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Journal of Mathematical Biology

Brian P Yurk
Animal movement behaviors vary spatially in response to environmental heterogeneity. An important problem in spatial ecology is to determine how large-scale population growth and dispersal patterns emerge within highly variable landscapes. We apply the method of homogenization to study the large-scale behavior of a reaction-diffusion-advection model of population growth and dispersal. Our model includes small-scale variation in the directed and random components of movement and growth rates, as well as large-scale drift...
October 14, 2017: Journal of Mathematical Biology
Elisa Sovrano
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary migration, that is independent of genotype, in absence of mutation and random drift. The focus is on a conjecture, that was raised up in literature of population genetics, about the possible uniqueness of polymorphic equilibria, which are known as clines, under particular circumstances...
October 11, 2017: Journal of Mathematical Biology
David B Damiano, Melissa R McGuirl
Single-photon emission computed tomography images of murine tumors are interpreted as the values of functions on a three-dimensional domain. Motivated by Morse theory, the local maxima of the tumor image functions are analyzed. This analysis captures tumor heterogeneity that cannot be identified with standard measures. Utilizing decreasing sequences of uptake values to filter the images, a modified form of the standard persistence diagrams for 0-dimensional persistent homology as well as novel childhood diagrams are constructed...
October 5, 2017: Journal of Mathematical Biology
Xiunan Wang, Xiao-Qiang Zhao
Insecticide-treated bed nets (ITNs) are among the most important and effective intervention measures against malaria. In order to investigate the impact of bed net use on disease control, we formulate a periodic vector-bias malaria model incorporating the juvenile stage of mosquitoes and the use of ITNs. We derive the vector reproduction ratio [Formula: see text] and the basic reproduction ratio [Formula: see text]. We show that the global dynamics of the model is completely determined by these two reproduction ratios...
September 30, 2017: Journal of Mathematical Biology
Matthew D Johnston, David F Anderson, Gheorghe Craciun, Robert Brijder
We study chemical reaction networks with discrete state spaces and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event. The conditions we derive involve creating a modified chemical reaction network called a domination-expanded reaction network and then checking properties of this network. Unlike previous results, our analysis allows algorithmic implementation via systems of equalities and inequalities and suggests sequences of reactions which may lead to extinction events...
September 26, 2017: Journal of Mathematical Biology
Grégoire Nadin, Martin Strugarek, Nicolas Vauchelet
We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a cytoplasmic effect similar to the Allee effect (e.g. Wolbachia in Aedes mosquitoes): the invading dynamics we model is bistable. We aim at quantifying the propagules (what does it take for an invasion to start?) and the invasive power (how far can an invading front go, and what can stop it?)...
September 22, 2017: Journal of Mathematical Biology
Christoforos Hadjichrysanthou, Mark Broom, Jan Rychtář
The behaviour of populations consisting of animals that interact with each other for their survival and reproduction is usually investigated assuming homogeneity amongst the animals. However, real populations are non-homogeneous. We focus on an established model of kleptoparasitism and investigate whether and how much population heterogeneities can affect the behaviour of kleptoparasitic populations. We consider a situation where animals can either discover food items by themselves or attempt to steal the food already discovered by other animals through aggressive interactions...
September 18, 2017: Journal of Mathematical Biology
Camille Coron, Manon Costa, Hélène Leman, Charline Smadi
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity...
September 15, 2017: Journal of Mathematical Biology
Dejun Fan, Pengmiao Hao, Dongyan Sun
In this paper, strongly connected and non-strongly connected multi-group viral models with time delays and general incidence functions are considered. Employing the Lyapunov functional method and a graph-theoretic approach, we show that the global dynamics of the strongly connected system are determined by the basic reproduction number under some reasonable conditions for incidence functions. In addition, we find a more complex and more interesting result for multi-group viral models with non-strongly connected networks because of the basic reproduction numbers corresponding to each strongly connected component...
September 9, 2017: Journal of Mathematical Biology
Zhichun Yang, Chuangxia Huang, Xingfu Zou
In this paper, a very general model of impulsive delay differential equations in n-patches is rigorously derived to describe the impulsive control of population of a single species over n-patches. The model allows an age structure consisting of immatures and matures, and also considers mobility and culling of both matures and immatures. Conditions are obtained for extinction and persistence of the model system under three special scenarios: (1) without impulsive control; (2) with impulsive culling of the immatures only; and (3) with impulsive culling of the matures only, respectively...
September 9, 2017: Journal of Mathematical Biology
Benedetta Pellacci, Gianmaria Verzini
We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. Our main result concerns the optimization of such threshold with respect to the fractional order [Formula: see text], the case [Formula: see text] corresponding to the standard Neumann Laplacian: when the habitat is not too fragmented, the principal positive eigenvalue can not have local minima for [Formula: see text]...
September 9, 2017: Journal of Mathematical Biology
Yu-Jhe Huang, Jonq Juang, Yu-Hao Liang, Hsin-Yu Wang
In this work, we consider an epidemic model in a two-layer network in which the dynamics of susceptible-infected-susceptible process in the physical layer coexists with that of a cyclic process of unaware-aware-unaware in the virtual layer. For such multiplex network, we shall define the basic reproduction number [Formula: see text] in the virtual layer, which is similar to the basic reproduction number [Formula: see text] defined in the physical layer. We show analytically that if [Formula: see text] and [Formula: see text], then the disease and information free equilibrium is globally stable and if [Formula: see text] and [Formula: see text], then the disease free and information saturated equilibrium is globally stable for all initial conditions except at the origin...
September 7, 2017: Journal of Mathematical Biology
B B Cael, Courtenay Strong
Phytoplankton exhibit pronounced morphological diversity, impacting a range of processes. Because these impacts are challenging to quantify, however, phytoplankton are often approximated as spheres, and when effects of non-sphericity are studied it is usually experimentally or via geometrical approximations. New methods for quantifying phytoplankton size and shape generally, so all phytoplankton are analyzable by the same procedure, can complement advances in microscopic imagery and automated classification to study the influence of shape in phytoplankton...
September 1, 2017: Journal of Mathematical Biology
Pierre-Alexandre Bliman, M Soledad Aronna, Flávio C Coelho, Moacyr A H B da Silva
The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human...
August 30, 2017: Journal of Mathematical Biology
Pengfei Song, Yanni Xiao
We proposed a delay differential model, associated with the response time for individuals to the current infection, to examine the media impact on the transmission dynamics of infectious diseases. We investigated the global bifurcation by considering the delay as a bifurcation parameter and examined the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical studies to identify ranges of parameters for coexisting multiple periodic solutions are guided by the bifurcation analysis and the Matlab package DDE-BIFTOOL developed by Engelborghs et al...
August 29, 2017: Journal of Mathematical Biology
Andrew Francis, Katharina T Huber, Vincent Moulton, Taoyang Wu
Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which every vertex has degree 1 or 3 and whose leaf-set is a fixed set X of taxa. This space, denoted [Formula: see text], is defined in terms of two operations on networks-the nearest neighbor interchange and triangle operations-which can be used to transform any network with leaf set X into any other network with that leaf set...
August 23, 2017: Journal of Mathematical Biology
Peter Clote, Amir H Bayegan
RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm...
August 5, 2017: Journal of Mathematical Biology
Jimin Zhang, Junping Shi, Xiaoyuan Chang
A coupled system of ordinary differential equations and partial differential equations is proposed to describe the interaction of pelagic algae, benthic algae and one essential nutrient in an oligotrophic shallow aquatic ecosystem with ample supply of light. The existence and uniqueness of non-negative steady states are completely determined for all possible parameter range, and these results characterize sharp threshold conditions for the regime shift from extinction to coexistence of pelagic and benthic algae...
August 1, 2017: Journal of Mathematical Biology
Edna Chilenje Manda, Faraimunashe Chirove
Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous systems of non linear ordinary differential equations by directly linking the within host dynamics capturing the interactions between Langerhans cells, CD4[Formula: see text] T-cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental HIV/AIDS model. The model captures the biological theories of the cells that take part in HIV transmission...
July 31, 2017: Journal of Mathematical Biology
Alex Gavryushkin, Chris Whidden, Frederick A Matsen
A time-tree is a rooted phylogenetic tree such that all internal nodes are equipped with absolute divergence dates and all leaf nodes are equipped with sampling dates. Such time-trees have become a central object of study in phylogenetics but little is known about the parameter space of such objects. Here we introduce and study a hierarchy of discrete approximations of the space of time-trees from the graph-theoretic and algorithmic point of view. One of the basic and widely used phylogenetic graphs, the [Formula: see text] graph, is the roughest approximation and bottom level of our hierarchy...
July 29, 2017: Journal of Mathematical Biology
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