Citation: Mengshi Shu, Rui Fu, Wendi Wang. A bacteriophage model based on CRISPR/Cas immune system in a chemostat[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1361-1377. doi: 10.3934/mbe.2017070
[1] | [ L. J. Allen,S. W. Vidurupola, Impact of variability in stochastic models of bacteria-phage dynamics applicable to phage therapy, Stochastic Analysis and Applications, 32 (2014): 427-449. |
[2] | [ I. Aviram,A. Rabinovitch, Bactria and lytic phage coexistence in a chemostat with periodic nutrient supply, Bulletin of Mathematical Biology, 76 (2014): 225-244. |
[3] | [ E. Beretta,Y. Kuang, Modeling and analysis of a marine bacteriophage infection, Mathematical Biosciences, 149 (1998): 57-76. |
[4] | [ E. Beretta,Y. Kuang, Modeling and analysis of a marine bacteriophage infection with latency period, Nonlinear Analysis: Real World Applications, 2 (2001): 35-74. |
[5] | [ B. J. Bohannan,R. E. Lenski, Linking genetic change to community evolution: Insights from studies of bacteria and bacteriophage, Ecology Letters, 3 (2000): 362-377. |
[6] | [ S. J. Brouns,M. M. Jore,M. Lundgren, Small CRISPR RNAs guide antiviral defense in prokaryotes, Science, 321 (2008): 960-964. |
[7] | [ A. Buckling,M. Brockhurst, Bacteria-virus coevolution, Evolutionary Systems Biology, 751 (2012): 347-370. |
[8] | [ J. J. Bull, C. S. Vegge and M. Schmerer, Phenotypic resistance and the dynamics of bacterial escape from phage control PloS One, 9 (2014), e94690. |
[9] | [ B. J. Cairns, A. R. Timms and V. Jansen, Quantitative models of vitro bacteriophage-host dynamics and their application to phage therapy PLoS Pathog, 5 (2009), e1000253. |
[10] | [ A. Calsina,J. J. Rivaud, A size structured model for bacteria-phages interaction, Nonlinear Analysis: Real World Applications, 15 (2014): 100-117. |
[11] | [ A. Campbell, Conditions for existence of bacteriophages, Evolution, 15 (1961): 153-165. |
[12] | [ C. L. Carrillo,R. J. Atterbury,A. El-Shibiny, Bacteriophage therapy to reduce Campylobacter jejuni colonization of broiler chickens, Applied and Environmental Microbiology, 71 (2005): 6554-6563. |
[13] | [ J. J. Dennehy, What can phages tell us about host-pathogen coevolution? International Journal of Evolutionary Biology, 2012 (2012), Article ID 396165, 12 pages. |
[14] | [ H. Deveau,J. E. Garneau,S. Moineau, CRISPR/Cas system and its role in phage-bacteria interactions, Annual Review of Microbiology, 64 (2010): 475-493. |
[15] | [ A. Dhooge,W. Govaerts,Y. A. Kuznetsov, MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans Math Software, 29 (2003): 141-164. |
[16] | [ P. van den Driessche,J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosciences, 180 (2002): 29-48. |
[17] | [ D. H. Duckworth, Who discovered bacteriophage?, Bacteriological Reviews, 40 (1976): 793-802. |
[18] | [ P. C. Fineran,E. Charpentier, Memory of viral infections by CRISPR-Cas adaptive immune systems: Acquisition of new information, Virology, 434 (2012): 202-209. |
[19] | [ J. E. Garneau,M. Dupuis, The CRISPR/Cas bacterial immune system cleaves bacteriophage and plasmid DNA, Nature, 468 (2010): 67-71. |
[20] | [ P. Gómez,A. Buckling, Bacteria-phage antagonistic coevolution in soil, Science, 332 (2011): 106-109. |
[21] | [ S. A. Gourley,Y. Kuang, A delay reaction-diffusion model of the spread of bacteriophage infection, SIAM Journal of Applied Mathematics, 65 (2004): 550-566. |
[22] | [ J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences, Springer-Verlag, New York, 1993. |
[23] | [ Z. Han,H. L. Smith, Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat, Mathematical Biosciences and Engineering, 9 (2012): 737-765. |
[24] | [ S. B. Hsu,S. Hubbell,P. Waltman, A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms, Applied Mathematics, 32 (1977): 366-383. |
[25] | [ S. B. Hsu, Limiting behavior for competing species, SIAM Journal on Applied Mathematics, 34 (1978): 760-763. |
[26] | [ P. Horvath,R. Barrangou, CRISPR/Cas the immune system of bacteria and archaea, Science, 327 (2010): 167-170. |
[27] | [ J. Iranzo,A. E. Lobkovsky,Y. I. Wolf, Evolutionary dynamics of the prokaryotic adaptive immunity system CRISPR-Cas in an explicit ecological context, Journal of Bacteriology, 195 (2013): 3834-3844. |
[28] | [ B. R. Levin,F. M. Stewart,L. Chao, Resource-limited growth, competition, and predation: A model, and experimental studies with bacteria and bacteriophage, American Naturalist, 111 (1977): 3-24. |
[29] | [ B. R. Levin, Nasty viruses, costly plasmids, population dynamics, and the conditions for establishing and maintaining CRISPR-mediated adaptive immunity in bacteria PLoS Genet, 6 (2010), e1001171. |
[30] | [ B. R. Levin, S. Moineau and M. Bushman, The population and evolutionary dynamics of phage and bacteria with CRISPR-mediated immunity PLoS Genet, 9 (2013), e1003312. |
[31] | [ T. Li, Analysis of bacterial immune system-A review, Acta Microbiologica Ssinica, 51 (2011): 1297-1303. |
[32] | [ M. Lin,H. F. Huo,Y. N. Li, A competitive model in a chemostat with nutrient recycling and antibiotic treatment, Nonlinear Analysis: Real World Applications, 13 (2012): 2540-2555. |
[33] | [ Y. Ma,H. Chang, A review on immune system of the bacteria and its self versus non-self discrimination, Chinese Veterinary Science, 42 (2012): 657-660. |
[34] | [ L. A. Marraffini,E. J. Sontheimer, Self versus non-self discrimination during CRISPR RNA-directed immunity, Nature, 463 (2010): 568-571. |
[35] | [ S. Matsuzaki,M. Rashel,J. Uchiyama, Bacteriophage therapy: a revitalized therapy against bacterial infectious diseases, Journal of Infection and Chemotherapy, 11 (2005): 211-219. |
[36] | [ K. Northcott,M. Imran, Competition in the presence of a virus in an aquatic system: an SIS model in the chemostat, Journal of Mathematical Biology, 64 (2012): 1043-1086. |
[37] | [ L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, 7. Springer-Verlag, New York, 1993. |
[38] | [ L. M. Proctor,J. A. Fuhrman, Viral mortality of marine bacteria and cyanobacteria, Nature, 343 (1990): 60-62. |
[39] | [ J. Reeks,J. H. Naismith,M. F. White, CRISPR interference: A structural perspective, Biochemical Journal, 453 (2013): 155-166. |
[40] | [ G. Robledo,F. Grognard,J. L. Gouzé, Global stability for a model of competition in the chemostat with microbial inputs, Nonlinear Analysis: Real World Applications, 13 (2012): 582-598. |
[41] | [ K. D. Seed,D. W. Lazinski, A bacteriophage encodes its own CRISPR/Cas adaptive response to evade host innate immunity, Nature, 494 (2013): 489-491. |
[42] | [ H. L. Smith,H. R. Thieme, Persistence of bacteria and phages in a chemostat, Journal of Mathematical Biology, 64 (2012): 951-979. |
[43] | [ H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, Journal of Mathematical Biology, 30 (1992): 755-763. |
[44] | [ H. R. Thieme, Persistence under relaxed point-dissipativity with application to an endemic model, SIAM J. Math. Anal., 24 (1993): 407-435. |
[45] | [ R. A. Usmani, Applied Linear Algebra, Marcel Dekker, New York, 1987. |
[46] | [ W. Wang,X. Zhao, An epidemic model in a patchy environment, Mathematical Biosciences, 190 (2004): 97-112. |
[47] | [ R. J. Weld,C. Butts,J. A. Heinemann, Models of phage growth and their applicability to phage therapy, Journal of Theoretical Biology, 227 (2004): 1-11. |
[48] | [ X. Zhao, Dynamical Systems in Population Biology, 2$^{nd}$ edition, Springer-Verlag, London, 2003. |