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Journal of Mathematical Biology

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https://www.readbyqxmd.com/read/28224236/wavenumber-selection-in-coupled-transport-equations
#1
Arnd Scheel, Angela Stevens
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.
February 21, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28220205/global-properties-of-nested-network-model-with-application-to-multi-epitope-hiv-ctl-dynamics
#2
Cameron Browne
Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model...
February 20, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28213682/mathematical-modelling-of-cytokines-mmps-and-fibronectin-fragments-in-osteoarthritic-cartilage
#3
Michelle Baker, Bindi S Brook, Markus R Owen
Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes...
February 17, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28213681/quantifying-functionals-of-age-distributions-in-the-wild-by-solving-an-operator-equation
#4
Hao Ji, Hans-Georg Müller, Nikos T Papadopoulos, James R Carey
Residual demography is a recent concept that has proved to be a useful tool to gain insights about the age distributions of wild populations, especially insects. We develop an operator equation that permits the derivation of functionals of the age distribution in wild populations, such as mean age, within the framework of residual demography. Our method combines information from an observed captive cohort, which consists of subjects that are sampled from the wild with unknown ages and then raised in the laboratory until death, and from a reference cohort that consists of subjects raised in the laboratory since birth of the same population...
February 17, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28197714/convergence-to-travelling-waves-in-fisher-s-population-genetics-model-with-a-non-lipschitzian-reaction-term
#5
Pavel Drábek, Peter Takáč
We consider a one-dimensional population genetics model for the advance of an advantageous gene. The model is described by the semilinear Fisher equation with unbalanced bistable non-Lipschitzian nonlinearity f(u). The "nonsmoothness" of f allows for the appearance of travelling waves with a new, more realistic profile. We study existence, uniqueness, and long-time asymptotic behavior of the solutions u(x, t), [Formula: see text]. We prove also the existence and uniqueness (up to a spatial shift) of a travelling wave U...
February 14, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28150175/macroscopic-coherent-structures-in-a-stochastic-neural-network-from-interface-dynamics-to-coarse-grained-bifurcation-analysis
#6
Daniele Avitable, Kyle C A Wedgwood
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory...
February 1, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28138760/oscillating-systems-with-cointegrated-phase-processes
#7
Jacob Østergaard, Anders Rahbek, Susanne Ditlevsen
We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system...
January 30, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28130571/gaussian-approximations-for-chemostat-models-in-finite-and-infinite-dimensions
#8
Bertrand Cloez, Coralie Fritsch
In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation. In this work, we are interested in the convergence of the fluctuation process. We consider this process in some Sobolev spaces and use central limit theorems on Hilbert space to prove its convergence in law to an infinite-dimensional Gaussian process...
January 27, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28130570/a-bayesian-estimation-approach-for-the-mortality-in-a-stage-structured-demographic-model
#9
E Lanzarone, S Pasquali, G Gilioli, E Marchesini
Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation...
January 27, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28124077/long-term-treatment-effects-in-chronic-myeloid-leukemia
#10
Apollos Besse, Thomas Lepoutre, Samuel Bernard
We propose and analyze a simplified version of a partial differential equation (PDE) model for chronic myeloid leukemia (CML) derived from an agent-based model proposed by Roeder et al. This model describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of the drug Imatinib on these cells. We first simplify the PDE model by noting that most of the dynamics occurs in a subspace of the original 2D state space. Then we determine the dominant eigenvalue of the corresponding linearized system that controls the long-term behavior of solutions...
January 25, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28124076/a-model-of-cell-surface-receptor-aggregation
#11
D Iron, J Rumsey
In this paper we construct and analyze a model of cell receptor aggregation. Experiments have shown that receptors in an aggregated state have greatly reduced mobility. We model the effects of this reduced mobility with a density dependent diffusion and study the impact of density dependent diffusion on aggregate formation in a one-dimensional domain. Critical values of receptor diffusivity and receptor activation are found and compared with numerical simulations. We find that the role of density dependant diffusion is quite limited in the formation of aggregate structures...
January 25, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28101632/a-discrete-time-model-for-population-persistence-in-habitats-with-time-varying-sizes
#12
Ying Zhou, William F Fagan
In this paper, we use periodic and stochastic integrodifference models to study the persistence of a single-species population in a habitat with temporally varying sizes. We extend a persistence metric for integral operators on bounded domains to that of integral operators on unbounded domains. Using this metric in the periodic model, we present new perspectives of the critical habitat size problem in the case of dynamically changing habitat sizes. Specifically, we extend the concept of critical habitat size to that of lower minimal limit size in a period-2 scenario, and prove the existence of the lower minimal limit size...
January 18, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28097419/modelling-wolbachia-infection-in-a-sex-structured-mosquito-population-carrying-west-nile-virus
#13
József Z Farkas, Stephen A Gourley, Rongsong Liu, Abdul-Aziz Yakubu
Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals...
January 17, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28097418/heterogeneous-network-epidemics-real-time-growth-variance-and-extinction-of-infection
#14
Frank Ball, Thomas House
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process...
January 17, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28097417/bistability-induced-by-generalist-natural-enemies-can-reverse-pest-invasions
#15
Sten Madec, Jérôme Casas, Guy Barles, Christelle Suppo
Analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. We aimed to formalize the conditions in which spatial biological control can be achieved by generalists, through an analytical approach based on reaction-diffusion equations. Using comparison principles, we obtain sufficient conditions for control and for invasion, based on scalar bistable partial differential equations...
January 17, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28062892/a-bifurcation-theorem-for-evolutionary-matrix-models-with-multiple-traits
#16
J M Cushing, F Martins, A A Pinto, Amy Veprauskas
One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1...
January 6, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28040877/existence-bifurcation-and-geometric-evolution-of-quasi-bilayers-in-the-multicomponent-functionalized-cahn-hilliard-equation
#17
Keith Promislow, Qiliang Wu
Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We present the multicomponent functionalized Cahn-Hilliard (mFCH) free energy as a model which allows competition between bilayers with distinct composition and between bilayers and higher codimensional structures, such as co-dimension two filaments and co-dimension three micelles...
December 31, 2016: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28040876/host-coexistence-in-a-model-for-two-host-one-parasitoid-interactions
#18
Valentina Clamer, Andrea Pugliese, Davide Liessi, Dimitri Breda
Building from a continuous-time host-parasitoid model introduced by Murdoch et al. (Am Nat 129:263-282, 1987), we study the dynamics of a 2 host-parasitoid model assuming, for the sake of simplicity, that larval stages have a fixed duration. If each host is subjected to density-dependent mortality in its larval stage, we obtain explicit conditions for the existence of an equilibrium where the two host species coexist with the parasitoid. However, if host demography is density-independent, equilibrium coexistence is impossible...
December 31, 2016: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28039494/demyelination-patterns-in-a-mathematical-model-of-multiple-sclerosis
#19
M C Lombardo, R Barresi, E Bilotta, F Gargano, P Pantano, M Sammartino
In this paper we derive a reaction-diffusion-chemotaxis model for the dynamics of multiple sclerosis. We focus on the early inflammatory phase of the disease characterized by activated local microglia, with the recruitment of a systemically activated immune response, and by oligodendrocyte apoptosis. The model consists of three equations describing the evolution of macrophages, cytokine and apoptotic oligodendrocytes. The main driving mechanism is the chemotactic motion of macrophages in response to a chemical gradient provided by the cytokines...
December 30, 2016: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/28035423/a-reaction-diffusion-model-for-radiation-induced-bystander-effects
#20
Oluwole Olobatuyi, Gerda de Vries, Thomas Hillen
We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR)...
December 29, 2016: Journal of Mathematical Biology
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