This paper presents two new theoretical frameworks to investigate the impact of immigration on the transmission dynamics of tuberculosis. For the basic model, we present new analysis on the existence and stability of equilibria. Then, we use numerical simulations of the model to illustrate the behavior of the system. We apply the model to Canadian reported data on tuberculosis and observe a good agreement between the model prediction and the data. For the extended model, which incorporated the recruitment of the latent and infectious in immigrants to the basic model, we find that the usual threshold condition does not apply and a unique equilibrium exists for all parameter values. This indicates that the disease does not disappear and becomes endemic in host areas. This finding is also supported by numerical simulations with the extended model. Our study suggests that immigrants have a considerable influence on the overall transmission dynamics behavior of tuberculosis.

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Keywords Endemic equilibrium, Global asymptotic stability, Immigrant, Threshold parameter, Tuberculosis
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Jia, Z.W., Tang, G.Y., Jin, Z., Dye, C., Vlas, S.J., Li, X.W., … Cao, W.C.. (2008). Modeling the impact of immigration on the epidemiology of tuberculosis. Theoretical Population Biology, 73(3), 437–448. doi:10.1016/j.tpb.2007.12.007