Math..