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Journal of Mathematical Biology

Mohammed Helal, Angélique Igel-Egalon, Abdelkader Lakmeche, Pauline Mazzocco, Angélique Perrillat-Mercerot, Laurent Pujo-Menjouet, Human Rezaei, Léon M Tine
Alzheimer's disease (AD) is a neuro-degenerative disease affecting more than 46 million people worldwide in 2015. AD is in part caused by the accumulation of A[Formula: see text] peptides inside the brain. These can aggregate to form insoluble oligomers or fibrils. Oligomers have the capacity to interact with neurons via membrane receptors such as prion proteins ([Formula: see text]). This interaction leads [Formula: see text] to be misfolded in oligomeric prion proteins ([Formula: see text]), transmitting a death signal to neurons...
August 11, 2018: Journal of Mathematical Biology
Niclas Kruff, Christian Lax, Volkmar Liebscher, Sebastian Walcher
The Rosenzweig-MacArthur system is a particular case of the Gause model, which is widely used to describe predator-prey systems. In the classical derivation, the interaction terms in the differential equation are essentially derived from considering handling time vs. search time, and moreover there exist derivations in the literature which are based on quasi-steady state assumptions. In the present paper we introduce a derivation of this model from first principles and singular perturbation reductions. We first establish a simple stochastic mass action model which leads to a three-dimensional ordinary differential equation, and systematically determine all possible singular perturbation reductions (in the sense of Tikhonov and Fenichel) to two-dimensional systems...
August 9, 2018: Journal of Mathematical Biology
Alexandru Hening, Dang H Nguyen, Sergiu C Ungureanu, Tak Kwong Wong
We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. To our knowledge, ergodic optimal control has not been used before to study harvesting strategies. However, it is a natural framework because the optimal harvesting strategy will never be such that the population is harvested to extinction-instead the harvested population converges to a unique invariant probability measure...
August 4, 2018: Journal of Mathematical Biology
Manh Hong Duong, Hoang Minh Tran, The Anh Han
The analysis of equilibrium points is of great importance in evolutionary game theory with numerous practical ramifications in ecology, population genetics, social sciences, economics and computer science. In contrast to previous analytical approaches which primarily focus on computing the expected number of internal equilibria, in this paper we study the distribution of the number of internal equilibria in a multi-player two-strategy random evolutionary game. We derive for the first time a closed formula for the probability that the game has a certain number of internal equilibria, for both normal and uniform distributions of the game payoff entries...
August 1, 2018: Journal of Mathematical Biology
Hisashi Inaba, Ryohei Saito, Nicolas Bacaër
In this paper, we formulate an age-structured epidemic model for the demographic transition in which we assume that the cultural norms leading to lower fertility are transmitted amongst individuals in the same way as infectious diseases. First, we formulate the basic model as an abstract homogeneous Cauchy problem on a Banach space to prove the existence, uniqueness, and well-posedness of solutions. Next based on the normalization arguments, we investigate the existence of nontrivial exponential solutions and then study the linearized stability at the exponential solutions using the idea of asynchronous exponential growth...
July 31, 2018: Journal of Mathematical Biology
Yao Li, Logan Chariker, Lai-Sang Young
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with "nonlinearities" in the time evolution of membrane potentials...
July 30, 2018: Journal of Mathematical Biology
Jie Ma, James P Keener
In pharmacokinetics, exact solutions to one-compartment models with nonlinear elimination kinetics cannot be found analytically, if dosages are assumed to be administered repetitively through extravascular routes (Tang and Xiao in J Pharmacokinet Pharmacodyn 34(6):807-827, 2007). Hence, for the corresponding impulsed dynamical system, alternative methods need to be developed to find approximate solutions. The primary purpose of this paper is to use the method of matched asymptotic expansions (Holmes Introduction to Perturbation Methods, vol 20...
July 28, 2018: Journal of Mathematical Biology
Zhuoqun Wang, Rick Durrett
This work is inspired by a 2013 paper from Arne Traulsen's lab at the Max Plank Institute for Evolutionary Biology (Wu et al. in PLoS Comput Biol 9:e1003381, 2013). They studied evolutionary games when the mutation rate is so small that each mutation goes to fixation before the next one occurs. It has been shown that for [Formula: see text] games the ranking of the strategies does not change as strength of selection is increased (Wu et al. in Phys Rev 82:046106, 2010). The point of the 2013 paper is that when there are three or more strategies the ordering can change as selection is increased...
July 28, 2018: Journal of Mathematical Biology
Judith R Miller
The Kirkpatrick-Barton model, well known to invasion biologists, is a pair of reaction-diffusion equations for the joint evolution of population density and the mean of a quantitative trait as functions of space and time. Here we prove the existence of two classes of coherent structures, namely "bounded trait mean differential" traveling waves and localized stationary solutions, using geometric singular perturbation theory. We also give numerical examples of these (when they appear to be stable) and of "unbounded trait mean differential" solutions...
July 27, 2018: Journal of Mathematical Biology
Anica Hoppe, Sonja Türpitz, Mike Steel
A recent paper (Manceau and Lambert in bioRxiv, 2017. ) developed a novel approach for describing two well-defined notions of 'species' based on a phylogenetic tree and a phenotypic partition. In this paper, we explore some further combinatorial properties of this approach and describe an extension that allows an arbitrary number of phenotypic partitions to be combined with a phylogenetic tree for these two species notions.
July 24, 2018: Journal of Mathematical Biology
François Bergeron, Christophe Reutenauer
Exploiting Markoff's theory for rational approximations of real numbers, we explicitly link how hard it is to approximate a given number to an idealized notion of growth capacity for plants which we express as a modular invariant function depending on this number. Assuming that our growth capacity is biologically relevant, this allows us to explain in a satisfying mathematical way why the golden ratio occurs in nature.
July 23, 2018: Journal of Mathematical Biology
A Iggidr, M O Souza
We consider a class of epidemiological models that includes most well-known dynamics for directly transmitted diseases, and some reduced models for indirectly transmitted diseases. We then propose a simple observer that can be applied to models in this class. The error analysis of this observer leads to a non-autonomous error equation, and a new bound for fundamental matrices is also presented. We analyse and implement this observer in two examples: the classical SIR model, and a reduced Bailey-Dietz model for vector-borne diseases...
July 21, 2018: Journal of Mathematical Biology
Simona Grusea, Willy Rodríguez, Didier Pinchon, Lounès Chikhi, Simon Boitard, Olivier Mazet
The increasing amount of genomic data currently available is expanding the horizons of population genetics inference. A wide range of methods have been published allowing to detect and date major changes in population size during the history of species. At the same time, there has been an increasing recognition that population structure can generate genetic data similar to those generated under models of population size change. Recently, Mazet et al. (Heredity 116(4):362-371, 2016) introduced the idea that, for any model of population structure, it is always possible to find a panmictic model with a particular function of population size-change having an identical distribution of [Formula: see text] (the time of the first coalescence for a sample of size two)...
July 20, 2018: Journal of Mathematical Biology
Xiaoming Zheng, Mohye Sweidan
The purpose of this paper is to develop a new coupled mathematical model of angiogenesis (new blood vessel growth) and tumor growth to study cancer development and anti-angiogenesis therapy. The angiogenesis part assumes the capillary to be a viscoelastic continuum whose stress depends on cell proliferation or death, and the tumor part is a Darcy's law model regarding the tumor mass as an incompressible fluid where the nutrient-dependent growth elicits volume change. For the coupled model, we provide both an inviscid analysis and a parameter sensitivity analysis of the angiogenesis model in response to a stationary hypoxic tumor, and a steady state analysis of the tumor growth in response to a fixed and long blood capillary...
July 17, 2018: Journal of Mathematical Biology
Helen Moore, Lewis Strauss, Urszula Ledzewicz
In this work, we demonstrate a mathematical technique for optimizing combination regimens with constraints. We apply the technique to a mathematical model for treatment of patients with chronic myeloid leukemia. The in-host model includes leukemic cell and immune system dynamics during treatment with tyrosine kinase inhibitors and immunomodulatory compounds. The model is minimal (semi-mechanistic) with just enough detail that all relevant therapeutic effects can be represented. The regimens are optimized to yield the highest possible reduction in disease burden, taking into account dosing constraints and side effect risks due to drug exposure...
July 10, 2018: Journal of Mathematical Biology
Michael Kopp, Elma Nassar, Etienne Pardoux
Continuous environmental change-such as slowly rising temperatures-may create permanent maladaptation of natural populations: Even if a population adapts evolutionarily, its mean phenotype will usually lag behind the phenotype favored in the current environment, and if the resulting phenotypic lag becomes too large, the population risks extinction. We analyze this scenario using a moving-optimum model, in which one or more quantitative traits are under stabilizing selection towards an optimal value that increases at a constant rate...
July 6, 2018: Journal of Mathematical Biology
J M Jaramillo, Junling Ma, P van den Driessche, Sanling Yuan
An important characteristic of influenza A is its ability to escape host immunity through antigenic drift. A novel influenza A strain that causes a pandemic confers full immunity to infected individuals. Yet when the pandemic strain drifts, these individuals will have decreased immunity to drifted strains in the following seasonal epidemics. We compute the required decrease in immunity so that a recurrence is possible. Models for influenza A must make assumptions on the contact structure on which the disease spreads...
July 4, 2018: Journal of Mathematical Biology
Odo Diekmann, Klaus Dietz, Thomas Hillen, Horst Thieme
Karl-Peter Hadeler is a first-generation pioneer in mathematical biology. His work inspired the contributions to this special issue. In this preface we give a brief biographical sketch of K.P. Hadelers scientific life and highlight his impact to the field.
July 2, 2018: Journal of Mathematical Biology
Lorenzo Contento, Danielle Hilhorst, Masayasu Mimura
Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among m ecological species for a limited resource necessary to their survival and growth. Notwithstanding their rather simple mathematical structure, such systems may display quite interesting behaviours. In particular, while for [Formula: see text] no coexistence of the two species is usually possible, if [Formula: see text] we may observe coexistence of all or a subset of the species, sensitively depending on the parameter values...
July 2, 2018: Journal of Mathematical Biology
Takuji Oba, Jun Kigami
Adaptive dynamics combines deterministic population dynamics of groups having different trait values and random process describing mutation and tries to predict the course of evolution of a species of interest. One of basic interests is to know which group survives, residents or mutants. By using invasion fitness as the primary tool, "invasion implies substitution" principle, IIS principle for short, has been established under the existence of a generating function in the sense of Brown and Vincent (Theor Popul Biol 31(1):140-166, 1987) and Vincent and Brown (Evolutionary game theory, natural selection, and darwinian dynamics...
July 2, 2018: Journal of Mathematical Biology
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