Threshold Dynamics for a Tuberculosis Model with Intervention Strategies
- Author:
- No author available
- Journal Title:
- Journal of Biomathematics
- Issue:
- 4
- DOI:
- No doi available
- Key Word:
- 肺结核;阈值;绝灭;一致持续;Tuberculosis;Threshold;Extinction;Uniform persistence
Abstract： A recent paper [4] explores the dynamics of the spread of tuberculosis (TB).The analysis there only numerically analyzes the disease spread and the effects of different invention strategies.In the present paper,the spread dynamics of the disease and the effects of different intervention strategies are analyzed theoretically.The main results of the model are:The basic reproduction number R0 is calculated.It is shown that this number characterizes the disease transmission dynamics:if R0 ＜ 1,there exists only the disease-free equilibrium which is locally asymptotically stable; and if R0 ＞ 1then there is a disease endemic equilibrium and the disease persists.Sufficient condition for the global stability of the disease-free equilibrium is also obtained.
- [1]黄友霞,王辉,苏丹丹.食饵有病的生态-流行病模型的稳定性研究[J].2008,(1).
- [2]De Leenheer P.,Smith HL..Virus dynamics: A global analysis[J].2003,63(4).
- [3]叶海平,丁永生.一类总人口在变化的HIV/AIDS传播的动力学模型[J].2010,(1).
- [4]Horst R. Thieme.Persistence under Relaxed Point-Dissipativity (with Application to an Endemic Model)[J].1993,24(2).
- [5]O.Diekmann,J.A.P.Heesterbeek,J.A.J.Metz.On the definition and the computation of the basic reproduction ratioR0in models for infectious diseases in heterogeneous populations[J].1990,28(4).
- [6]van den Driessche P.,Watmough J..Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J].2002,180(special issue si).
- [7]Pienaar, E.,Fluitt, A.M.,Whitney, S.E.,etc.A model of tuberculosis transmission and intervention strategies in an urban residential area[J].2010,34(2).
- [8]侯晓星,张群英.一类具时滞的禽流感模型[J].2010,(1).