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Journal of Mathematical Biology

Frank Ball, Tom Britton, Ka Yin Leung, David Sirl
A Markovian Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size [Formula: see text], assuming that the degrees of individuals are bounded...
March 13, 2019: Journal of Mathematical Biology
Mark A Lewis, Zhisheng Shuai, P van den Driessche
A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identifies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied to the analysis of single and multiple control strategies in ecology and epidemiology, and this provides new biological insights.
March 11, 2019: Journal of Mathematical Biology
Matthew J Labrum, Richard Gomulkiewicz
Previous metapopulation models developed to examine consequences of habitat destruction and metapopulation Allee effects are biologically plausible for only small degrees of habitat destruction. For larger, realistic amounts of habitat destruction, those models fail to capture a metapopulation Allee effect. We here present a new model that allows biologically meaningful metapopulation Allee effects at all feasible levels of habitat destruction. When applied to metacommunities of competitive species that face habitat destruction, this new model shows that metapopulation Allee effects may drastically alter predictions about the fates of the competitors compared to when Allee effects are ignored...
March 8, 2019: Journal of Mathematical Biology
Bertram Düring, Carsten Gottschlich, Stephan Huckemann, Lisa Maria Kreusser, Carola-Bibiane Schönlieb
Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy...
March 4, 2019: Journal of Mathematical Biology
K Kaouri, P K Maini, P A Skourides, N Christodoulou, S J Chapman
Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism. We present a new analysis of experimental data that supports the existence of this coupling during apical constriction...
March 2, 2019: Journal of Mathematical Biology
Yijun Lou, Kaihui Liu, Daihai He, Daozhou Gao, Shigui Ruan
Diapause, a period of arrested development caused by adverse environmental conditions, serves as a key survival mechanism for insects and other invertebrate organisms in temperate and subtropical areas. In this paper, a novel modelling framework, motivated by mosquito species, is proposed to investigate the effects of diapause on seasonal population growth, where the diapause period is taken as an independent growth process, during which the population dynamics are completely different from that in the normal developmental and post-diapause periods...
March 1, 2019: Journal of Mathematical Biology
Jorge Duarte, Cristina Januário, Nuno Martins, Svitlana Rogovchenko, Yuriy Rogovchenko
Despite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the year incidence rates of a number of endemic infectious diseases may fluctuate dramatically. This influences the dynamics of mathematical models describing the spread of infection and often leads to chaotic oscillations. In this paper, we are concerned with a generalization of a classical Susceptible-Infected-Recovered epidemic model which accounts for seasonal effects...
February 26, 2019: Journal of Mathematical Biology
Jean-Christophe Poggiale, Clément Aldebert, Benjamin Girardot, Bob W Kooi
We study a predator-prey model with different characteristic time scales for the prey and predator populations, assuming that the predator dynamics is much slower than the prey one. Geometrical Singular Perturbation theory provides the mathematical framework for analyzing the dynamical properties of the model. This model exhibits a Hopf bifurcation and we prove that when this bifurcation occurs, a canard phenomenon arises. We provide an analytic expression to get an approximation of the bifurcation parameter value for which a maximal canard solution occurs...
February 20, 2019: Journal of Mathematical Biology
Yan Wang, Junping Shi, Jinfeng Wang
A reaction-diffusion-advection equation with strong Allee effect growth rate is proposed to model a single species stream population in a unidirectional flow. Here random undirected movement of individuals in the environment is described by passive diffusion, and an advective term is used to describe the directed movement in a river caused by the flow. Under biologically reasonable boundary conditions, the existence of multiple positive steady states is shown when both the diffusion coefficient and the advection rate are small, which lead to different asymptotic behavior for different initial conditions...
February 19, 2019: Journal of Mathematical Biology
Gabriel Maciel, Chris Cosner, Robert Stephen Cantrell, Frithjof Lutscher
Many types of organisms disperse through heterogeneous environments as part of their life histories. For various models of dispersal, including reaction-advection-diffusion models in continuously varying environments, it has been shown by pairwise invasibility analysis that dispersal strategies which generate an ideal free distribution are evolutionarily steady strategies (ESS, also known as evolutionarily stable strategies) and are neighborhood invader strategies (NIS). That is, populations using such strategies can both invade and resist invasion by populations using strategies that do not produce an ideal free distribution...
February 19, 2019: Journal of Mathematical Biology
Wonhyung Choi, Seunghyeon Baek, Inkyung Ahn
In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka-Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region...
February 18, 2019: Journal of Mathematical Biology
Damir Hasić, Eric Tannier
Gene tree/species tree reconciliation is a recent decisive progress in phylogenetic methods, accounting for the possible differences between gene histories and species histories. Reconciliation consists in explaining these differences by gene-scale events such as duplication, loss, transfer, which translates mathematically into a mapping between gene tree nodes and species tree nodes or branches. Gene conversion is a frequent and important evolutionary event, which results in the replacement of a gene by a copy of another from the same species and in the same gene tree...
February 15, 2019: Journal of Mathematical Biology
Lina Herbst, Heyang Li, Mike Steel
In phylogenetic studies, biologists often wish to estimate the ancestral discrete character state at an interior vertex v of an evolutionary tree T from the states that are observed at the leaves of the tree. A simple and fast estimation method-maximum parsimony-takes the ancestral state at v to be any state that minimises the number of state changes in T required to explain its evolution on T. In this paper, we investigate the reconstruction accuracy of this estimation method further, under a simple symmetric model of state change, and obtain a number of new results, both for 2-state characters, and r-state characters ([Formula: see text])...
February 13, 2019: Journal of Mathematical Biology
Michael T Meehan, Daniel G Cocks, Johannes Müller, Emma S McBryde
We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected removal rates are arbitrary functions of the infection age, [Formula: see text], and use the direct Lyapunov method to establish the global asymptotic stability of the equilibrium solutions. In particular, we show that the basic reproduction number, [Formula: see text], represents a sharp threshold parameter such that for [Formula: see text], the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when [Formula: see text], i...
February 9, 2019: Journal of Mathematical Biology
Klodeta Kura, Doran Khamis, Claire El Mouden, Michael B Bonsall
Vector-borne diseases are a major public health concern inflicting high levels of disease morbidity and mortality. Vector control is one of the principal methods available to manage infectious disease burden. One approach, releasing modified vectors (such as sterile or GM mosquitoes) Into the wild population has been suggested as an effective method of vector control. However, the effects of dispersal and the spatial distribution of disease vectors (such as mosquitoes) remain poorly studied. Here, we develop a novel mathematical framework using an integrodifference equation (discrete in time and continuous in space) approach to understand the impact of releasing sterile insects into the wild population in a spatially explicit environment...
February 7, 2019: Journal of Mathematical Biology
Mireille Bossy, Joaquín Fontbona, Héctor Olivero
In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic version of the Hodgkin-Huxley model, and that pairs of neurons interact through both electrical and chemical synapses, the global connectivity being of mean field type. When the leak conductance is strictly positive, we prove that if the initial voltages are uniformly bounded and the electrical interaction between neurons is strong enough, then, uniformly in the number of neurons, the whole system synchronizes exponentially fast as time goes to infinity, up to some error controlled by (and vanishing with) the channels noise level...
February 2, 2019: Journal of Mathematical Biology
Aili Wang, Yanni Xiao, Robert Smith
Releasing infectious pests could successfully control and eventually maintain the number of pests below a threshold level. To address this from a mathematical point of view, two non-smooth microbial pest-management models with threshold policy are proposed and investigated in the present paper. First, we establish an impulsive model with state-dependent control to describe the cultural control strategies, including releasing infectious pests and spraying chemical pesticide. We examine the existence and stability of an order-1 periodic solution, the existence of order-k periodic solutions and chaotic phenomena of this model by analyzing the properties of the Poincaré map...
January 31, 2019: Journal of Mathematical Biology
Maria Simonsen Speed, David Joseph Balding, Asger Hobolth
In population genetics, the Dirichlet (also called the Balding-Nichols) model has for 20 years been considered the key model to approximate the distribution of allele fractions within populations in a multi-allelic setting. It has often been noted that the Dirichlet assumption is approximate because positive correlations among alleles cannot be accommodated under the Dirichlet model. However, the validity of the Dirichlet distribution has never been systematically investigated in a general framework. This paper attempts to address this problem by providing a general overview of how allele fraction data under the most common multi-allelic mutational structures should be modeled...
January 28, 2019: Journal of Mathematical Biology
Gerold Alsmeyer, Kilian Raschel
In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means absorption at one of the axes. Despite connections with some classical probabilistic models (standard two-type Galton-Watson process, two-urn model), exact formulae for the probabilities of absorption seem to be difficult to come by and one must therefore resort to good approximations...
January 25, 2019: Journal of Mathematical Biology
Daniel C De Souza, Michael C Mackey
Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose grave problems for patients. Likewise, periodically administered chemotherapy has the unintended side effect of establishing periodic fluctuations in circulating white cells, red cell precursors and/or platelets. These fluctuations, either spontaneous or induced, often have serious consequences for the patient (e.g. neutropenia, anemia, or thrombocytopenia respectively) which exogenously administered cytokines can partially correct...
January 12, 2019: Journal of Mathematical Biology
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