Abstract
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.
Highlights
Tuberculosis (TB), mainly caused by Mycobacterium tuberculosis, is a widespread infectious disease and has become a global public health issue
5.2 Global stability This subsection is devoted to showing the global stability of T∗, which implies that the attractor A only contains the unique endemic steady state
We proposed and investigated a class of age-structured SEIR epidemic model with immigration
Summary
Tuberculosis (TB), mainly caused by Mycobacterium tuberculosis, is a widespread infectious disease and has become a global public health issue. In Section , we investigate the asymptotic smoothness of the semi-flow generated by our model and the existence of compact attractor. In Section , we show our dynamics results, including the existence and global stability of the unique endemic steady state.
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