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- All Subjects: Bacteriophages
- All Subjects: Infection
- Creators: Smith, Hal
Description
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
Description
Using a simple $SI$ infection model, I uncover the
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more.
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more.
ContributorsFarrell, Alexander E. (Author) / Thieme, Horst R (Thesis advisor) / Smith, Hal (Committee member) / Kuang, Yang (Committee member) / Tang, Wenbo (Committee member) / Collins, James (Committee member) / Arizona State University (Publisher)
Created2017