Abstract
A tuberculosis (TB) transmission model involving migrant workers is proposed and investigated. The basic reproduction number R0 is calculated, and is shown to be a threshold parameter for the disease to persist or become extinct in the population. The existence and global attractivity of an endemic equilibrium, if R0 > 1, is also established under some technical conditions. A case study, based on the TB epidemiological and other statistical data in China, indicates that the disease spread can be controlled if effective measures are taken to reduce the reactivation rate of exposed/latent migrant workers. Impact of the migration rate and direction, as well as the duration of home visit stay, on the control of disease spread is also examined numerically.
Highlights
Tuberculosis (TB) caused by infection with the Mycobacterium tuberculosis (M. tuberculosis) is an airborne infectious disease that is preventable and curable [45]
In [22], a three-population TB model was formulated to examine the impact of latently-infected new immigrations on the TB incidence rate of the host immigration countries and the importance of cross-infection between foreignborn and local-born population in Canada and UK. Motivated by these studies and the aforementioned situation in China involving a large number of migrant workers, we develop in this paper a TB model with migration to investigate TB transmission in China
We prove that there is a unique disease-free equilibrium and the disease always dies out when R0 < 1; while the disease uniformly persists in the population and there is at least one endemic equilibrium when R0 > 1
Summary
Tuberculosis (TB) caused by infection with the Mycobacterium tuberculosis (M. tuberculosis) is an airborne infectious disease that is preventable and curable [45]. We show that when R0 > 1, the system has a unique globally attractive endemic equilibrium provided the migration rates of migrant workers from villages to towns/cities and of infectious migrant workers from towns/cities to villages are very small.
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