A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes

Previous Article
Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks
MBE Home
This Issue
Next Article

2015, 12(3): 625-642. doi: 10.3934/mbe.2015.12.625

A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes

Chang Gong ^1, , Jennifer J. Linderman ^2, and Denise Kirschner ^3,

1.	6775 Medical Science Building II, Ann Arbor, MI 48109-5620, United States
2.	B28-G045W NCRC, Ann Arbor, MI 48109-5620, United States
3.	6730 Medical Science Building II, Ann Arbor, MI 48109-5620, United States

Received January 2015 Revised January 2015 Published February 2015

Abstract
Related Papers

Granulomas play a centric role in tuberculosis (TB) infection progression. Multiple granulomas usually develop within a single host. These granulomas are not synchronized in size or bacteria load, and will follow different trajectories over time. How the fate of individual granulomas influence overall infection outcome at host scale is not understood, although computational models have been developed to predict single granuloma behavior. Here we present a within-host population model that tracks granulomas in two key organs during Mycobacteria tuberculosis (Mtb) infection: lung and lymph nodes (LN). We capture various time courses of TB progression, including latency and reactivation. The model predicts that there is no steady state; rather it is a continuous process of progressing to active disease over differing time periods. This is consistent with recently posed ideas suggesting that latent TB exists as a spectrum of states and not a single state. The model also predicts a dual role for granuloma development in LNs during Mtb infection: in early phases of infection granulomas suppress infection by providing additional antigens to the site of immune priming; however, this induces a more rapid reactivation at later stages by disrupting immune responses. We identify mechanisms that strongly correlate with better host-level outcomes, including elimination of uncontained lung granulomas by inducing low levels of lung tissue damage and inhibition of bacteria dissemination within the lung.

Keywords: within-host model., TB, granuloma, ODE model, infectious disease.

Mathematics Subject Classification: Primary: 97M60; Secondary: 92B0.

Citation: Chang Gong, Jennifer J. Linderman, Denise Kirschner. A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes. Mathematical Biosciences & Engineering, 2015, 12 (3) : 625-642. doi: 10.3934/mbe.2015.12.625

References:

[1]	I. Y. Adamson, Drug-induced pulmonary fibrosis,, Environmental health perspectives, 55 (1984), 25. Google Scholar
[2]	C. E. Barry, H. I. Boshoff, V. Dartois, T. Dick, S. Ehrt, J. Flynn, D. Schnappinger, R. J. Wilkinson and D. Young, The spectrum of latent tuberculosis: Rethinking the biology and intervention strategies,, Nature reviews. Microbiology, 7 (2009), 845. doi: 10.1038/nrmicro2236. Google Scholar
[3]	S. M. Blower, A. R. McLean, T. C. Porco, 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. Google Scholar
[4]	P.-J. Cardona, New insights on the nature of latent tuberculosis infection and its treatment,, Inflammation & allergy drug targets, 6 (2007), 27. doi: 10.2174/187152807780077282. Google Scholar
[5]	C. Castillo-Chávez and J. Aparicio, Mathematical modelling of tuberculosis epidemics,, Mathematical Biosciences and Engineering, 6 (2009), 209. doi: 10.3934/mbe.2009.6.209. Google Scholar
[6]	C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis,, Journal of mathematical biology, 35 (1997), 629. doi: 10.1007/s002850050069. Google Scholar
[7]	A. A. Chackerian, J. M. Alt, T. V. Perera, C. C. Dascher and S. M. Behar, Dissemination of Mycobacterium tuberculosis Is Influenced by Host Factors and Precedes the Initiation of T-Cell Immunity,, Infection and Immunity, 70 (2002), 4501. doi: 10.1128/IAI.70.8.4501-4509.2002. Google Scholar
[8]	N. A. Cilfone, C. R. Perry, D. E. Kirschner and J. J. Linderman, Multi-scale modeling predicts a balance of tumor necrosis factor-$\alpha$ and interleukin-10 controls the granuloma environment during Mycobacterium tuberculosis infection,, PloS one, 8 (2013). doi: 10.1371/journal.pone.0068680. Google Scholar
[9]	M. T. Coleman, R. Y. Chen, M. Lee, P. L. Lin, L. E. Dodd, P. Maiello, L. E. Via, Y. Kim, G. Marriner, V. Dartois, C. Scanga, C. Janssen, J. Wang, E. Klein, S. N. Cho, C. E. Barry 3rd and J. L. Flynn, PET/CT imaging reveals a therapeutic response to oxazolidinones in macaques and humans with tuberculosis,, Sci Transl Med, 6 (2014). doi: 10.1126/scitranslmed.3009500. Google Scholar
[10]	J. A. Cooper, D. A. White and R. A. Matthay, Drug-induced pulmonary disease. Part 1: Cytotoxic drugs,, The American review of respiratory disease, 133 (1986), 321. Google Scholar
[11]	E. L. Corbett, C. J. Watt, N. Walker, D. Maher, B. G. Williams, M. C. Raviglione and C. Dye, The growing burden of tuberculosis: Global trends and interactions with the HIV epidemic,, Archives of internal medicine, 163 (2003), 1009. doi: 10.1001/archinte.163.9.1009. Google Scholar
[12]	M. H. Daba, K. E. El-Tahir, M. N. Al-Arifi and O. A. Gubara, Drug-induced pulmonary fibrosis,, 2004., (). Google Scholar
[13]	O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, Journal of the Royal Society, 7 (2010), 873. doi: 10.1098/rsif.2009.0386. Google Scholar
[14]	C. Dye, G. P. Garnett, K. Sleeman and B. G. Williams, Prospects for worldwide tuberculosis control under the WHO DOTS strategy,, The Lancet, 352 (1998), 1886. doi: 10.1016/S0140-6736(98)03199-7. Google Scholar
[15]	M. Fallahi-Sichani, J. L. Flynn, J. J. Linderman and D. E. Kirschner, Differential risk of tuberculosis reactivation among anti-TNF therapies is due to drug binding kinetics and permeability,, Journal of immunology (Baltimore, 188* (2012), 3169. doi: 10.4049/jimmunol.1103298. Google Scholar*
[16]	M. Fallahi-Sichani, D. E. Kirschner and J. J. Linderman, NF-$\kappa$B Signaling Dynamics Play a Key Role in Infection Control in Tuberculosis,, Frontiers in physiology, (2012). doi: 10.3389/fphys.2012.00170. Google Scholar
[17]	M. Fallahi-Sichani, M. A. Schaller, D. E. Kirschner, S. L. Kunkel and J. J. Linderman, Identification of key processes that control tumor necrosis factor availability in a tuberculosis granuloma,, PLoS computational biology, 6 (2010). doi: 10.1371/journal.pcbi.1000778. Google Scholar
[18]	Z. Feng, C. Castillo-Chavez and A. F. Capurro, A model for tuberculosis with exogenous reinfection,, Theoretical population biology, 57 (2000), 235. doi: 10.1006/tpbi.2000.1451. Google Scholar
[19]	J. L. Flynn and J. Chan, Immunology of tuberculosis,, Annual review of immunology, 19 (2001), 93. Google Scholar
[20]	C. Gong, J. T. Mattila, M. Miller, J. L. Flynn, J. J. Linderman and D. Kirschner, Predicting lymph node output efficiency using systems biology,, Journal of theoretical biology, 335 (2013), 169. doi: 10.1016/j.jtbi.2013.06.016. Google Scholar
[21]	G. Guzzetta, M. Ajelli, Z. Yang, S. Merler, C. Furlanello and D. Kirschner, Modeling socio-demography to capture tuberculosis transmission dynamics in a low burden setting,, Journal of theoretical biology, 289 (2011), 197. doi: 10.1016/j.jtbi.2011.08.032. Google Scholar
[22]	D. Kirschner, Dynamics of co-infection with M. Tuberculosis and HIV-1,, Theoretical population biology, 55 (1999), 94. Google Scholar
[23]	D. E. Kirschner, S. T. Chang, T. W. Riggs, N. Perry and J. J. Linderman, Toward a multiscale model of antigen presentation in immunity,, Immunological reviews, 216 (2007), 93. Google Scholar
[24]	P. L. Lin, T. Coleman, J. P. J. Carney, B. J. Lopresti, J. Tomko, D. Fillmore, V. Dartois, C. Scanga, L. J. Frye, Ch. Janssen, E. Klein, C. E. Barry and Joanne L Flynn, Radiologic responses in cynomolgous macaques for assessing tuberculosis chemotherapy regimens,, Antimicrobial agents and chemotherapy, 57 (2013), 4237. doi: 10.1128/AAC.00277-13. Google Scholar
[25]	P. L. Lin, C. B. Ford, M. T. Coleman, A. J. Myers, R. Gawande, T. Ioerger, J. Sacchettini, S. M. Fortune and J. L. Flynn, Sterilization of granulomas is common in active and latent tuberculosis despite within-host variability in bacterial killing,, Nature medicine, 20 (2014), 75. doi: 10.1038/nm.3412. Google Scholar
[26]	P. L. Lin, M. Rodgers, L. Smith, M. Bigbee, A. Myers, C. Bigbee, I. Chiosea, S. V. Capuano, C. Fuhrman, E. Klein and J. L. Flynn, Quantitative comparison of active and latent tuberculosis in the cynomolgus macaque model,, Infection and immunity, 77 (2009), 4631. doi: 10.1128/IAI.00592-09. Google Scholar
[27]	J. J. Linderman, T. Riggs, M. Pande, M. Miller, S. Marino and D. E. Kirschner, Characterizing the dynamics of CD4+ T cell priming within a lymph node,, Journal of immunology (Baltimore, 184* (2010), 2873. doi: 10.4049/jimmunol.0903117. Google Scholar*
[28]	G. Magombedze, W. Garira and E. Mwenje, Modelling the human immune response mechanisms to mycobacterium tuberculosis infection in the lungs,, Mathematical biosciences and engineering : MBE, 3 (2006), 661. doi: 10.3934/mbe.2006.3.661. Google Scholar
[29]	G. Magombedze and N. Mulder, A mathematical representation of the development of Mycobacterium tuberculosis active, latent and dormant stages,, Journal of theoretical biology, 292 (2012), 44. doi: 10.1016/j.jtbi.2011.09.025. Google Scholar
[30]	S. Marino, M. El-Kebir and D. Kirschner, A hybrid multi-compartment model of granuloma formation and T cell priming in tuberculosis,, Journal of theoretical biology, 280 (2011), 50. doi: 10.1016/j.jtbi.2011.03.022. Google Scholar
[31]	S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, Journal of theoretical biology, 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011. Google Scholar
[32]	S. Marino and D. E. Kirschner, The human immune response to Mycobacterium tuberculosis in lung and lymph node,, Journal of theoretical biology, 227 (2004), 463. doi: 10.1016/j.jtbi.2003.11.023. Google Scholar
[33]	S. Marino, J. J. Linderman and D. E. Kirschner, A multifaceted approach to modeling the immune response in tuberculosis,, Wiley interdisciplinary reviews. Systems biology and medicine, 3 (2011), 479. doi: 10.1002/wsbm.131. Google Scholar
[34]	F. A. Milner, M. Iannelli and Z. Feng, A Two-Strain Tuberculosis Model with Age of Infection,, SIAM Journal on Applied Mathematics, 62 (2002), 1634. doi: 10.1137/S003613990038205X. Google Scholar
[35]	B. M. Murphy, B. H. Singer, S. Anderson and D. Kirschner, Comparing epidemic tuberculosis in demographically distinct heterogeneous populations,, Mathematical Biosciences, 180 (2002), 161. doi: 10.1016/S0025-5564(02)00133-5. Google Scholar
[36]	B. M. Murphy, B. H. Singer and D. Kirschner, On treatment of tuberculosis in heterogeneous populations,, Journal of Theoretical Biology, 223 (2003), 391. doi: 10.1016/S0022-5193(03)00038-9. Google Scholar
[37]	A. O'Garra, P. S. Redford, F. W. McNab, C. I. Bloom, R. J. Wilkinson and M. P. R. Berry, The immune response in tuberculosis,, Annual review of immunology, 31 (2013), 475. doi: 10.1146/annurev-immunol-032712-095939. Google Scholar
[38]	W. H. Organization, Global Tuberculosis Report 2013,, 2013., (). Google Scholar
[39]	R. Pabst, J. Westermann and H. J. Rothkotter, Immunoarchitecture of regenerated splenic and lymph node transplants,, Int Rev Cytol, 128 (1991), 215. doi: 10.1016/S0074-7696(08)60500-8. Google Scholar
[40]	T. H. Petersen, E. A. Calle, L. Zhao, E. J. Lee, L. Gui, M. B. Raredon, K. Gavrilov, T. Yi, Z. W. Zhuang, C. Breuer, E. Herzog and L. E. Niklason, Tissue-engineered lungs for in vivo implantation,, Science, 329 (2010), 538. doi: 10.1126/science.1189345. Google Scholar
[41]	L. Ramakrishnan, Revisiting the role of the granuloma in tuberculosis,, Nature reviews. Immunology, 12 (2012), 352. doi: 10.1038/nri3211. Google Scholar
[42]	J. Rengarajan, B. R. Bloom and E. J. Rubin, Genome-wide requirements for Mycobacterium tuberculosis adaptation and survival in macrophages,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 8327. doi: 10.1073/pnas.0503272102. Google Scholar
[43]	J. L. Segovia-Juarez, S. Ganguli and D. Kirschner, Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model,, Journal of theoretical biology, 231 (2004), 357. doi: 10.1016/j.jtbi.2004.06.031. Google Scholar
[44]	B. H. Singer and D. E. Kirschner, Influence of backward bifurcation on interpretation of r(0) in a model of epidemic tuberculosis with reinfection,, Mathematical biosciences and engineering: MBE, 1 (2004), 81. doi: 10.3934/mbe.2004.1.81. Google Scholar
[45]	L. E. Via, D. M. Weiner, D. Schimel, P. L. Lin, E. Dayao, S. L. Tankersley, Y. Cai, M. T. Coleman, J. Tomko, P. Paripati, M. Orandle, R. J. Kastenmayer, M. Tartakovsky, A. Rosenthal, D. Portevin, S. Y. Eum, S. Lahouar, S. Gagneux, D. B. Young, J. L. Flynn and C. E. Barry, Differential virulence and disease progression following Mycobacterium tuberculosis complex infection of the common marmoset (Callithrix jacchus),, Infection and immunity, 81 (2013), 2909. doi: 10.1128/IAI.00632-13. Google Scholar
[46]	J. E. Wigginton and D. Kirschner, A Model to Predict Cell-Mediated Immune Regulatory Mechanisms During Human Infection with Mycobacterium tuberculosis,, The Journal of Immunology, 166 (2001), 1951. doi: 10.4049/jimmunol.166.3.1951. Google Scholar
[47]	P. Ye and D. E. Kirschner, Reevaluation of T Cell Receptor Excision Circles as a Measure of Human Recent Thymic Emigrants,, The Journal of Immunology, 168 (2002), 4968. doi: 10.4049/jimmunol.168.10.4968. Google Scholar
[48]	D. Young, J. Stark and D. Kirschner, Systems biology of persistent infection: Tuberculosis as a case study,, Nature reviews. Microbiology, 6 (2008), 520. doi: 10.1038/nrmicro1919. Google Scholar

show all references

References:

[1]	I. Y. Adamson, Drug-induced pulmonary fibrosis,, Environmental health perspectives, 55 (1984), 25. Google Scholar
[2]	C. E. Barry, H. I. Boshoff, V. Dartois, T. Dick, S. Ehrt, J. Flynn, D. Schnappinger, R. J. Wilkinson and D. Young, The spectrum of latent tuberculosis: Rethinking the biology and intervention strategies,, Nature reviews. Microbiology, 7 (2009), 845. doi: 10.1038/nrmicro2236. Google Scholar
[3]	S. M. Blower, A. R. McLean, T. C. Porco, 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. Google Scholar
[4]	P.-J. Cardona, New insights on the nature of latent tuberculosis infection and its treatment,, Inflammation & allergy drug targets, 6 (2007), 27. doi: 10.2174/187152807780077282. Google Scholar
[5]	C. Castillo-Chávez and J. Aparicio, Mathematical modelling of tuberculosis epidemics,, Mathematical Biosciences and Engineering, 6 (2009), 209. doi: 10.3934/mbe.2009.6.209. Google Scholar
[6]	C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis,, Journal of mathematical biology, 35 (1997), 629. doi: 10.1007/s002850050069. Google Scholar
[7]	A. A. Chackerian, J. M. Alt, T. V. Perera, C. C. Dascher and S. M. Behar, Dissemination of Mycobacterium tuberculosis Is Influenced by Host Factors and Precedes the Initiation of T-Cell Immunity,, Infection and Immunity, 70 (2002), 4501. doi: 10.1128/IAI.70.8.4501-4509.2002. Google Scholar
[8]	N. A. Cilfone, C. R. Perry, D. E. Kirschner and J. J. Linderman, Multi-scale modeling predicts a balance of tumor necrosis factor-$\alpha$ and interleukin-10 controls the granuloma environment during Mycobacterium tuberculosis infection,, PloS one, 8 (2013). doi: 10.1371/journal.pone.0068680. Google Scholar
[9]	M. T. Coleman, R. Y. Chen, M. Lee, P. L. Lin, L. E. Dodd, P. Maiello, L. E. Via, Y. Kim, G. Marriner, V. Dartois, C. Scanga, C. Janssen, J. Wang, E. Klein, S. N. Cho, C. E. Barry 3rd and J. L. Flynn, PET/CT imaging reveals a therapeutic response to oxazolidinones in macaques and humans with tuberculosis,, Sci Transl Med, 6 (2014). doi: 10.1126/scitranslmed.3009500. Google Scholar
[10]	J. A. Cooper, D. A. White and R. A. Matthay, Drug-induced pulmonary disease. Part 1: Cytotoxic drugs,, The American review of respiratory disease, 133 (1986), 321. Google Scholar
[11]	E. L. Corbett, C. J. Watt, N. Walker, D. Maher, B. G. Williams, M. C. Raviglione and C. Dye, The growing burden of tuberculosis: Global trends and interactions with the HIV epidemic,, Archives of internal medicine, 163 (2003), 1009. doi: 10.1001/archinte.163.9.1009. Google Scholar
[12]	M. H. Daba, K. E. El-Tahir, M. N. Al-Arifi and O. A. Gubara, Drug-induced pulmonary fibrosis,, 2004., (). Google Scholar
[13]	O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, Journal of the Royal Society, 7 (2010), 873. doi: 10.1098/rsif.2009.0386. Google Scholar
[14]	C. Dye, G. P. Garnett, K. Sleeman and B. G. Williams, Prospects for worldwide tuberculosis control under the WHO DOTS strategy,, The Lancet, 352 (1998), 1886. doi: 10.1016/S0140-6736(98)03199-7. Google Scholar
[15]	M. Fallahi-Sichani, J. L. Flynn, J. J. Linderman and D. E. Kirschner, Differential risk of tuberculosis reactivation among anti-TNF therapies is due to drug binding kinetics and permeability,, Journal of immunology (Baltimore, 188* (2012), 3169. doi: 10.4049/jimmunol.1103298. Google Scholar*
[16]	M. Fallahi-Sichani, D. E. Kirschner and J. J. Linderman, NF-$\kappa$B Signaling Dynamics Play a Key Role in Infection Control in Tuberculosis,, Frontiers in physiology, (2012). doi: 10.3389/fphys.2012.00170. Google Scholar
[17]	M. Fallahi-Sichani, M. A. Schaller, D. E. Kirschner, S. L. Kunkel and J. J. Linderman, Identification of key processes that control tumor necrosis factor availability in a tuberculosis granuloma,, PLoS computational biology, 6 (2010). doi: 10.1371/journal.pcbi.1000778. Google Scholar
[18]	Z. Feng, C. Castillo-Chavez and A. F. Capurro, A model for tuberculosis with exogenous reinfection,, Theoretical population biology, 57 (2000), 235. doi: 10.1006/tpbi.2000.1451. Google Scholar
[19]	J. L. Flynn and J. Chan, Immunology of tuberculosis,, Annual review of immunology, 19 (2001), 93. Google Scholar
[20]	C. Gong, J. T. Mattila, M. Miller, J. L. Flynn, J. J. Linderman and D. Kirschner, Predicting lymph node output efficiency using systems biology,, Journal of theoretical biology, 335 (2013), 169. doi: 10.1016/j.jtbi.2013.06.016. Google Scholar
[21]	G. Guzzetta, M. Ajelli, Z. Yang, S. Merler, C. Furlanello and D. Kirschner, Modeling socio-demography to capture tuberculosis transmission dynamics in a low burden setting,, Journal of theoretical biology, 289 (2011), 197. doi: 10.1016/j.jtbi.2011.08.032. Google Scholar
[22]	D. Kirschner, Dynamics of co-infection with M. Tuberculosis and HIV-1,, Theoretical population biology, 55 (1999), 94. Google Scholar
[23]	D. E. Kirschner, S. T. Chang, T. W. Riggs, N. Perry and J. J. Linderman, Toward a multiscale model of antigen presentation in immunity,, Immunological reviews, 216 (2007), 93. Google Scholar
[24]	P. L. Lin, T. Coleman, J. P. J. Carney, B. J. Lopresti, J. Tomko, D. Fillmore, V. Dartois, C. Scanga, L. J. Frye, Ch. Janssen, E. Klein, C. E. Barry and Joanne L Flynn, Radiologic responses in cynomolgous macaques for assessing tuberculosis chemotherapy regimens,, Antimicrobial agents and chemotherapy, 57 (2013), 4237. doi: 10.1128/AAC.00277-13. Google Scholar
[25]	P. L. Lin, C. B. Ford, M. T. Coleman, A. J. Myers, R. Gawande, T. Ioerger, J. Sacchettini, S. M. Fortune and J. L. Flynn, Sterilization of granulomas is common in active and latent tuberculosis despite within-host variability in bacterial killing,, Nature medicine, 20 (2014), 75. doi: 10.1038/nm.3412. Google Scholar
[26]	P. L. Lin, M. Rodgers, L. Smith, M. Bigbee, A. Myers, C. Bigbee, I. Chiosea, S. V. Capuano, C. Fuhrman, E. Klein and J. L. Flynn, Quantitative comparison of active and latent tuberculosis in the cynomolgus macaque model,, Infection and immunity, 77 (2009), 4631. doi: 10.1128/IAI.00592-09. Google Scholar
[27]	J. J. Linderman, T. Riggs, M. Pande, M. Miller, S. Marino and D. E. Kirschner, Characterizing the dynamics of CD4+ T cell priming within a lymph node,, Journal of immunology (Baltimore, 184* (2010), 2873. doi: 10.4049/jimmunol.0903117. Google Scholar*
[28]	G. Magombedze, W. Garira and E. Mwenje, Modelling the human immune response mechanisms to mycobacterium tuberculosis infection in the lungs,, Mathematical biosciences and engineering : MBE, 3 (2006), 661. doi: 10.3934/mbe.2006.3.661. Google Scholar
[29]	G. Magombedze and N. Mulder, A mathematical representation of the development of Mycobacterium tuberculosis active, latent and dormant stages,, Journal of theoretical biology, 292 (2012), 44. doi: 10.1016/j.jtbi.2011.09.025. Google Scholar
[30]	S. Marino, M. El-Kebir and D. Kirschner, A hybrid multi-compartment model of granuloma formation and T cell priming in tuberculosis,, Journal of theoretical biology, 280 (2011), 50. doi: 10.1016/j.jtbi.2011.03.022. Google Scholar
[31]	S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, Journal of theoretical biology, 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011. Google Scholar
[32]	S. Marino and D. E. Kirschner, The human immune response to Mycobacterium tuberculosis in lung and lymph node,, Journal of theoretical biology, 227 (2004), 463. doi: 10.1016/j.jtbi.2003.11.023. Google Scholar
[33]	S. Marino, J. J. Linderman and D. E. Kirschner, A multifaceted approach to modeling the immune response in tuberculosis,, Wiley interdisciplinary reviews. Systems biology and medicine, 3 (2011), 479. doi: 10.1002/wsbm.131. Google Scholar
[34]	F. A. Milner, M. Iannelli and Z. Feng, A Two-Strain Tuberculosis Model with Age of Infection,, SIAM Journal on Applied Mathematics, 62 (2002), 1634. doi: 10.1137/S003613990038205X. Google Scholar
[35]	B. M. Murphy, B. H. Singer, S. Anderson and D. Kirschner, Comparing epidemic tuberculosis in demographically distinct heterogeneous populations,, Mathematical Biosciences, 180 (2002), 161. doi: 10.1016/S0025-5564(02)00133-5. Google Scholar
[36]	B. M. Murphy, B. H. Singer and D. Kirschner, On treatment of tuberculosis in heterogeneous populations,, Journal of Theoretical Biology, 223 (2003), 391. doi: 10.1016/S0022-5193(03)00038-9. Google Scholar
[37]	A. O'Garra, P. S. Redford, F. W. McNab, C. I. Bloom, R. J. Wilkinson and M. P. R. Berry, The immune response in tuberculosis,, Annual review of immunology, 31 (2013), 475. doi: 10.1146/annurev-immunol-032712-095939. Google Scholar
[38]	W. H. Organization, Global Tuberculosis Report 2013,, 2013., (). Google Scholar
[39]	R. Pabst, J. Westermann and H. J. Rothkotter, Immunoarchitecture of regenerated splenic and lymph node transplants,, Int Rev Cytol, 128 (1991), 215. doi: 10.1016/S0074-7696(08)60500-8. Google Scholar
[40]	T. H. Petersen, E. A. Calle, L. Zhao, E. J. Lee, L. Gui, M. B. Raredon, K. Gavrilov, T. Yi, Z. W. Zhuang, C. Breuer, E. Herzog and L. E. Niklason, Tissue-engineered lungs for in vivo implantation,, Science, 329 (2010), 538. doi: 10.1126/science.1189345. Google Scholar
[41]	L. Ramakrishnan, Revisiting the role of the granuloma in tuberculosis,, Nature reviews. Immunology, 12 (2012), 352. doi: 10.1038/nri3211. Google Scholar
[42]	J. Rengarajan, B. R. Bloom and E. J. Rubin, Genome-wide requirements for Mycobacterium tuberculosis adaptation and survival in macrophages,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 8327. doi: 10.1073/pnas.0503272102. Google Scholar
[43]	J. L. Segovia-Juarez, S. Ganguli and D. Kirschner, Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model,, Journal of theoretical biology, 231 (2004), 357. doi: 10.1016/j.jtbi.2004.06.031. Google Scholar
[44]	B. H. Singer and D. E. Kirschner, Influence of backward bifurcation on interpretation of r(0) in a model of epidemic tuberculosis with reinfection,, Mathematical biosciences and engineering: MBE, 1 (2004), 81. doi: 10.3934/mbe.2004.1.81. Google Scholar
[45]	L. E. Via, D. M. Weiner, D. Schimel, P. L. Lin, E. Dayao, S. L. Tankersley, Y. Cai, M. T. Coleman, J. Tomko, P. Paripati, M. Orandle, R. J. Kastenmayer, M. Tartakovsky, A. Rosenthal, D. Portevin, S. Y. Eum, S. Lahouar, S. Gagneux, D. B. Young, J. L. Flynn and C. E. Barry, Differential virulence and disease progression following Mycobacterium tuberculosis complex infection of the common marmoset (Callithrix jacchus),, Infection and immunity, 81 (2013), 2909. doi: 10.1128/IAI.00632-13. Google Scholar
[46]	J. E. Wigginton and D. Kirschner, A Model to Predict Cell-Mediated Immune Regulatory Mechanisms During Human Infection with Mycobacterium tuberculosis,, The Journal of Immunology, 166 (2001), 1951. doi: 10.4049/jimmunol.166.3.1951. Google Scholar
[47]	P. Ye and D. E. Kirschner, Reevaluation of T Cell Receptor Excision Circles as a Measure of Human Recent Thymic Emigrants,, The Journal of Immunology, 168 (2002), 4968. doi: 10.4049/jimmunol.168.10.4968. Google Scholar
[48]	D. Young, J. Stark and D. Kirschner, Systems biology of persistent infection: Tuberculosis as a case study,, Nature reviews. Microbiology, 6 (2008), 520. doi: 10.1038/nrmicro1919. Google Scholar

[1]	Adam Sullivan, Folashade Agusto, Sharon Bewick, Chunlei Su, Suzanne Lenhart, Xiaopeng Zhao. A mathematical model for within-host Toxoplasma gondii invasion dynamics. Mathematical Biosciences & Engineering, 2012, 9 (3) : 647-662. doi: 10.3934/mbe.2012.9.647
[2]	Cameron J. Browne, Sergei S. Pilyugin. Global analysis of age-structured within-host virus model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 1999-2017. doi: 10.3934/dcdsb.2013.18.1999
[3]	Surabhi Pandey, Ezio Venturino. A TB model: Is disease eradication possible in India?. Mathematical Biosciences & Engineering, 2018, 15 (1) : 233-254. doi: 10.3934/mbe.2018010
[4]	Yilong Li, Shigui Ruan, Dongmei Xiao. The Within-Host dynamics of malaria infection with immune response. Mathematical Biosciences & Engineering, 2011, 8 (4) : 999-1018. doi: 10.3934/mbe.2011.8.999
[5]	Andrei Korobeinikov, Conor Dempsey. A continuous phenotype space model of RNA virus evolution within a host. Mathematical Biosciences & Engineering, 2014, 11 (4) : 919-927. doi: 10.3934/mbe.2014.11.919
[6]	Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 633-659. doi: 10.3934/mbe.2007.4.633
[7]	C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381-400. doi: 10.3934/mbe.2015008
[8]	Min Zhu, Xiaofei Guo, Zhigui Lin. The risk index for an SIR epidemic model and spatial spreading of the infectious disease. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1565-1583. doi: 10.3934/mbe.2017081
[9]	W. E. Fitzgibbon, J. J. Morgan. Analysis of a reaction diffusion model for a reservoir supported spread of infectious disease. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-21. doi: 10.3934/dcdsb.2019137
[10]	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
[11]	Xia Wang, Yuming Chen. An age-structured vector-borne disease model with horizontal transmission in the host. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1099-1116. doi: 10.3934/mbe.2018049
[12]	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
[13]	Tao Feng, Zhipeng Qiu. Global analysis of a stochastic TB model with vaccination and treatment. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2923-2939. doi: 10.3934/dcdsb.2018292
[14]	Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479
[15]	Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707
[16]	Cristiana J. Silva, Delfim F. M. Torres. A TB-HIV/AIDS coinfection model and optimal control treatment. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4639-4663. doi: 10.3934/dcds.2015.35.4639
[17]	Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri. A two-strain TB model with multiple latent stages. Mathematical Biosciences & Engineering, 2016, 13 (4) : 741-785. doi: 10.3934/mbe.2016017
[18]	Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq, Ebraheem O. Alzahrani. A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 937-956. doi: 10.3934/dcdss.2020055
[19]	Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model. Mathematical Biosciences & Engineering, 2005, 2 (4) : 743-751. doi: 10.3934/mbe.2005.2.743
[20]	Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915

2018 Impact Factor: 1.313

American Institute of Mathematical Sciences