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Bulletin of Mathematical Biology

Vladimir Kozlov, Sergey Vakulenko, Uno Wennergren
This paper considers a model of foodwebs taking into account species extinction and invasion. We show that system stability depends not only on usual parameters (mortality rates, self-limitation coefficients, and resource abundances), but also on an additional parameter ("biodiversity potential"). The main result is as follows. For foodwebs with random parameters, we obtain an estimate of probability that the foodweb exposed to invasion survives. This estimate involves different system parameters, size and its topological properties...
October 19, 2016: Bulletin of Mathematical Biology
Mariya Ptashnyk, Brian Seguin
The microscopic structure and anisotropy of plant cell walls greatly influence the mechanical properties, morphogenesis, and growth of plant cells and tissues. The microscopic structure and properties of cell walls are determined by the orientation and mechanical properties of the cellulose microfibrils and the mechanical properties of the cell wall matrix. Viewing the shape of a plant cell as a square prism with the axis aligning with the primary direction of expansion and growth, the orientation of the microfibrils within the side walls, i...
October 19, 2016: Bulletin of Mathematical Biology
Rachelle N Binny, Alex James, Michael J Plank
Collective cell migration and proliferation are integral to tissue repair, embryonic development, the immune response and cancer. Central to collective cell migration and proliferation are interactions among neighbouring cells, such as volume exclusion, contact inhibition and adhesion. These individual-level processes can have important effects on population-level outcomes, such as growth rate and equilibrium density. We develop an individual-based model of cell migration and proliferation that includes these interactions...
October 19, 2016: Bulletin of Mathematical Biology
Martin Vyska, Christopher Gilligan
We analyse the dynamical behaviour of a simple, widely used model that integrates epidemiological dynamics with disease control and economic constraint on the control resources. We consider both the deterministic model and its stochastic counterpart. Despite its simplicity, the model exhibits mathematically rich dynamics, including multiple stable fixed points and stable limit cycles arising from global bifurcations. We show that the existence of the limit cycles in the deterministic model has important consequences in modelling the range of potential effects the control can have...
October 18, 2016: Bulletin of Mathematical Biology
David Baca-Carrasco, Jorge X Velasco-Hernández
Since the first major outbreak reported on the island Yap in 2007, the Zika virus spread has alerted the scientific community worldwide. Zika is an arbovirus transmitted by Aedes mosquitoes; particularly in Central and South America, the main vector is the same mosquito that transmits dengue and chikungunya, Aedes aegypti. Seeking to understand the dynamics of spread of the Zika, in this paper, three mathematical models are presented, in which vector transmission of the virus, sexual contact transmission and migration are considered...
October 14, 2016: Bulletin of Mathematical Biology
Jimmy Garnier, Mark A Lewis
Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure...
October 14, 2016: Bulletin of Mathematical Biology
Xianghong Zhang, Sanyi Tang, Robert A Cheke, Huaiping Zhu
Dengue fever has rapidly become the world's most common vector-borne viral disease. Use of endosymbiotic Wolbachia is an innovative technology to prevent vector mosquitoes from reproducing and so break the cycle of dengue transmission. However, strategies such as population eradication and replacement will only succeed if appropriate augmentations with Wolbachia-infected mosquitoes that take account of a variety of factors are carried out. Here, we describe the spread of Wolbachia in mosquito populations using an impulsive differential system with four state variables, incorporating the effects of cytoplasmic incompatibility and the augmentation of Wolbachia-infected mosquitoes with different sex ratios...
October 12, 2016: Bulletin of Mathematical Biology
Raluca Eftimie, Joseph J Gillard, Doreen A Cantrell
The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales...
October 6, 2016: Bulletin of Mathematical Biology
Jorge A Falcón-Lezama, Ruth A Martínez-Vega, Pablo A Kuri-Morales, José Ramos-Castañeda, Ben Adams
Dengue is a growing public health problem in tropical and subtropical cities. It is transmitted by mosquitoes, and the main strategy for epidemic prevention and control is insecticide fumigation. Effective management is, however, proving elusive. People's day-to-day movement about the city is believed to be an important factor in the epidemiological dynamics. We use a simple model to examine the fundamental roles of broad demographic and spatial structures in epidemic initiation, growth and control. We show that the key factors are local dilution, characterised by the vector-host ratio, and spatial connectivity, characterised by the extent of habitually variable movement patterns...
October 4, 2016: Bulletin of Mathematical Biology
Yuqin Zhao, Daniel T Wood, Hristo V Kojouharov, Yang Kuang, Dobromir T Dimitrov
Mechanistic mathematical models are increasingly used to evaluate the effectiveness of different interventions for HIV prevention and to inform public health decisions. By focusing exclusively on the impact of the interventions, the importance of the demographic processes in these studies is often underestimated. In this paper, we use simple deterministic models to assess the effectiveness of pre-exposure prophylaxis in reducing the HIV transmission and to explore the influence of the recruitment mechanisms on the epidemic and effectiveness projections...
October 4, 2016: Bulletin of Mathematical Biology
Brian P Yurk
The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection-diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters...
September 27, 2016: Bulletin of Mathematical Biology
Rosemary O'Connell, Yoichiro Mori
Cortical spreading depression (SD) is a spreading disruption in brain ionic homeostasis during which neurons experience complete and prolonged depolarizations. SD is generally believed to be the physiological substrate of migraine aura and is associated with many other brain pathologies. Here, we perform simulations with a model of SD treating brain tissue as a triphasic continuum of neurons, glia and the extracellular space. A thermodynamically consistent incorporation of the major biophysical effects, including ionic electrodiffusion and osmotic water flow, allows for the computation of important physiological variables including the extracellular voltage (DC) shift...
October 2016: Bulletin of Mathematical Biology
Alexander B Beams, Damon J A Toth, Karim Khader, Frederick R Adler
Antibiotic overuse has promoted the spread of antibiotic resistance. To compound the issue, treating individuals dually infected with antibiotic-resistant and antibiotic-vulnerable strains can make their infections completely resistant through competitive release. We formulate mathematical models of transmission dynamics accounting for dual infections and extensions accounting for lag times between infection and treatment or between cure and ending treatment. Analysis using the Next-Generation Matrix reveals how competition within hosts and the costs of resistance determine whether vulnerable and resistant strains persist, coexist, or drive each other to extinction...
September 2016: Bulletin of Mathematical Biology
Arianna Bianchi, Kevin J Painter, Jonathan A Sherratt
Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: (1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case and (2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network...
September 2016: Bulletin of Mathematical Biology
Philippe Gambette, Leo van Iersel, Steven Kelk, Fabio Pardi, Celine Scornavacca
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental questions that arise in this context is whether the evolution of a gene with one copy in all species can be explained by a given network. In mathematical terms, this is often translated in the following way: is a given phylogenetic tree contained in a given phylogenetic network? Recently this tree containment problem has been widely investigated from a computational perspective, but most studies have only focused on the topology of the phylogenies, ignoring a piece of information that, in the case of phylogenetic trees, is routinely inferred by evolutionary analyses: branch lengths...
September 2016: Bulletin of Mathematical Biology
Necibe Tuncer, Hayriye Gulbudak, Vincent L Cannataro, Maia Martcheva
In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006-2007 Kenya outbreak...
September 2016: Bulletin of Mathematical Biology
Andrés Pomi
Every cognitive activity has a neural representation in the brain. When humans deal with abstract mathematical structures, for instance finite groups, certain patterns of activity are occurring in the brain that constitute their neural representation. A formal neurocognitive theory must account for all the activities developed by our brain and provide a possible neural representation for them. Associative memories are neural network models that have a good chance of achieving a universal representation of cognitive phenomena...
September 2016: Bulletin of Mathematical Biology
Juliette Bouhours, Mark A Lewis
Climate change impacts population distributions, forcing some species to migrate poleward if they are to survive and keep up with the suitable habitat that is shifting with the temperature isoclines. Previous studies have analysed whether populations have the capacity to keep up with shifting temperature isoclines, and have mathematically determined the combination of growth and dispersal that is needed to achieve this. However, the rate of isocline movement can be highly variable, with much uncertainty associated with yearly shifts...
September 2016: Bulletin of Mathematical Biology
Kalle Parvinen, Åke Brännström
Species that compete for access to or use of sites, such as parasitic mites attaching to honey bees or apple maggots laying eggs in fruits, can potentially increase their fitness by carefully selecting sites at which they face little or no competition. Here, we systematically investigate the evolution of site-selection strategies among animals competing for discrete sites. By developing and analyzing a mechanistic and population-dynamical model of site selection in which searching individuals encounter sites sequentially and can choose to accept or continue to search based on how many conspecifics are already there, we give a complete characterization of the different site-selection strategies that can evolve...
August 2016: Bulletin of Mathematical Biology
Judith Pérez-Velázquez, Meltem Gölgeli, Rodolfo García-Contreras
Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation...
August 2016: Bulletin of Mathematical Biology
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