American Institute of Mathematical Sciences

Advanced
2005, 2(3): 535-560. doi: 10.3934/mbe.2005.2.535

A Metapopulation Model Of Granuloma Formation In The Lung During Infection With Mycobacterium Tuberculosis

Suman Ganguli 1, , David Gammack 2, and  Denise E. Kirschner 3,

1. 

Biosystems Group, University of California, San Francisco, 513 Parnassus Ave., San Francisco, CA 94143, United States
2. 

Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109, United States
3. 

Department of Microbiology and Immunology, University of Michigan Medical School, 1150 Medical Center Drive, Ann Arbor, MI 48109, United States

Received  January 2005 Revised  July 2005 Published  August 2005

The immune response to Mycobacterium tuberculosis infection (Mtb) is the formation of unique lesions, called granulomas. How well these granulomas form and function is a key issue that might explain why individuals experience different disease outcomes. The spatial structures of these granulomas are not well understood. In this paper, we use a metapopulation framework to develop a spatio-temporal model of the immune response to Mtb. Using this model, we are able to investigate the spatial organization of the immune response in the lungs to Mtb. We identify both host and pathogen factors that contribute to successful infection control. Additionally, we identify specific spatial interactions and mechanisms important for successful granuloma formation. These results can be further studied in the experimental setting.
Keywords: chemotaxis, metapopulation, mathematical model, diffusion., granuloma, Mycobacterium tuberculosis.
Mathematics Subject Classification: 92C9.
Citation: Suman Ganguli, David Gammack, Denise E. Kirschner. A Metapopulation Model Of Granuloma Formation In The Lung During Infection With Mycobacterium Tuberculosis. Mathematical Biosciences & Engineering, 2005, 2 (3) : 535-560. doi: 10.3934/mbe.2005.2.535
[1]

Eduardo Ibargüen-Mondragón, Lourdes Esteva, Edith Mariela Burbano-Rosero. Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma. Mathematical Biosciences & Engineering, 2018, 15 (2) : 407-428. doi: 10.3934/mbe.2018018
[2]

Fabrizio Clarelli, Roberto Natalini. A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions. Mathematical Biosciences & Engineering, 2010, 7 (2) : 277-300. doi: 10.3934/mbe.2010.7.277
[3]

Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973
[4]

Abba B. Gumel, Baojun Song. Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis. Mathematical Biosciences & Engineering, 2008, 5 (3) : 437-455. doi: 10.3934/mbe.2008.5.437
[5]

Dashun Xu, Z. Feng. A metapopulation model with local competitions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 495-510. doi: 10.3934/dcdsb.2009.12.495
[6]

Gesham Magombedze, Winston Garira, Eddie Mwenje. Modelling the human immune response mechanisms to mycobacterium tuberculosis infection in the lungs. Mathematical Biosciences & Engineering, 2006, 3 (4) : 661-682. doi: 10.3934/mbe.2006.3.661
[7]

Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209
[8]

Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real. Optimal control of vaccine distribution in a rabies metapopulation model. Mathematical Biosciences & Engineering, 2008, 5 (2) : 219-238. doi: 10.3934/mbe.2008.5.219
[9]

Alan J. Terry. Pulse vaccination strategies in a metapopulation SIR model. Mathematical Biosciences & Engineering, 2010, 7 (2) : 455-477. doi: 10.3934/mbe.2010.7.455
[10]

Zhilan Feng, Robert Swihart, Yingfei Yi, Huaiping Zhu. Coexistence in a metapopulation model with explicit local dynamics. Mathematical Biosciences & Engineering, 2004, 1 (1) : 131-145. doi: 10.3934/mbe.2004.1.131
[11]

Expeditho Mtisi, Herieth Rwezaura, Jean Michel Tchuenche. A mathematical analysis of malaria and tuberculosis co-dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 827-864. doi: 10.3934/dcdsb.2009.12.827
[12]

Zhi-An Wang, Kun Zhao. Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model. Communications on Pure & Applied Analysis, 2013, 12 (6) : 3027-3046. doi: 10.3934/cpaa.2013.12.3027
[13]

Chunhua Jin. Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1675-1688. doi: 10.3934/dcdsb.2018069
[14]

Xinli Hu. Threshold dynamics for a Tuberculosis model with seasonality. Mathematical Biosciences & Engineering, 2012, 9 (1) : 111-122. doi: 10.3934/mbe.2012.9.111
[15]

Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis. A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme. Mathematical Biosciences & Engineering, 2014, 11 (4) : 679-721. doi: 10.3934/mbe.2014.11.679
[16]

Britnee Crawford, Christopher Kribs-Zaleta. A metapopulation model for sylvatic T. cruzi transmission with vector migration. Mathematical Biosciences & Engineering, 2014, 11 (3) : 471-509. doi: 10.3934/mbe.2014.11.471
[17]

Danyun He, Qian Wang, Wing-Cheong Lo. Mathematical analysis of macrophage-bacteria interaction in tuberculosis infection. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3387-3413. doi: 10.3934/dcdsb.2018239
[18]

Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres. Optimal control of a Tuberculosis model with state and control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 321-337. doi: 10.3934/mbe.2017021
[19]

Marco Di Francesco, Alexander Lorz, Peter A. Markowich. Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1437-1453. doi: 10.3934/dcds.2010.28.1437
[20]

Jiashan Zheng. Boundedness of solutions to a quasilinear higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 627-643. doi: 10.3934/dcds.2017026

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences