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Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Initial community evenness has been shown to be a key factor in preserving the functional stability of an ecosystem, but has not been accounted for in previous modelling studies. We formulate a model that allows the initial evenness of the community to be varied in order to investigate the consequent impact on system diversity. We consider a community of four interacting bacterial species, and present a stochastic, spatial individual-based model simulating the ecosystem dynamics. Interactions take place on a two-dimensional lattice. The model incorporates three processes: reproduction, competition and mobility. In addition to variable initial evenness, multiple competition schemes are implemented, modelling various possible communities, which results in diverse coexistence and extinction scenarios. Simulations show that long-term system behaviour is strongly dependent on initial evenness and competition structure. The system is generally unstable; higher initial evenness has a small stabilizing effect on ecosystem dynamics by extending the time until the first extinction., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Oxygenic photoautotrophs are, paradoxically, subject to photoinhibition of their photosynthetic apparatus, in particular one of its major components, the Photosystem II (PSII). Photoinhibition is generalized across species, light conditions and habitats, imposing substantial metabolic costs that lower photosynthetic productivity and constrain the niches of photoautotrophy. As a process driven by light reaching PSII, light attenuation in optically thick samples influences both the actual extent, and the detection, of photoinhibition. Chlorophyll fluorescence is widely used to measure photoinhibition, but fluorescence-based parameters are affected by light attenuation of both downwelling incident radiation traversing the sample to reach PSII, and emitted fluorescence upwelling through the sample. We used modelling, experimental manipulation of within-sample light attenuation, and meta-analysis of published data, to show substantial, differential effects of light attenuation and depth-integration of emitted fluorescence upon measurements of photoinhibition. Numerical simulations and experimental manipulation of light attenuation indicated that PSII photoinactivation tracked using chlorophyll fluorescence can appear to be over three times lower than the inherent cellular susceptibility to photoinactivation, in optically-dense samples such as leaves or biofilms. The meta-analysis of published data showed that this general trend was unknowingly present in the literature, revealing an overall difference of more than five times between optically thick leaves and optically thin cell suspensions. Although fluorescence-based parameters may provide ecophysiologically relevant information for characterizing the sample as a whole, light attenuation and depth integration can vary between samples independently of their intrinsic physiology. They should be used with caution when aiming to quantify in absolute terms inherent photoinhibition-related parameters in optically thick samples., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 The Authors. Published by Elsevier Ltd.. All rights reserved.)

COVID-19 testing has become a standard approach for estimating prevalence which then assist in public health decision making to contain and mitigate the spread of the disease. The sampling designs used are often biased in that they do not reflect the true underlying populations. For instance, individuals with strong symptoms are more likely to be tested than those with no symptoms. This results in biased estimates of prevalence (too high). Typical post-sampling corrections are not always possible. Here we present a simple bias correction methodology derived and adapted from a correction for publication bias in meta analysis studies. The methodology is general enough to allow a wide variety of customization making it more useful in practice. Implementation is easily done using already collected information. Via a simulation and two real datasets, we show that the bias corrections can provide dramatic reductions in estimation error., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is typically noisy and non-quantitative. In addition, these models can have a high computational cost, limiting the number of feasible simulations, and therefore rendering most traditional parameter estimation methods unsuitable. In this paper, we present a pipeline that uses Gaussian process learning to estimate biological parameters from noisy, non-quantitative image data when the model has a high computational cost. This approach is first successfully tested on a parametric function with the goal of retrieving the original parameters. We then apply it to estimating parameters in a biological setting by fitting artificial in-situ hybridization (ISH) data of the developing murine limb bud. We expect that this method will be of use in a variety of modeling scenarios where quantitative data is missing and the use of standard parameter estimation approaches in biological modeling is prohibited by the computational cost of the model., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

This paper deals with the study of spatial and spatio-temporal patterns in the reaction-diffusion FitzHugh-Nagumo model on growing curved domains. This is carried out on two exemplar cases: a torus and a sphere. We compute bifurcation boundaries for the homogeneous steady state when the homogeneous system is monostable. We exhibit Turing and Turing-Hopf bifurcations, as well as additional patterning outside of these bifurcation regimes due to the multistability of patterned states. We consider static and growing domains, where the growth is slow, isotropic, and exponential in time, allowing for a simple analytical calculation of these bifurcations in terms of model parameters. Numerical simulations allow us to discuss the role played by the growth and the curvature of the domains on the pattern selection on the torus and the sphere. We demonstrate parameter regimes where the linear theory can successfully predict the kind of pattern (homogeneous and heterogeneous oscillations and stationary spatial patterns) but not their detailed nonlinear structure. We also find parameter regimes where the linear theory fails, such as Hopf regimes which give rise to spatial patterning (depending on geometric details), where we suspect that multistability plays a key role in the departure from homogeneity. Finally we also demonstrate effects due to the evolution of nonuniform patterns under growth, suggesting important roles for growth in reaction-diffusion systems beyond modifying instability regimes., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

This paper proposes two spatio-temporal epidemic network models based on popularity and similarity optimization (PSO), called r-SI and r-SIS, respectively, in which new connections take both popularity and similarity into account. In the spatial dimension, the epidemic process is described by the diffusion equation; in the time dimension, the growth of an epidemic is described by the logistic map. Both models are represented by partial differential equations, and can be easily solved. Simulations are performed on both artificial and real networks, demonstrating the effectiveness of the two models., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Drug target interaction prediction is a very labor-intensive and expensive experimental process which has motivated researchers to focus on in silico prediction to provide information on potential interaction. In recent years, researchers have proposed several computational approaches for predicting new drug target interactions. In this paper, we present CFSBoost, a simple and computationally cheap ensemble boosting classification model for identification and prediction of drug-target interactions using evolutionary and structural features. CFSBoost uses a simple yet novel feature group selection procedure which allows the model to be computationally very cheap while being able to achieve state of the art performance. The ensemble model uses extra tree as weak learners inside a boosting scheme while holding on to the best model per iteration. We tested our method of four benchmark datasets, which are also referred as gold standard datasets. Our method was able to achieve better score in terms of area under receiver operating characteristic (auROC) curve on 2 out of the 4 datasets. It was also able to achieve higher area under precision recall (auPR) curve on 3 out of the 4 datasets. It has been argued by researchers that auPR metric is more suitable than auROC for comparison of performance on imbalanced datasets such our benchmark datasets. Our reported result shows that, despite of its simplicity in design, CFSBoost's performance is very satisfactory comparing to other literatures. We also provide 5 new possible interactions for each dataset based on CFSBoost's prediction score., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Individual animal movement has been a focus of intense research and considerable controversy over the last two decades, however the understanding of wider ecological implications of various movement behaviours is lacking. In this paper, we consider this issue in the context of pattern formation. Using an individual-based modelling approach and computer simulations, we first show that density dependence ("auto-taxis") of the individual movement in a population of random walkers typically results in the formation of a strongly heterogeneous population distribution consisting of clearly defined animal clusters or patches. We then show that, when the movement takes place in a large spatial domain, the properties of the clusters are significantly different in the populations of Brownian and non-Brownian walkers. Whilst clusters tend to be stable in the case of Brownian motion, in the population of Levy walkers clusters are dynamical so that the number of clusters fluctuates in the course of time. We also show that the population dynamics of non-Brownian walkers exhibits two different time scales: a short time scale of the relaxation of the initial condition and a long time scale when one type of dynamics is replaced by another. Finally, we show that the distribution of sample values in the populations of Brownian and non-Brownian walkers is significantly different., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

The immune system mounts a response to an infection by activating T cells. T cell activation occurs when dendritic cells, which have already interacted with the pathogen, scan a T cell that is cognate for (responsive to) the pathogen. This often occurs inside lymph nodes. The time it takes for this scanning event to occur, indeed the probability that it will occur at all, depends on many factors, including the rate that T cells and dendritic cells enter and leave the lymph node as well as the geometry of the lymph node and of course other cellular and molecular parameters. In this paper, we develop a hybrid stochastic-deterministic mathematical model at the tissue scale of the lymph node and simulate dendritic cells and cognate T cells to investigate the most important physiological factors leading to a successful and timely immune response after a vaccination. We use an agent-based model to describe the small population of cognate naive T cells and a partial differential equation description for the concentration of mature dendritic cells. We estimate the model parameters based on the known literature and measurements previously taken in our lab. We perform a parameter sensitivity analysis to quantify the sensitivity of the model results to the parameters. The results show that increasing T cell inflow through high endothelial venules, restricting cellular egress via the efferent lymph and increasing the total dendritic cell count by improving vaccinations are the among the most important physiological factors leading to an improved immune response. We also find that increasing the physical size of lymph nodes improves the overall likelihood that an immune response will take place but has a fairly weak effect on the response rate. The nature of dendritic cell trafficking through the LN (either passive or active transport) seems to have little effect on the overall immune response except if a change in overall egress time is observed., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

While deterministic metapopulation models for the spread of epidemics between populations have been well-studied in the literature, variability in disease transmission rates and interaction rates between individual agents or populations suggests the need to consider stochastic fluctuations in model parameters in order to more fully represent realistic epidemics. In the present paper, we have extended a stochastic SIS epidemic model - which introduces stochastic perturbations in the form of white noise to the force of infection (the rate of disease transmission from classes of infected to susceptible populations) - to spatial networks, thereby obtaining a stochastic epidemic metapopulation model. We solved the stochastic model numerically and found that white noise terms do not drastically change the overall long-term dynamics of the system (for sufficiently small variance of the noise) relative to the dynamics of a corresponding deterministic system. The primary difference between the stochastic and deterministic metapopulation models is that for large time, solutions tend to quasi-stationary distributions in the stochastic setting, rather than to constant steady states in the deterministic setting. We then considered different approaches to controlling the spread of a stochastic SIS epidemic over spatial networks, comparing results for a spectrum of controls utilizing local to global information about the state of the epidemic. Variation in white noise was shown to be able to counteract the treatment rate (treated curing rate) of the epidemic, requiring greater treatment rates on the part of the control and suggesting that in real-life epidemics one should be mindful of such random variations in order for a treatment to be effective. Additionally, we point out some problems using white noise perturbations as a model, but show that a truncated noise process gives qualitatively comparable behaviors without these issues., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

The human brain is a small organ which uses a disproportionate amount of the total metabolic energy production in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing patterns, e.g., seizures, thus emphasizing the importance of the glial K + buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a four compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen-glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Highlights • We have corrected the paper in order to present more clearly the experimental results and also to comment more the simulations done for the present Boolean model. • As demanded by reviewers, we have added a short presentation of the R. Thomas' theory, and also a recall of the earlier Boolean model proposed with him for the experiments of stimulation of Bidens pilosus. • Eventually, we have tried to present the perspectives of a hybrid approach from the continuous model previously proposed for Bidens. Abstract This paper presents a new model of memory functions in plants, which improves the previous approaches done by René Thomas and colleagues. We have decomposed the plant memory processing into three main functions: learning, storing and recalling. We propose as main mechanism for these three functions the occurrence of a calcium wave consecutive to an environmental stimulus, followed by the activation of specific genes and proteins changing their phosphorylated state. Feedback is ensured by Calcium Dependent Protein Kinases and oxidative phosphorylation. [ABSTRACT FROM AUTHOR]

Robert Rosen's (M,R) system is an abstract biological network architecture that is allegedly both irreducible to sub-models of its component states and non-computable on a Turing machine. (M,R) stands as an obstacle to both reductionist and mechanistic presentations of systems biology, principally due to its self-referential structure. If (M,R) has the properties claimed for it, computational systems biology will not be possible, or at best will be a science of approximate simulations rather than accurate models. Several attempts have been made, at both empirical and theoretical levels, to disprove this assertion by instantiating (M,R) in software architectures. So far, these efforts have been inconclusive. In this paper, we attempt to demonstrate why - by showing how both finite state machine and stream X-machine formal architectures fail to capture the self-referential requirements of (M,R). We then show that a solution may be found in communicating X-machines, which remove self-reference using parallel computation, and then synthesise such machine architectures with object-orientation to create a formal basis for future software instantiations of (M,R) systems., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Understanding the principle of RNA-protein interactions (RPIs) is of critical importance to provide insights into post-transcriptional gene regulation and is useful to guide studies about many complex diseases. The limitations and difficulties associated with experimental determination of RPIs, call an urgent need to computational methods for RPI prediction. In this paper, we proposed a machine learning method to detect RNA-protein interactions based on sequence information. We used motif information and repetitive patterns, which have been extracted from experimentally validated RNA-protein interactions, in combination with sequence composition as descriptors to build a model to RPI prediction via a random forest classifier. About 20% of the "sequence motifs" and "nucleotide composition" features have been selected as the informative features with the feature selection methods. These results suggest that these two feature types contribute effectively in RPI detection. Results of 10-fold cross-validation experiments on three non-redundant benchmark datasets show a better performance of the proposed method in comparison with the current state-of-the-art methods in terms of various performance measures. In addition, the results revealed that the accuracy of the RPI prediction methods could vary considerably across different organisms. We have implemented the proposed method, namely rpiCOOL, as a stand-alone tool with a user friendly graphical user interface (GUI) that enables the researchers to predict RNA-protein interaction. The rpiCOOL is freely available at http://biocool.ir/rpicool.html for non-commercial uses., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this paper, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiation-induced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses that are not obtained using a traditional radiobiological model., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Most cancer treatments efficacy depends on tumor metastasis suppression, where tumor suppressor genes play an important role. Maspin (Mammary Serine Protease Inhibitor), an non-inhibitory serpin has been reported as a potential tumor suppressor to influence cell migration, adhesion, proliferation and apoptosis in in vitro and in vivo experiments in last two decades. Lack of computational investigations hinders its ability to go through clinical trials. Previously, we reported first computational model for maspin effects on tumor growth using artificial neural network and cellular automata paradigm with in vitro data support. This paper extends the previous in silico model by encompassing how maspin influences cell migration and the cell-extracellular matrix interaction in subcellular level. A feedforward neural network was used to define each cell behavior (proliferation, quiescence, apoptosis) which followed a cell-cycle algorithm to show the microenvironment impacts over tumor growth. Furthermore, the model concentrates how the in silico experiments results can further confirm the fact that maspin reduces cell migration using specific in vitro data verification method. The data collected from in vitro and in silico experiments formulates an unsupervised learning problem which can be solved by using different clustering algorithms. A density based clustering technique was developed to measure the similarity between two datasets based on the number of links between instances. Our proposed clustering algorithm first finds the nearest neighbors of each instance, and then redefines the similarity between pairs of instances in terms of how many nearest neighbors share the two instances. The number of links between two instances is defined as the number of common neighbors they have. The results showed significant resemblances with in vitro experimental data. The results also offer a new insight into the dynamics of maspin and establish as a metastasis suppressor gene for further molecular research., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

When biological cells divide, they divide on a given angle. It has been shown experimentally that the orientation of cell division angle for a single cell can be described by a probability density function. However, the way in which the probability density function underlying cell division orientation influences population or tissue scale morphogenesis is unknown. Here we show that a computational approach, with thousands of stochastic simulations modeling growth and division of a population of cells, can be used to investigate this unknown. In this paper we examine two potential forms of the probability density function: a wrapped normal distribution and a binomial distribution. Our results demonstrate that for the wrapped normal distribution the standard deviation of the division angle, potentially interpreted as biological noise, controls the degree of tissue scale anisotropy. For the binomial distribution, we demonstrate a mechanism by which direction and degree of tissue scale anisotropy can be tuned via the probability of each division angle. We anticipate that the method presented in this paper and the results of these simulations will be a starting point for further investigation of this topic. [ABSTRACT FROM AUTHOR]

This paper develops a three-dimensional spatially distributed model of brain cellular metabolism and investigates how the locus of the synaptic activity in reference to the capillaries and diffusion affects the behavior of the model, a type of analysis which is impossible to carry out in spatially lumped models, which are shown to be consistent spatially averaged approximations of the distributed model. To avoid a geometrically detailed modeling of the complex structure of the tissue consisting of different cell types and the extracellular space, the distributed model is based on a novel multi-domain formulation of reaction-diffusion equations, accounting also for separate mitochondria. The model reduction relating the spatially distributed model and lower dimensional reduced models, including the well-mixed spatially lumped compartment model, is carefully explained. We illustrate the effects of losing the spatial resolution with a computed example which is based on a reduced one-dimensional distributed radial model, and look into how the model behaves when the locus of the synaptic activity in reference to the capillaries is changed. By averaging the fluxes and concentrations in the distributed radial model to correspond to quantities in a lumped model, and further by estimating the parameters in the lumped, we conclude that varying the locus of the synaptic activity in reference to the capillaries alters significantly the lumped model parameters. This observation seems to be consequential for parameter estimation procedures from data when the spatial resolution is insufficient to determine the locus of the activity, indicating that the model uncertainty is an inherent feature of lumped models., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

• A new two-patch pollination-mutualisms system including interacting species is analyzed. • Rigorous analysis on the model exhibits existence of stable positive equilibria. • Dispersal can make the pollinator approach higher total population abundance than if non-diffusing. • The result is effective even though the mutualistic plant approaches a low density. • The result is effective even though the system is in source-sink populations. In this paper, we consider a two-patch pollination-mutualism model with dispersal, which is derived from resource-service exchange between the plant and pollinator. The pollinator is assumed to persist in one patch in the presence of pollination-mutualisms, while it can (or cannot) survive alone in the other. Rigorous study on the model exhibits that solutions of the equations are nonnegative and bounded, and there exist stable positive equilibria under conditions. Theoretical analysis on the equilibria demonstrates that if the pollinator can survive alone in the other patch, a small dispersal can make the pollinator approach higher total population abundance than if non-dispersing. If the pollinator cannot survive alone in the other patch, a small or large dispersal can make the pollinator approach higher size than if non-dispersing, which is not intuitive. A novel prediction of this work is that the pollinator with dispersal can reach high population abundance even though the mutualistic plant approaches a low density, while constructing a high-quality patch for pollinator can lead to extra individuals for both plant and pollinator via dispersal. Numerical simulations confirm and extend our results. [ABSTRACT FROM AUTHOR]

• Both essential and non-essential genes differ from random sequences the same in length. • The composition of nucleotides within sequences differs in these groups. • The distribution of nucleotides within sequences differs in these groups. • Essential genes constitute a representative group of genes for each bacterium. Proteins encoded by genes are engaged in most of the processes within a cell. Typing a minimal set of genes required for survival is still a challenging task. Essential genes seem to be more conservative and are usually responsible for basic functions, for instance, genetic information flow or energy production. Despite persistent advances in experimental methods, computer predictions may constitute an important part of this investigation. Firstly, they may embrace a huge amount of data and provide some characteristic patterns. Furthermore, they enable scientists to build models for predicting essential genes which are not yet verified experimentally. Some papers indicate interesting dependencies within essential genes sequences using different computer models. In this paper, an author took a three-step analysis for a deeper understanding of the fundamentals of essential and non-essential genes. Beginning from a simple nucleotide composition and finishing at long-range correlations, presents some characteristic patterns that are expected to be developed in future studies. [ABSTRACT FROM AUTHOR]

Highlights • We propose a variable weight test for both rare and common variants association based on affected sib pairs. • The variable weight structure makes it possible to analyze rare and common variants simultaneously. • The new method can improve the power of simultaneously detecting rare and common variants. • The proposed method is more powerful than the existing and related methods for detecting effects of rare and common variants. Abstract Current genome-wide association analysis has identified a great number of rare and common variants associated with common complex traits, however, more effective approaches for detecting associations between rare and common variants with common diseases are still demanded. Approaches for detecting rare variant association analysis will compromise the power when detecting the effects of rare and common variants simultaneously. In this paper, we extend an existing method of testing for rare variant association based on affected sib pairs (TOW-sib) and propose a variable weight test for rare and common variants association based on affected sib pairs (abbreviated as VW-TOWsib). The VW-TOWsib can be used to achieve the purpose of detecting the association of rare and common variants with complex diseases. Simulation results in various scenarios show that our proposed method is more powerful than existing methods for detecting effects of rare and common variants. At the same time, the VW-TOWsib also performs well as a method for rare variant association analysis. [ABSTRACT FROM AUTHOR]

Highlights • We explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment, presenting sufficient conditions for coexistence or competitive exclusion. • If the only difference between the two competing populations is a diffusion strategy, we explore how harvesting can either promote coexistence or lead one of the species to extinction. • If, without harvesting, the two species coexist, we evaluate the relation of harvesting rates that keep the coexistence pattern, as well as give sufficient estimates when one of the competitors goes extinct. All the results are illustrated with numerical simulations, including sharpness of estimates. Abstract The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of "close enough" to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion. [ABSTRACT FROM AUTHOR]

Highlights • We study tumor microcalcification in complex, evolving geometries with deformable membranes. • Enhanced membrane deformability promotes tumor growth and tumor calcification. • Correlations between the extents of the mammographic and pathologic tumor change from linear to quadratic as the membrane deformability increases. Abstract In this paper, we apply the diffuse domain framework developed in Chen and Lowengrub (Tumor growth in complex, evolving microenvironmental geometries: A diffuse domain approach, J. Theor. Biol. 361 (2014) 14–30) to study the effects of a deformable basement membrane (BM) on the growth of a tumor in a confined, ductal geometry, such as ductal carcinoma in situ (DCIS). We use a continuum model of tumor microcalcification and investigate the tumor extent beyond the microcalcification. In order to solve the governing equations efficiently, we develop a stable nonlinear multigrid finite difference method. Two dimensional simulations are performed where the adhesion between tumor cells and the basement membrane is varied. Additional simulations considering the variation of duct radius and membrane stiffness are also conducted. The results demonstrate that enhanced membrane deformability promotes tumor growth and tumor calcification. When the duct radius is small, the cell-BM adhesion is weak or when the membrane is slightly deformed, the mammographic and pathologic tumor extents are linearly correlated, as predicted by Macklin et al. (J. Theor. Biol. 301 (2012) 122–140) using an agent-based model that does not account for the deformability of the basement membrane and the active forces that the membrane imparts on the tumor cells. Interestingly, we predict that when the duct radius is large, there is strong cell-BM adhesion or the membrane is highly deformed, the extents of the mammographic and pathologic tumors are instead quadratically correlated. The simulations can help surgeons to measure DCIS surgical margins while removing less non-cancerous tissue, and can improve targeting of intra- and post-operative radiotherapy. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model describing the transmission of two-strain Dengue virus between mosquitoes and humans, incorporating vector control and awareness of susceptible humans, is proposed. By using the next generation matrix method, we obtain the threshold values to identify the existence and stability of three equilibria states, that is, a disease-free state, a state where only one serotype is present and another state where both serotypes coexist. Further, explicit conditions determining the persistence of this disease are also obtained. In addition, we investigate the sensitivity analysis of threshold conditions and the optimal control strategy for this disease. Theoretical results and numerical simulations suggest that the measures of enhancing awareness of the infected and susceptible human self-protection should be taken and the mosquito control measure is necessary in order to prevent the transmission of Dengue virus from mosquitoes to humans. [ABSTRACT FROM AUTHOR]

Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model considering the two key ingredients, in which the contacts are grouped into two classes: strong contacts and normal ones. Next, we present a unified edge-based compartmental approach to the spread dynamics on Erdös–Rényi (ER) networks and validate its results by extensive numerical simulations. In case that epidemic is totally drug-resistant, we both numerically and theoretically show a continuous growth of epidemics with infection probability when number of strong contacts is not enough for the emergence of null threshold. If the epidemic owns partial resistance, we would observe evident discontinuous growth with infection probability (discontinuous transitions) and larger final epidemic sizes for few strong contacts, instead of emergence of null threshold with increase of strong contacts. Inhibiting effect of infection threshold, positive roles of strong contacts and strength of strong contacts in promoting outbreaks are also approved. Throughout this paper, we could drive exact predictions through the analytical approach, showing good agreements with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a periodic SIS epidemic model with time delay and transport-related infection in a patchy environment. The basic reproduction number R 0 is derived which determines the global dynamics of the model system: if R 0  < 1, the disease-free periodic state is globally attractive while there exists at least one positive periodic state and the disease persists if R 0  > 1. Numerical simulations are performed to confirm the analytical results and to explore the dependence of R 0 on the transport-related infection parameters and the amplitude of fluctuations. [ABSTRACT FROM AUTHOR]

The theory of invasions and invasion speeds has traditionally been studied in macroscopic systems. Surprisingly, microbial invasions have received less attention. Although microbes share many of the features associated with competition between larger-bodied organisms, they also exhibit distinctive behaviors that require new mathematical treatments to fully understand invasions in microbial systems. Most notable is the possibility for long-distance interactions, including competition between populations mediated by diffusible toxins and cooperation among individuals of a single population using quorum sensing. In this paper, we model bacterial invasion using a system of coupled partial differential equations based on Fisher's equation. Our model considers a competitive system with diffusible toxins that, in some cases, are expressed in response to quorum sensing. First, we derive analytical approximations for invasion speeds in the limits of fast and slow toxin diffusion. We then test the validity of our analytical approximations and explore intermediate rates of toxin diffusion using numerical simulations. Interestingly, we find that toxins should diffuse quickly when used offensively, but that there are two optimal strategies when toxins are used as a defense mechanism. Specifically, toxins should diffuse quickly when their killing efficacy is high, but should diffuse slowly when their killing efficacy is low. Our approach permits an explicit investigation of the properties and characteristics of diffusible compounds used in non-local competition, and is relevant for microbial systems and select macroscopic taxa, such as plants and corals, that can interact through biochemicals. [ABSTRACT FROM AUTHOR]

Hormone suppression has been the primary modality of treatment for prostate cancer. However long-term androgen deprivation may induce androgen-independent (AI) recurrence. Intermittent androgen suppression (IAS) is a potential way to delay or avoid the AI relapse. Mathematical models of tumor growth and treatment are simple while they are capable of capturing the essence of complicated interactions. Game theory models have analyzed that tumor cells can enhance their fitness by adopting genetically determined survival strategies. In this paper, we consider the survival strategies as the competitive advantage of tumor cells and propose a new model to mimic the prostate tumor growth in IAS therapy. Then we investigate the competition effect in tumor development by numerical simulations. The results indicate that successfully IAS-controlled states can be achieved even though the net growth rate of AI cells is positive for any androgen level. There is crucial difference between the previous models and the new one in the phase diagram of successful and unsuccessful tumor control by IAS administration, which means that the suggestions from the models for medication can be different. Furthermore we introduce quadratic logistic terms to the competition model to simulate the tumor growth in the environment with a finite carrying capacity considering the nutrients or inhibitors. The simulations show that the tumor growth can reach an equilibrium state or an oscillatory state with the net growth rate of AI cells being androgen independent. Our results suggest that the competition and the restraint of a limited environment can enhance the possibility of relapse prevention. [ABSTRACT FROM AUTHOR]

• A PNP (or PDE) model is formulated for the mechanism of electrocyte. • The superposition of two membrane potentials is rigorously explained by PNP model. • Classical membrane (or ODE) model can not explain the above superposition principle. • PNP model reduces to the membrane model at leading order by asymptotic analysis. In this paper, we developed a one-dimensional model for electric potential generation of electrocytes in electric eels. The model is based on the Poisson–Nernst–Planck system for ion transport coupled with membrane fluxes including the Hodgkin–Huxley type. Using asymptotic analysis, we derived a simplified zero-dimensional model, which we denote as the membrane model in this paper, as a leading order approximation. Our analysis provides justification for the assumption in membrane models that electric potential is constant in the intracellular space. This is essential to explain the superposition of two membrane potentials that leads to a significant transcellular potential. Numerical simulations are also carried out to support our analytical findings. [ABSTRACT FROM AUTHOR]

In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and numerical analysis of stability of the steady states of the model we identify parameter regions associated with recovery and resistant phenotypes, as well as possible chronic infections. Dynamics of the system in these regimes is illustrated by numerical simulations of the model. [ABSTRACT FROM AUTHOR]

Individual migration plays a crucial role in evolutionary dynamics of population on networks. In this paper, we generalize the networked ultimatum game by diluting population structures as well as endowing individuals with migration ability, and investigate evolutionary dynamics of fairness on graphs with migration in the ultimatum game. We first revisit the impact of node degree on the evolution of fairness. Interestingly, numerical simulations reveal that there exists an optimal value of node degree resulting in the maximal offer level of populations. Then we explore the effects of dilution and migration on the evolution of fairness, and find that both the dilution of population structures and the endowment of migration ability to individuals would lead to the drop of offer level, while the rise of acceptance level of populations. Notably, natural selection even favors the evolution of self-incompatible strategies, when either vacancy rate or migration rate exceeds a critical threshold. To confirm our simulation results, we also propose an analytical method to study the evolutionary dynamics of fairness on graphs with migration. This method can be applied to explore any games governed by pairwise interactions in finite populations. [ABSTRACT FROM AUTHOR]

• A PNP (or PDE) model is formulated for the mechanism of electrocyte discharge. • Time variation of the electric fields is essential for the conservation of total current. • PNP model reduces to an ordinary differential equations model at leading order by asymptotic analysis. • Delay in contact leads to interesting dynamics and new features, compared to the non-contact case investigated previously. In this paper, we investigate the electric discharge of electrocytes by extending our previous work on the generation of electric potential. We first give a complete formulation of a single cell unit consisting of an electrocyte and a resistor, based on a Poisson-Nernst-Planck (PNP) system with various membrane currents as interfacial conditions for the electrocyte and a Maxwell's model for the resistor. Our previous work can be treated as a special case with an infinite resistor (or open circuit). Using asymptotic analysis, we simplify our PNP system and reduce it to an ordinary differential equation (ODE) based model. Unlike the case of an infinite resistor, our numerical simulations of the new model reveal several distinct features. A finite current is generated, which leads to non-constant electric potentials in the bulk of intracellular and extracellular regions. Furthermore, the current induces an additional action potential (AP) at the non-innervated membrane, contrary to the case of an open circuit where an AP is generated only at the innervated membrane. The voltage drop inside the electrocyte is caused by an internal resistance due to mobile ions. We show that our single cell model can be used as the basis for a system with stacked electrocytes and the total current during the discharge of an electric eel can be estimated by using our model. [ABSTRACT FROM AUTHOR]