Journal
APPLIED MATHEMATICAL MODELLING
Volume 75, Issue -, Pages 769-786Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2019.07.003
Keywords
Age-structured TB model; The exponential progress rate; C-0-semigroup; Global stability; Uniform persistence
Funding
- National Natural Science Foundation of China [11301314, 11671142, 11371087]
- Natural Science Foundation of Shaanxi Province in China [2019JM-081]
- Natural Science Foundation of Shaanxi Provincial Department of Education in China [18JK0092]
- national key program for infectious diseases of China [2017ZX10201302]
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This paper deals with the global dynamic analysis for a tuberculosis transmission model with age-structure and the exponential progress rate. The time delay in the progression from the latent individuals to becoming the infectious individuals is also considered in our model. The basic reproduction number R-0 of the model is defined. It is proved that R-0 = 1 is a threshold to determine the disease extinction or persistence. The disease free equilibrium is globally stable (unstable) if R-0 <1 (if R-0 > 1). There exists an endemic equilibrium and the system is uniformly persistent if R-0 > 1. The global stability of the endemic equilibrium is given when R-0 > 1. At end, the model is applied to describe tuberculosis transmission in China. The number of total population, the number of the annual new TB cases, the annual PPD positive rate, and the prevalent rate all match the statistical data well. (C) 2019 Elsevier Inc. All rights reserved.
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