Figure 5.1.
NIN simulation with $n=3$ and parameters: $r_1=6,r_2=5,r_3=3,e_1=3,e_2=2,e_3=1,n_1=n_2=n_3=1,a_1=1,a_2=3,a_3=0.5$
-
Previous Article
Global existence and regularity results for strongly coupled nonregular parabolic systems via iterative methods
- DCDS-B Home
- This Issue
-
Next Article
Malaria incidence and anopheles mosquito density in irrigated and adjacent non-irrigated villages of Niono in Mali
May
2017, 22(3): 859-875.
doi: 10.3934/dcdsb.2017043
Persistence in phage-bacteria communities with nested and one-to-one infection networks
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA |
We show that a bacteria and bacteriophage system with either a perfectly nested or a one-to-one infection network is permanent, a.k.a uniformly persistent, provided that bacteria that are superior competitors for nutrient devote the least to defence against infection and the virus that are the most efficient at infectinghost have the smallest host range.By ensuring that the density-dependent reduction in bacterial growth rates are independent of bacterial strain, we are able to arrive at the permanence conclusion sought by Jover et al [
Keywords:
Persistence,
permanence,
community assembly,
phage-bacteria infection network,
nested infection network,
Lyapunov function.
Mathematics Subject Classification:
Primary: 92D40; Secondary: 37B2.
Citation:
Dan A. Korytowski, Hal L. Smith. Persistence in phage-bacteria communities with nested and one-to-one infection networks. Discrete and Continuous Dynamical Systems - B,
2017, 22
(3)
: 859-875.
doi: 10.3934/dcdsb.2017043
![]()
References:
| [1] |
J. Hale,
Ordinary Differential Equations Robert E. Krieger Publishing Co. , Malabar, Fl, 1980. |
| [2] |
J. Hofbauer and K. Sigmund,
Evolutionary Games Cambridge Univ. Press, 1998. |
| [3] |
L. F. Jover, M. H. Cortez and J. S. Weitz,
Mechanisms of multi-strain coexistence in host-phage systems with nested infection networks, Journal of Theoretical Biology, 332 (2013), 65-77.
doi: 10.1016/j.jtbi.2013.04.011. |
| [4] |
D. Korytowski and H. L. Smith,
How nested and monogamous infection networks in host-phage communities come to be, Theoretical Ecology, 8 (2015), 111-120.
doi: 10.1007/s12080-014-0236-6. |
| [5] |
D. Korytowski and H. L. Smith,
Persistence in Phage-Bacteria Communities with Nested and One-to-One Infection Networks arXiv: 1505.03827 [q-bio. PE]. |
| [6] |
H. Smith and H. Thieme,
Dynamical Systems and Population Persistence GSM 118, Amer. Math. Soc. , Providence R. I. , 2011. |
| [7] |
H. Smith and P. Waltman,
The Theory of the Chemostat Cambridge Univ. Press, 1995. |
| [8] |
H. R. Thieme,
Persistence under relaxed point-dissipativity (with applications to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
| [9] |
T. F. Thingstad,
Elements of a theory for the mechanisms controlling abundance, diversity, and biogeochemical role of lytic bacterial viruses in aquatic systems, Limnol. Oceanogr., 45 (2000), 1320-1328.
doi: 10.4319/lo.2000.45.6.1320. |
show all references
References:
| [1] |
J. Hale,
Ordinary Differential Equations Robert E. Krieger Publishing Co. , Malabar, Fl, 1980. |
| [2] |
J. Hofbauer and K. Sigmund,
Evolutionary Games Cambridge Univ. Press, 1998. |
| [3] |
L. F. Jover, M. H. Cortez and J. S. Weitz,
Mechanisms of multi-strain coexistence in host-phage systems with nested infection networks, Journal of Theoretical Biology, 332 (2013), 65-77.
doi: 10.1016/j.jtbi.2013.04.011. |
| [4] |
D. Korytowski and H. L. Smith,
How nested and monogamous infection networks in host-phage communities come to be, Theoretical Ecology, 8 (2015), 111-120.
doi: 10.1007/s12080-014-0236-6. |
| [5] |
D. Korytowski and H. L. Smith,
Persistence in Phage-Bacteria Communities with Nested and One-to-One Infection Networks arXiv: 1505.03827 [q-bio. PE]. |
| [6] |
H. Smith and H. Thieme,
Dynamical Systems and Population Persistence GSM 118, Amer. Math. Soc. , Providence R. I. , 2011. |
| [7] |
H. Smith and P. Waltman,
The Theory of the Chemostat Cambridge Univ. Press, 1995. |
| [8] |
H. R. Thieme,
Persistence under relaxed point-dissipativity (with applications to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
| [9] |
T. F. Thingstad,
Elements of a theory for the mechanisms controlling abundance, diversity, and biogeochemical role of lytic bacterial viruses in aquatic systems, Limnol. Oceanogr., 45 (2000), 1320-1328.
doi: 10.4319/lo.2000.45.6.1320. |
| [1] |
Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of phage infection of bacteria in a petri dish. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 471-496. doi: 10.3934/dcdsb.2016.21.471 |
| [2] |
Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria. Networks and Heterogeneous Media, 2013, 8 (1) : 327-342. doi: 10.3934/nhm.2013.8.327 |
| [3] |
Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155 |
| [4] |
Danyun He, Qian Wang, Wing-Cheong Lo. Mathematical analysis of macrophage-bacteria interaction in tuberculosis infection. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3387-3413. doi: 10.3934/dcdsb.2018239 |
| [5] |
Ariel D. Weinberger, Alan S. Perelson. Persistence and emergence of X4 virus in HIV infection. Mathematical Biosciences & Engineering, 2011, 8 (2) : 605-626. doi: 10.3934/mbe.2011.8.605 |
| [6] |
Curtis L. Wesley, Linda J. S. Allen, Michel Langlais. Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 195-211. doi: 10.3934/mbe.2010.7.195 |
| [7] |
Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure and Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002 |
| [8] |
Yu Yang, Yueping Dong, Yasuhiro Takeuchi. Global dynamics of a latent HIV infection model with general incidence function and multiple delays. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 783-800. doi: 10.3934/dcdsb.2018207 |
| [9] |
Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences & Engineering, 2015, 12 (4) : 859-877. doi: 10.3934/mbe.2015.12.859 |
| [10] |
D. Warren, K Najarian. Learning theory applied to Sigmoid network classification of protein biological function using primary protein structure. Conference Publications, 2003, 2003 (Special) : 898-904. doi: 10.3934/proc.2003.2003.898 |
| [11] |
Hongming Yang, C. Y. Chung, Xiaojiao Tong, Pingping Bing. Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function. Journal of Industrial and Management Optimization, 2008, 4 (3) : 617-630. doi: 10.3934/jimo.2008.4.617 |
| [12] |
Yuantian Xia, Juxiang Zhou, Tianwei Xu, Wei Gao. An improved deep convolutional neural network model with kernel loss function in image classification. Mathematical Foundations of Computing, 2020, 3 (1) : 51-64. doi: 10.3934/mfc.2020005 |
| [13] |
Jinliang Wang, Xiu Dong. Analysis of an HIV infection model incorporating latency age and infection age. Mathematical Biosciences & Engineering, 2018, 15 (3) : 569-594. doi: 10.3934/mbe.2018026 |
| [14] |
Jaouad Danane. Optimal control of viral infection model with saturated infection rate. Numerical Algebra, Control and Optimization, 2021, 11 (3) : 363-375. doi: 10.3934/naco.2020031 |
| [15] |
Miguel Atencia, Esther García-Garaluz, Gonzalo Joya. The ratio of hidden HIV infection in Cuba. Mathematical Biosciences & Engineering, 2013, 10 (4) : 959-977. doi: 10.3934/mbe.2013.10.959 |
| [16] |
Nicola Bellomo, Youshan Tao. Stabilization in a chemotaxis model for virus infection. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 105-117. doi: 10.3934/dcdss.2020006 |
| [17] |
Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267 |
| [18] |
Jiangtao Mo, Liqun Qi, Zengxin Wei. A network simplex algorithm for simple manufacturing network model. Journal of Industrial and Management Optimization, 2005, 1 (2) : 251-273. doi: 10.3934/jimo.2005.1.251 |
| [19] |
Paul L. Salceanu, H. L. Smith. Lyapunov exponents and persistence in discrete dynamical systems. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 187-203. doi: 10.3934/dcdsb.2009.12.187 |
| [20] |
Frédéric Grognard, Frédéric Mazenc, Alain Rapaport. Polytopic Lyapunov functions for persistence analysis of competing species. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 73-93. doi: 10.3934/dcdsb.2007.8.73 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]