Threshold dynamical analysis on a class of age-structured tuberculosis model with immigration of population

Advances in Difference Equations

Lili Liu¹  Zhen Jin¹  Xinzhi Ren² 

[1] Complex Systems Research Center, Shanxi University, Taiyuan, China;Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing, China

关键词: tuberculosis model;    age-structured;    immigration;    global stability;    Lyapunov functional;   

DOI  :  10.1186/s13662-017-1295-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Some studies show that latency and relapse, especially the age-dependent latency and relapse, may affect the transmission dynamics of tuberculosis model. Meanwhile, the immigration of infected individuals induces the loss of disease-free steady state and hence no basic reproduction number. In our work, a class of age-structured tuberculosis model with immigration is proposed, where the new individuals can immigrate into the susceptible, latent, infectious and removed compartments. We show that the endemic steady state is unique and globally asymptotically stable by using the Lyapunov functional. Numerical simulations are given to support our theoretical results.

【 授权许可】

CC BY