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Journal of Mathematical Biology

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
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
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
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
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
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
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
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
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
Nicolas P Rebuli, N G Bean, J V Ross
Deterministic epidemic models are attractive due to their compact nature, allowing substantial complexity with computational efficiency. This partly explains their dominance in epidemic modelling. However, the small numbers of infectious individuals at early and late stages of an epidemic, in combination with the stochastic nature of transmission and recovery events, are critically important to understanding disease dynamics. This motivates the use of a stochastic model, with continuous-time Markov chains being a popular choice...
December 24, 2016: Journal of Mathematical Biology
Benjamin Armbruster, Ekkehard Beck
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field approximation of the underlying stochastic SIR process on contact networks, only few rigorous approaches exist and these use complex semigroup and martingale techniques to prove that the expected fraction of the susceptible and infected nodes of the stochastic SIR process on a complete graph converges as the number of nodes increases to the solution of the mean-field ODE model...
December 21, 2016: Journal of Mathematical Biology
Bryce Morsky, Ross Cressman, C T Bauch
Tags are conspicuous attributes of organisms that affect the behaviour of other organisms toward the holder, and have previously been used to explore group formation and altruism. Homophilic imitation, a form of tag-based selection, occurs when organisms imitate those with similar tags. Here we further explore the use of tag-based selection by developing homophilic replicator equations to model homophilic imitation dynamics. We assume that replicators have both tags (sometimes called traits) and strategies...
December 19, 2016: Journal of Mathematical Biology
Olivier Gallinato, Masahito Ohta, Clair Poignard, Takashi Suzuki
In this paper, a free boundary problem for cell protrusion formation is studied theoretically and numerically. The cell membrane is precisely described thanks to a level set function, whose motion is due to specific signalling pathways. The aim is to model the chemical interactions between the cell and its environment, in the process of invadopodia or pseudopodia formation. The model consists of Laplace equation with Dirichlet condition inside the cell coupled to Laplace equation with Neumann condition in the outer domain...
December 5, 2016: Journal of Mathematical Biology
Xiao He, Sining Zheng
In any reaction-diffusion system of predator-prey models, the population densities of species are determined by the interactions between them, together with the influences from the spatial environments surrounding them. Generally, the prey species would die out when their birth rate is too low, the habitat size is too small, the predator grows too fast, or the predation pressure is too high. To save the endangered prey species, some human interference is useful, such as creating a protection zone where the prey could cross the boundary freely but the predator is prohibited from entering...
December 3, 2016: Journal of Mathematical Biology
Marc Hellmuth, Peter F Stadler, Nicolas Wieseke
The concepts of orthology, paralogy, and xenology play a key role in molecular evolution. Orthology and paralogy distinguish whether a pair of genes originated by speciation or duplication. The corresponding binary relations on a set of genes form complementary cographs. Allowing more than two types of ancestral event types leads to symmetric symbolic ultrametrics. Horizontal gene transfer, which leads to xenologous gene pairs, however, is inherent asymmetric since one offspring copy "jumps" into another genome, while the other continues to be inherited vertically...
November 30, 2016: Journal of Mathematical Biology
Rebecca Neukirch, Anton Bovier
In this paper we analyse the genetic evolution of a diploid hermaphroditic population, which is modelled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet et al. (J Math Biol 67(3):569-607, 2013) have shown that, on the mutation time-scale, the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness. We prove that, under the assumption that a dominant allele is also the fittest one, the recessive allele survives for a time of order at least [Formula: see text], where K is the size of the population and [Formula: see text]...
November 28, 2016: Journal of Mathematical Biology
Lei Wang, Xiao-Song Yang
A famous food-chain model proposed by Hastings and Powell is numerically restudied. The existence and uniform hyperbolicity of chaotic invariant sets are demonstrated by means of the topological horseshoe theory and the Conley-Moser conditions, indicating that, for a fixed cross section, the second return Poincaré map of the model possesses a closed uniformly hyperbolic chaotic invariant set, on which it is topologically conjugate to the 2-shift map.
November 19, 2016: Journal of Mathematical Biology
Jernej Rus
In 2013 a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in Gradišar et al. (Nat Chem Bio 9:362-366, 2013). It was since observed that a polyhedron P can be realized by interlocking pairs of polypeptide chains if its corresponding graph G(P) admits a strong trace. It was since also demonstrated that a similar strategy can also be expanded to self-assembly of designed DNA (Kočar, Nat commun 7:1-8, 2016). In this direction, in the present paper we characterize graphs which admit closed walk which traverses every edge exactly once in each direction and for every vertex v, there is no subset N of its neighbors, with [Formula: see text], such that every time the walk enters v from N, it also exits to a vertex in N...
November 16, 2016: Journal of Mathematical Biology
Nicolas Bacaër
An explicit formula is found for the rate of extinction of subcritical linear birth-and-death processes in a random environment. The formula is illustrated by numerical computations of the eigenvalue with largest real part of the truncated matrix for the master equation. The generating function of the corresponding eigenvector satisfies a Fuchsian system of singular differential equations. A particular attention is set on the case of two environments, which leads to Riemann's differential equation.
November 16, 2016: Journal of Mathematical Biology
Thomas J X Li, Christian M Reidys
In this paper we study properties of topological RNA structures, i.e. RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having genus zero. We derive a new bivariate generating function whose singular expansion allows us to analyze the distributions of arcs, stacks, hairpin- , interior- and multi-loops. We then extend this analysis to H-type pseudoknots, kissing hairpins as well as 3-knots and compute their respective expectation values...
November 16, 2016: Journal of Mathematical Biology
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