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Journal of Mathematical Biology

Soledad Berríos, Julio López Fenner, Aude Maignan
We show that an inhomogeneous Bernoulli site percolation process running upon a fullerene's dual [Formula: see text] can be used for representing bivalents attached to the nuclear envelope in mouse Mus M. Domesticus 2n = 40 meiotic spermatocytes during pachytene. It is shown that the induced clustering generated by overlapping percolation domains correctly reproduces the probability distribution observed in the experiments (data) after fine tuning the parameters.
June 19, 2018: Journal of Mathematical Biology
Peter Czuppon, Arne Traulsen
We study the fixation probability of a mutant type when introduced into a resident population. We implement a stochastic competitive Lotka-Volterra model with two types and intra- and interspecific competition. The model further allows for stochastically varying population sizes. The competition coefficients are interpreted in terms of inverse payoffs emerging from an evolutionary game. Since our study focuses on the impact of the competition values, we assume the same net growth rate for both types. In this general framework, we derive a formula for the fixation probability [Formula: see text] of the mutant type under weak selection...
June 7, 2018: Journal of Mathematical Biology
Vladimir Shchur, Rasmus Nielsen
The number of individuals in a random sample with close relatives in the sample is a quantity of interest when designing Genome Wide Association Studies and other cohort based genetic, and non-genetic, studies. In this paper, we develop expressions for the distribution and expectation of the number of p-th cousins in a sample from a population of size N under two diploid Wright-Fisher models. We also develop simple asymptotic expressions for large values of N. For example, the expected proportion of individuals with at least one p-th cousin in a sample of K individuals, for a diploid dioecious Wright-Fisher model, is approximately [Formula: see text]...
June 6, 2018: Journal of Mathematical Biology
Peter Czuppon, Peter Pfaffelhuber
Gene expression is influenced by extrinsic noise (involving a fluctuating environment of cellular processes) and intrinsic noise (referring to fluctuations within a cell under constant environment). We study the standard model of gene expression including an (in-)active gene, mRNA and protein. Gene expression is regulated in the sense that the protein feeds back and either represses (negative feedback) or enhances (positive feedback) its production at the stage of transcription. While it is well-known that negative (positive) feedback reduces (increases) intrinsic noise, we give a precise result on the resulting fluctuations in protein numbers...
May 24, 2018: Journal of Mathematical Biology
Alex P Farrell, James P Collins, Amy L Greer, Horst R Thieme
In simple SI epidemic and endemic models, three classes of incidence functions are identified for their potential to be associated with host extinction: weakly upper density-dependent incidences are never associated with host extinction. Power incidences that depend on the number of susceptibles and infectives by powers strictly between 0 and 1 are associated with initial-constellation-dependent host extinction for all parameter values. Homogeneous incidences, of which frequency-dependent incidence is a very particular case, and power incidences are associated with global host extinction for certain parameter constellations and with host survival for others...
May 21, 2018: Journal of Mathematical Biology
O Diekmann, W F de Graaf, M E E Kretzschmar, P F M Teunis
The aim is to describe the distribution of immune status (as captured by antibody level) on the basis of a within-host submodel for continuous waning and occasional boosting. Inspired by Feller's fundamental work and the more recent delay equation formulation of models for the dynamics of physiologically structured populations, we derive, for given force of infection, a linear renewal equation. The solution is obtained by generation expansion, with the generation number corresponding to the number of times the individual became infected...
May 15, 2018: Journal of Mathematical Biology
Jinxian Li, Jing Wang, Zhen Jin
This paper investigates the effects of the community structure of a network on the spread of an epidemic. To this end, we first establish a susceptible-infected-recovered (SIR) model in a two-community network with an arbitrary joint degree distribution. The network is formulated as a probability generating function. We also obtain the sufficient conditions for disease outbreak and extinction, which involve the first-order and second-order moments of the degree distribution. As an example, we then study the effect of community structure on epidemic spread in a complex network with a Poisson joint degree distribution...
May 11, 2018: Journal of Mathematical Biology
Andrea Pugliese, Fabio Milner
A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]...
May 9, 2018: Journal of Mathematical Biology
Lulu Wang, Zhen Jin, Hao Wang
To study the effects of an environmental toxin, such as fine particles in hazy weather, on the spread of infectious diseases, we derive a toxin-dependent dynamic model that incorporates the birth rate with the toxin-dependent switching mode, the mortality rate, and infection rate with the toxin-dependent saturation effect. We analyze the model by showing the positive invariance, existence and stability of equilibria, and bifurcations. Numerical simulation is adopted to verify the mathematical results and exhibit transcritical and Hopf bifurcations...
May 9, 2018: Journal of Mathematical Biology
Anton Bovier, Loren Coquille, Rebecca Neukirch
We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. Neukirch and Bovier (J Math Biol 75:145-198, 2017) proved that sexual reproduction allows unfit alleles to survive in individuals with mixed genotype much longer than they would in populations reproducing asexually. In the present paper we prove that this indeed opens the possibility that individuals with a pure genotype can reinvade in the population after the appearance of further mutations...
May 8, 2018: Journal of Mathematical Biology
Jane S MacDonald, Frithjof Lutscher
Moving-habitat models aim to characterize conditions for population persistence under climate-change scenarios. Existing models do not incorporate individual-level movement behavior near habitat edges. These small-scale details have recently been shown to be crucially important for large-scale predictions of population spread and persistence in patchy landscapes. In this work, we extend previous moving-habitat models by including individual movement behavior. Our analysis shows that populations might be able to persist under faster climate change than previous models predicted...
May 8, 2018: Journal of Mathematical Biology
Alexis Erich S Almocera, Van Kinh Nguyen, Esteban A Hernandez-Vargas
Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively...
May 8, 2018: Journal of Mathematical Biology
E M Rutter, H T Banks, K B Flores
Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction-diffusion equation, where the parameters describing diffusion (D) and proliferation ([Formula: see text]) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and [Formula: see text] using the Prohorov metric, for a variety of probability distribution functions...
May 8, 2018: Journal of Mathematical Biology
Caitlin Lienkaemper, Lisa Lamberti, James Drain, Niko Beerenwinkel, Alex Gavryushkin
We present an efficient computational approach for detecting genetic interactions from fitness comparison data together with a geometric interpretation using polyhedral cones associated to partial orderings. Genetic interactions are defined by linear forms with integer coefficients in the fitness variables assigned to genotypes. These forms generalize several popular approaches to study interactions, including Fourier-Walsh coefficients, interaction coordinates, and circuits. We assume that fitness measurements come with high uncertainty or are even unavailable, as is the case for many empirical studies, and derive interactions only from comparisons of genotypes with respect to their fitness, i...
May 7, 2018: Journal of Mathematical Biology
Andrey Garnaev, Wade Trappe
In medical treatments, a fundamental dilemma often arises: on the one hand, an increase in a drug's dose could lead to a stronger, therapeutic treatment response, but on the other hand this could also lead to increased toxicity risks. In this paper, we propose to solve this dilemma using a Nash bargaining approach. To do so, we reformulate the tradeoff problem in an equivalent form as a dilemma between a drug's beneficial response and the drug's safety, where the dilemma then becomes a two-objective problem with safety and response as the objectives...
May 7, 2018: Journal of Mathematical Biology
Thierry Colin, Guillaume Dechristé, Jérôme Fehrenbach, Ludivine Guillaume, Valérie Lobjois, Clair Poignard
Biological tissues accumulate mechanical stress during their growth. The mere measurement of the stored stress is not an easy task. We address here the spherical case and our experiments consist in performing an incision of a spherical microtissue (tumor spheroid) grown in vitro. On the theoretical part we derive a compatibility condition on the stored stress in spherical symmetry, which imposes a relation between the circumferential and radial stored stress. The numerical implementation uses the hyperelastic model of Ciarlet and Geymonat...
May 7, 2018: Journal of Mathematical Biology
C M Saad-Roy, Junling Ma, P van den Driessche
Zika virus is a human disease that may lead to neurological disorders in affected individuals, and may be transmitted vectorially (by mosquitoes) or sexually. A mathematical model of Zika virus transmission is formulated, taking into account mosquitoes, sexually active males and females, inactive individuals, and considering both vector transmission and sexual transmission from infectious males to susceptible females. Basic reproduction numbers are computed, and disease control strategies are evaluated. The effect of the incidence function used to model sexual transmission from infectious males to susceptible females is investigated...
April 25, 2018: Journal of Mathematical Biology
Jason McClelland, David Koslicki
Both the weighted and unweighted UniFrac distances have been very successfully employed to assess if two communities differ, but do not give any information about how two communities differ. We take advantage of recent observations that the UniFrac metric is equivalent to the so-called earth mover's distance (also known as the Kantorovich-Rubinstein metric) to develop an algorithm that not only computes the UniFrac distance in linear time and space, but also simultaneously finds which operational taxonomic units are responsible for the observed differences between samples...
April 25, 2018: Journal of Mathematical Biology
Steffen E Eikenberry, Abba B Gumel
Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics...
April 24, 2018: Journal of Mathematical Biology
Oluwole Olobatuyi, Gerda de Vries, Thomas Hillen
In experimental studies, it has been found that certain cell lines are more sensitive to low-dose radiation than would be expected from the classical Linear-Quadratic model (LQ model). In fact, it is frequently observed that cells incur more damage at low dose (say 0.3 Gy) than at higher dose (say 1 Gy). This effect has been termed hyper-radiosensitivity (HRS). The effect depends on the type of cells and on their phase in the cell cycle when radiation is applied. Experiments have shown that the G2-checkpoint plays an important role in the HRS effects...
April 20, 2018: Journal of Mathematical Biology
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