Persistent high incidence of tuberculosis among immigrants in a low-incidence country: Impact of immigrants with early or late latency

Hongbin Guo; Jianhong Wu; Hongbin Guo; Jianhong Wu

doi:10.3934/mbe.2011.8.695

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 3: 695-709. doi: 10.3934/mbe.2011.8.695

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Persistent high incidence of tuberculosis among immigrants in a low-incidence country: Impact of immigrants with early or late latency

Hongbin Guo ,
Jianhong Wu

1.
Centre for Disease Modeling, Department of Mathematics and Statistics, York University, 4700 Keele Street Toronto, ON, M3J 1P3

Received: 01 March 2009 Accepted: 29 June 2018 Published: 01 June 2011
MSC : Primary: 92D30; Secondary: 34D23.

Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB incidence to developed countries poses an increasing challenge in the global TB control. Here a simple compartmental TB model with constant immigration, early and late latency is developed in order to investigate the impact of new immigrants with latent TB on the overall TB incidence, and to compare the difference contributed by different proportions of latently-infected new immigrants with high or low risk to develop active TB shortly after arrival. The global dynamics of the system is completely classified, numerical simulations are carried out for different scenarios, and potential applications to public health policy are discussed.
- Lyapunov function,
- Tuberculosis,
- immigration,
- compartmental model,
- incidence rate,
- latent TB infection (LTBI).,
- global stability
Citation: Hongbin Guo, Jianhong Wu. Persistent high incidence of tuberculosis among immigrants in a low-incidence country: Impact of immigrants with early or late latency[J]. Mathematical Biosciences and Engineering, 2011, 8(3): 695-709. doi: 10.3934/mbe.2011.8.695

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Abstract

Spread of tuberculosis (TB) due to the immigration from some developing countries with high TB incidence to developed countries poses an increasing challenge in the global TB control. Here a simple compartmental TB model with constant immigration, early and late latency is developed in order to investigate the impact of new immigrants with latent TB on the overall TB incidence, and to compare the difference contributed by different proportions of latently-infected new immigrants with high or low risk to develop active TB shortly after arrival. The global dynamics of the system is completely classified, numerical simulations are carried out for different scenarios, and potential applications to public health policy are discussed.
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