Open AccessThreshold dynamics for a Tuberculosis model with seasonality
Author(s) -
Xinli Hu
Publication year - 2012
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2012.9.111
Subject(s) - basic reproduction number , tuberculosis , mathematics , stability theory , class (philosophy) , dynamics (music) , epidemic model , statistical physics , mathematical economics , demography , computer science , physics , medicine , population , nonlinear system , artificial intelligence , pathology , quantum mechanics , sociology , acoustics
In this paper, we investigate a SEILR tuberculosis model incorporating the effect of seasonal fluctuation, where the loss of sight class is considered. The basic reproduction number R₀ is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if R₀ < 1, and there exists at least one positive periodic solution and the disease is uniformly persistent if R₀ > 1. Numerical simulations are provided to illustrate analytical results.