2011, 8(3): 695-709. doi: 10.3934/mbe.2011.8.695

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

1. 

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

Received  March 2009 Revised  December 2010 Published  June 2011

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.
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. Mathematical Biosciences & Engineering, 2011, 8 (3) : 695-709. doi: 10.3934/mbe.2011.8.695
References:
[1]

R. M. Anderson and R. M. May, "Infectious Diseases of Humans: Dynamics and Control,", Oxford University Press, (1992).

[2]

S. M. Blower, A. R. Mclean, T. C. Proco, P. M. Small, P. C. Hopewell, M. A. Sanchez and A. R. Moss, The intrinsic transmission dynamics of tuberculosis epidemics,, Nature Medicine, 1 (1995), 815. doi: 10.1038/nm0895-815.

[3]

S. M. Blower, P. M. Small and P. C. Hopewell, Control strategies for tuberculosis epidemics: New models for old problems,, Science, 273 (1996), 497. doi: 10.1126/science.273.5274.497.

[4]

F. Brauer and P. van den Driessche, Models for transmission of disease with immigration of infectives,, Math. Biosci., 171 (2001), 143. doi: 10.1016/S0025-5564(01)00057-8.

[5]

F. Brauer, P. van den Driessche and J. Wu, editors, "Mathematical Epidemiology,", Lecture Notes in Mathematics, 1945 (2008).

[6]

Canada Immigration Center (CIC), Facts and figures of immigration in Canada., Available from: \url{http://www.cic.gc.ca/english/resources/statistics/menu-fact.asp}, ().

[7]

C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis,, J. Math. Biol., 35 (1997), 629. doi: 10.1007/s002850050069.

[8]

C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosci. Eng., 1 (2004), 361.

[9]

T. Cohen and M. Murray, Incident tuberculosis among recent US immigrants and exogenous reinfection,, Emerg. Infec. Dises., 11 (2005), 725.

[10]

Communicable Diseases Intelligence, Tuberculosis notifications in Australia, 2005,, Commun. Dis. Intell., 31 (2007), 71.

[11]

A. Fanning, Globalization of tuberculosis,, Canadian Med. Asso. J., 158 (1998), 611.

[12]

E. Geng, B. Kreiswirth, C. Driver, J. Li, J. Burzynski, P. DellaLatta, A. LaPaz and N. W. Schluger, Changes in the transmission of tuberculosis in New York City from 1990-1999,, N. Engl. J. Med., 346 (2002), 1453. doi: 10.1056/NEJMoa012972.

[13]

H. Guo and M. Y. Li, Mathematical analysis of a model for latent tuberculosis,, Canadian Appl. Math. Quart., 14 (2006), 185.

[14]

H. Guo, M. Y. Li and Z. Shuai, A graph-theoretic approach to the method of global Lyapunov functions,, Proc. Amer. Math. Soc., 136 (2008), 2793. doi: 10.1090/S0002-9939-08-09341-6.

[15]

Health Canada, Tuberculosis in Canada,, 2001. Available from: \url{http://www.hc-sc.gc.ca/pphb-dgspsp/publicat/tbcan01/pdf/tbcan-2001-e.pdf}, 2001 ().

[16]

Health Canada, Canadian guidelines for the investigation and follow-up of individuals under medical surveillance for TB after arrival in Canada,, Canada Communicable Disease Report, 27 (2002).

[17]

Health Protection Agency, UK TB update,, 2007. Available from: \url{http://www.hpa.org.uk}., 2007 ().

[18]

Health Protection Agency, Recent trends in tuberculosis: 2000-2005,, Annual surveillance report, (2006).

[19]

E. Hemandez-Garduno, D. Kunimoto, L. Wang, M. Rodrigues, R. K. Elwood, W. Black, S. Mak and J. M. FitzGerald, Predictors of clustering of tuberculosis in Greater Vancouver: A molecular epidemiology study,, Can. Med. Assoc. J., 167 (2002), 349.

[20]

J. Inigo, D. Garcia de Viedma, A. Arce, E. Palenque, N. A. Rodriguez, E. Rodriguez, M. J. R. Serrano, S. Andres, E. Bouza and F. Chaves, Analysis of changes in recent tuberculosis transmission patterns after a sharp increase in immigration,, J. Clinical Microbio., 45 (2007), 63. doi: 10.1128/JCM.01644-06.

[21]

S. Kulaga, M. Behr, K. Musana, J. Brinkman, D. Menzies, P. Brassard, D. Kunimoto, T.-N. Tannenbaum, L. Thibert, L. Joseph, J.-F. Boivin and K. Schwartzman, Molecular epidemiology of tuberculosis in Montreal,, CMAJ., 167 (2002), 353.

[22]

J. P. LaSalle, "The Stability of Dynamical Systems,", Regional Conference Series in Applied Mathematics, (1976).

[23]

T. Lillebaek, A. B. Andersen, J. Bauer, A. Dirksen, S. Glismann, P. de Haas and A. Kok-Jensen, Risk of Mycobacterium tuberculosis transmission in a low-incidence country due to immigration from high-incidence areas,, J. Clinical Microbio., 39 (2001), 855. doi: 10.1128/JCM.39.3.855-861.2001.

[24]

T. Lillebaek, A. B. Andersen, A. Dirksen, E. Smith, L. T. Skovgaard and A. Kok-Jensen, Persistent high incidence of tuberculosis in immigrants in a low-incidence country,, Emerging Infectious Disease, 8 (2002), 679.

[25]

C. C. McCluskey and P. van den Driessche, Global analysis of two tuberculosis models,, J. Dynam. Diff. Eqs., 16 (2004), 139. doi: 10.1023/B:JODY.0000041283.66784.3e.

[26]

M. T. Mckenna, E. McCray and I. Onorato, The epidemiology of tuberculosis among foreign-born persons in the United States, 1986 to 1993,, N. Engl. J. Med., 332 (1995), 1071. doi: 10.1056/NEJM199504203321606.

[27]

M. E. McPherson, H. Kelly, M. S. Patel and D. Leslie, Persistent risk of tuberculosis in migrants a decade after arrival in Australia,, Medical J. of Australia, 188 (2008), 528.

[28]

D. Menzies, Screening immigrants to Canada for tuberculosis: Chest radiography or tuberculin skin testing?,, Canadian Med. Asso. J., 169 (2003), 1035.

[29]

D. Menzies, Controlling TB among foreign-born within industrialized countries: Expensive Band-Aids,, Am. J. Respiratory Crit. Care Med., 164 (2001), 914.

[30]

M. B. Murray, Molecular epidemiology and the dynamics of tuberculosis transmission among foreign-born people,, Canadian Med. Asso. J., 167 (2002), 355.

[31]

B. M. Murphy, B. H. Singer, S. Anderson and D. Kirschner, Comparing epidemic tuberculosis in demographically distict heterogenous populations,, Math. Biosci., 180 (2002), 161. doi: 10.1016/S0025-5564(02)00133-5.

[32]

S. Patel, A. E. Parsyan, J. Gunn, M. A. Barry, C. Reed, S. Sharnprapai and C. R. Horsburgh, Risk of progression to active tuberculosis among foreign-born persons with latent tuberculosis,, Chest., 131 (2007), 1811. doi: 10.1378/chest.06-2601.

[33]

T. C. Porco and S. M. Blower, Quantifying the intrinsic transmission dynamics of tuberculosis,, Theor. Popu. Bio., 54 (1998), 117. doi: 10.1006/tpbi.1998.1366.

[34]

Public Health Agency of Canada, Tuberculosis in Canada 2002,, 2005. Available from: \url{http://www.phac-aspc.gc.ca/publicat/tbcan02/index.html}., 2005 ().

[35]

Statistics Canada, 2001 Census of Canada,, Available from: \url{http://www.statcan.ca/menu-en.htm}., ().

[36]

E. A. Talbot, M. Moore, E. McCray and N. J. Binkin, Tuberculosis among foreign-born persons in the United States, 1993-1998,, J. Amer. Med. Asso., 284 (2000), 2894. doi: 10.1001/jama.284.22.2894.

[37]

WHO, "Global Tuberculosis Control: Surveillance, Planning and Financing,", World Heath Organization, (2008).

[38]

Y. Zhou, K. Khan, Z. Feng and J. Wu, Projection of Canadian tuberculosis incidence with increasing immigration,, J. Theore. Bio., 254 (2008), 215. doi: 10.1016/j.jtbi.2008.05.026.

[39]

E. Ziv, C. L. Daley and S. M. Blower, Early therapy for latent tuberculosis infection,, Amer. J. Epidemiol., 153 (2001), 381. doi: 10.1093/aje/153.4.381.

show all references

References:
[1]

R. M. Anderson and R. M. May, "Infectious Diseases of Humans: Dynamics and Control,", Oxford University Press, (1992).

[2]

S. M. Blower, A. R. Mclean, T. C. Proco, P. M. Small, P. C. Hopewell, M. A. Sanchez and A. R. Moss, The intrinsic transmission dynamics of tuberculosis epidemics,, Nature Medicine, 1 (1995), 815. doi: 10.1038/nm0895-815.

[3]

S. M. Blower, P. M. Small and P. C. Hopewell, Control strategies for tuberculosis epidemics: New models for old problems,, Science, 273 (1996), 497. doi: 10.1126/science.273.5274.497.

[4]

F. Brauer and P. van den Driessche, Models for transmission of disease with immigration of infectives,, Math. Biosci., 171 (2001), 143. doi: 10.1016/S0025-5564(01)00057-8.

[5]

F. Brauer, P. van den Driessche and J. Wu, editors, "Mathematical Epidemiology,", Lecture Notes in Mathematics, 1945 (2008).

[6]

Canada Immigration Center (CIC), Facts and figures of immigration in Canada., Available from: \url{http://www.cic.gc.ca/english/resources/statistics/menu-fact.asp}, ().

[7]

C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis,, J. Math. Biol., 35 (1997), 629. doi: 10.1007/s002850050069.

[8]

C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosci. Eng., 1 (2004), 361.

[9]

T. Cohen and M. Murray, Incident tuberculosis among recent US immigrants and exogenous reinfection,, Emerg. Infec. Dises., 11 (2005), 725.

[10]

Communicable Diseases Intelligence, Tuberculosis notifications in Australia, 2005,, Commun. Dis. Intell., 31 (2007), 71.

[11]

A. Fanning, Globalization of tuberculosis,, Canadian Med. Asso. J., 158 (1998), 611.

[12]

E. Geng, B. Kreiswirth, C. Driver, J. Li, J. Burzynski, P. DellaLatta, A. LaPaz and N. W. Schluger, Changes in the transmission of tuberculosis in New York City from 1990-1999,, N. Engl. J. Med., 346 (2002), 1453. doi: 10.1056/NEJMoa012972.

[13]

H. Guo and M. Y. Li, Mathematical analysis of a model for latent tuberculosis,, Canadian Appl. Math. Quart., 14 (2006), 185.

[14]

H. Guo, M. Y. Li and Z. Shuai, A graph-theoretic approach to the method of global Lyapunov functions,, Proc. Amer. Math. Soc., 136 (2008), 2793. doi: 10.1090/S0002-9939-08-09341-6.

[15]

Health Canada, Tuberculosis in Canada,, 2001. Available from: \url{http://www.hc-sc.gc.ca/pphb-dgspsp/publicat/tbcan01/pdf/tbcan-2001-e.pdf}, 2001 ().

[16]

Health Canada, Canadian guidelines for the investigation and follow-up of individuals under medical surveillance for TB after arrival in Canada,, Canada Communicable Disease Report, 27 (2002).

[17]

Health Protection Agency, UK TB update,, 2007. Available from: \url{http://www.hpa.org.uk}., 2007 ().

[18]

Health Protection Agency, Recent trends in tuberculosis: 2000-2005,, Annual surveillance report, (2006).

[19]

E. Hemandez-Garduno, D. Kunimoto, L. Wang, M. Rodrigues, R. K. Elwood, W. Black, S. Mak and J. M. FitzGerald, Predictors of clustering of tuberculosis in Greater Vancouver: A molecular epidemiology study,, Can. Med. Assoc. J., 167 (2002), 349.

[20]

J. Inigo, D. Garcia de Viedma, A. Arce, E. Palenque, N. A. Rodriguez, E. Rodriguez, M. J. R. Serrano, S. Andres, E. Bouza and F. Chaves, Analysis of changes in recent tuberculosis transmission patterns after a sharp increase in immigration,, J. Clinical Microbio., 45 (2007), 63. doi: 10.1128/JCM.01644-06.

[21]

S. Kulaga, M. Behr, K. Musana, J. Brinkman, D. Menzies, P. Brassard, D. Kunimoto, T.-N. Tannenbaum, L. Thibert, L. Joseph, J.-F. Boivin and K. Schwartzman, Molecular epidemiology of tuberculosis in Montreal,, CMAJ., 167 (2002), 353.

[22]

J. P. LaSalle, "The Stability of Dynamical Systems,", Regional Conference Series in Applied Mathematics, (1976).

[23]

T. Lillebaek, A. B. Andersen, J. Bauer, A. Dirksen, S. Glismann, P. de Haas and A. Kok-Jensen, Risk of Mycobacterium tuberculosis transmission in a low-incidence country due to immigration from high-incidence areas,, J. Clinical Microbio., 39 (2001), 855. doi: 10.1128/JCM.39.3.855-861.2001.

[24]

T. Lillebaek, A. B. Andersen, A. Dirksen, E. Smith, L. T. Skovgaard and A. Kok-Jensen, Persistent high incidence of tuberculosis in immigrants in a low-incidence country,, Emerging Infectious Disease, 8 (2002), 679.

[25]

C. C. McCluskey and P. van den Driessche, Global analysis of two tuberculosis models,, J. Dynam. Diff. Eqs., 16 (2004), 139. doi: 10.1023/B:JODY.0000041283.66784.3e.

[26]

M. T. Mckenna, E. McCray and I. Onorato, The epidemiology of tuberculosis among foreign-born persons in the United States, 1986 to 1993,, N. Engl. J. Med., 332 (1995), 1071. doi: 10.1056/NEJM199504203321606.

[27]

M. E. McPherson, H. Kelly, M. S. Patel and D. Leslie, Persistent risk of tuberculosis in migrants a decade after arrival in Australia,, Medical J. of Australia, 188 (2008), 528.

[28]

D. Menzies, Screening immigrants to Canada for tuberculosis: Chest radiography or tuberculin skin testing?,, Canadian Med. Asso. J., 169 (2003), 1035.

[29]

D. Menzies, Controlling TB among foreign-born within industrialized countries: Expensive Band-Aids,, Am. J. Respiratory Crit. Care Med., 164 (2001), 914.

[30]

M. B. Murray, Molecular epidemiology and the dynamics of tuberculosis transmission among foreign-born people,, Canadian Med. Asso. J., 167 (2002), 355.

[31]

B. M. Murphy, B. H. Singer, S. Anderson and D. Kirschner, Comparing epidemic tuberculosis in demographically distict heterogenous populations,, Math. Biosci., 180 (2002), 161. doi: 10.1016/S0025-5564(02)00133-5.

[32]

S. Patel, A. E. Parsyan, J. Gunn, M. A. Barry, C. Reed, S. Sharnprapai and C. R. Horsburgh, Risk of progression to active tuberculosis among foreign-born persons with latent tuberculosis,, Chest., 131 (2007), 1811. doi: 10.1378/chest.06-2601.

[33]

T. C. Porco and S. M. Blower, Quantifying the intrinsic transmission dynamics of tuberculosis,, Theor. Popu. Bio., 54 (1998), 117. doi: 10.1006/tpbi.1998.1366.

[34]

Public Health Agency of Canada, Tuberculosis in Canada 2002,, 2005. Available from: \url{http://www.phac-aspc.gc.ca/publicat/tbcan02/index.html}., 2005 ().

[35]

Statistics Canada, 2001 Census of Canada,, Available from: \url{http://www.statcan.ca/menu-en.htm}., ().

[36]

E. A. Talbot, M. Moore, E. McCray and N. J. Binkin, Tuberculosis among foreign-born persons in the United States, 1993-1998,, J. Amer. Med. Asso., 284 (2000), 2894. doi: 10.1001/jama.284.22.2894.

[37]

WHO, "Global Tuberculosis Control: Surveillance, Planning and Financing,", World Heath Organization, (2008).

[38]

Y. Zhou, K. Khan, Z. Feng and J. Wu, Projection of Canadian tuberculosis incidence with increasing immigration,, J. Theore. Bio., 254 (2008), 215. doi: 10.1016/j.jtbi.2008.05.026.

[39]

E. Ziv, C. L. Daley and S. M. Blower, Early therapy for latent tuberculosis infection,, Amer. J. Epidemiol., 153 (2001), 381. doi: 10.1093/aje/153.4.381.

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