Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in chemistry. An important class of system that would be intractable if expressed as reactions or ordinary differential equations can be efficiently simulated when expressed as rules. In this paper we demonstrate the utility of the rule-based approach for epidemiological modelling presenting a suite of seven models illustrating the spread of infectious disease under different scenarios: wearing masks, infection via fomites and prevention by hand-washing, the concept of vector-borne diseases, testing and contact tracing interventions, disease propagation within motif-structured populations with shared environments such as schools, and superspreading events. Rule-based models allow to combine transparent modelling approach with scalability and compositionality and therefore can facilitate the study of aspects of infectious disease propagation in a richer context than would otherwise be feasible.

The war of attrition in game theory is a model of a stand-off situation between two opponents where the winner is determined by its persistence. We model a stand-off between a predator and a prey when the prey is hiding and the predator is waiting for the prey to come out from its refuge, or when the two are locked in a situation of mutual threat of injury or even death. The stand-off is resolved when the predator gives up or when the prey tries to escape. Instead of using the asymmetric war of attrition, we embed the stand-off as an integral part of the predator-prey model of Rosenzweig and MacArthur derived from first principles. We apply this model to study the coevolution of the giving-up rates of the prey and the predator, using the adaptive dynamics approach. We find that the long term evolutionary process leads to three qualitatively different scenarios: the predator gives up immediately, while the prey never gives up; the predator never gives up, while the prey adopts any giving-up rate greater than or equal to a given positive threshold value; the predator goes extinct. We observe that some results are the same as for the asymmetric war of attrition, but others are quite different.

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington's landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

The world faces a great unforeseen challenge through the COVID-19 pandemic caused by coronavirus SARS-CoV-2. The virus genome structure and evolution are positioned front and center for further understanding insights on vaccine development, monitoring of transmission trajectories, and prevention of zoonotic infections of new coronaviruses. Of particular interest are genomic elements Inverse Repeats (IRs), which maintain genome stability, regulate gene expressions, and are the targets of mutations. However, little research attention is given to the IR content analysis in the SARS-CoV-2 genome. In this study, we propose a geometric analysis method and using the method to investigate the distributions of IRs in SARS-CoV-2 and its related coronavirus genomes. The method represents each genomic IR sequence pair as a single point and constructs the geometric shape of the genome using the IRs. Thus, the IR shape can be considered as the signature of the genome. The genomes of different coronaviruses are then compared using the constructed IR shapes. The results demonstrate that SARS-CoV-2 genome, specifically, has an abundance of IRs, and the IRs in coronavirus genomes show an increase during evolution events.

Erratum in J Theor Biol. 2022 Jul 7;544:111137.

We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the nonlocal interactions. In both cases, nonlocal interactions can create spatial patterns of population densities in which highly populated clumps alternate with unpopulated regions. These non-populated regions provide spatial niches for a weaker competitor to establish in the community and persist in conditions in which local models predict competitive exclusion. Moreover, depending on the balance between local and nonlocal competition intensity, the clumps of the weaker competitor vary from M-like structures with higher densities of individuals accumulating at the edges of each clump to triangular structures with most individuals occupying their centers. These results suggest that long-range competition, through the creation of spatial patterns in population densities, might be a key driving force behind the rich diversity of species observed in natural ecological communities.

We study the mechanics of mechanoreceptor hairs in response to electro- and acousto-stimuli to expand the theory of tuning within filiform mechano-sensory systems and show the physical, biological and parametric feasibility of electroreception in comparison to aerodynamic sensing. We begin by analysing two well-known mechanosensory systems, the MeD1 spider trichobothria and the cricket cercal hair, offering a systematic appraisal of the physics of mechanosensory hair motion. Then we explore the biologically relevant parameter space of mechanoreceptor hairs by varying each oscillator parameter, thereby extending the theory to general arthropods. In doing so, we readily identify combinations of parameters for which a hair shows an enhanced or distinct response to either electric or aerodynamic stimuli. Overall, we find distinct behaviours in the two systems with novel insight provided through the parameter-space analysis. We show how the parameter space and balance of parameters therein of the resonant spider system are organised to produce a highly tuneable hair system through variation of hair length, whilst the broader parameter space of the non-resonant cricket system responds equally to a wider range of driving frequencies with increased capacity for high temporal resolution. From our analysis, we hypothesise the existence of two distinct types of mechanoreceptive system: the general system where hairs of all lengths are poised to detect both electro- and acousto- stimuli, and a stimuli-specific system where the sensitivity and specificity of the hairs to the different stimuli changes with length.

BACKGROUND: A good treatment for type 1 diabetes mellitus (T1DM) requires accurate measurements of blood glucose levels. Continuous glucose monitors (CGM) measure the glucose concentration in the interstitial fluid of the abdominal subcutaneous adipose tissue. However, glucose measured in the abdominal interstitial fluid does not represent blood glucose concentrations accurately due to the complex blood transport through the body and glucose diffusion in interstitial fluid. METHODS: To gain insight into this problem, a phenomenological-based semiphysical model (PBSM) of glucose transport by volumetric flow and diffusion from the bloodstream to interstitial fluid was constructed. A published 10-step modeling procedure was used to obtain a model for glucose transport time through the blood vessels and from the blood capillaries to the interstitial fluid, glucose diffusion within the interstitial fluid, and glucose diffusion through the semipermeable coating of the sensor needle. For this model, a healthy person is considered at rest with average parameters. RESULTS: The simulations performed using the PBSM allow obtaining the glucose transport time from the liver to the sensor needle. In this way, it is possible to reconstruct an accurate dynamic measurement of blood glucose from the measurements in the interstitial fluid of the abdominal subcutaneous adipose tissue. CONCLUSIONS: PBSMs with parameters interpretability illustrate the connection of glucose concentrations in the interstitial fluid with that currently in the blood. Implementing this model in a CGM will result in more reliable measurements of blood glucose levels for T1DM treatment.

Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number Refft below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come.

The sterile insect technique (SIT) involves periodically releasing artificially sterilized insects to inhibit normal mating between wild insect pests, ultimately resulting in the eradication of wild pest populations. It has often been discussed whether releasing either one sex, mainly males, of sterile insects (i.e., a unisexual release) can enhance the pest-control effect of the SIT more than releasing both sexes (i.e., a bisexual release). We constructed a mathematical model to examine the contribution of sterile males and females to the pest-control effect and the synergy between them. We consider that males seek out and court females in accord with their own female searching ability and preference, and that females subsequently choose one male from among males courting them in accordance with their own preference. Using this model, we compared the pest-control effect of bisexual and unisexual release, focusing on the difference in mating systems of the targeted insects. We showed that for swarm-type mating systems (with few courtship chances with higher encounter rates), bisexual release was the most effective, irrespective of the relative female searching ability between wild and sterile males. In this case, sterile females indirectly reduce wild females mating with either male by absorbing courtship from both wild and sterile males. By contrast, bisexual release is the most effective for scramble-type mating systems (more courtship chances with lower encounter rates) only when the female searching ability of sterile males is lower than that of wild males. In this case, sterile females absorb courtship from males with higher searching abilities. Therefore, the net impact of sterile females depends on the difference in sexual performance between wild and sterile males. Because the sexual performance of sterile insects is often degraded during the process of sterilization, we suggest that bisexual release can be a compatible measure to efficiently suppress wild pest populations.

One of the most important questions in cell biology is how cell fate is determined when exposed to extreme stresses such as heat shock. It has been long understood that organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of denatured or unfolded proteins triggers the synthesis of heat shock proteins (HSPs) through the heat shock transcription factor, e.g., heat shock factor 1 (HSF1). In this study, a dynamical model validated with experiments is presented to analyse the role of HSF1 SUMOylation in response to heat shock. Key features of this model are inclusion of heat shock response and SUMOylation of HSF1, and HSP synthesis at molecular level, describing the dynamical evolution of the key variables involved in the regulation of HSPs. The model has been employed to predict the SUMOylation levels of HSF1 with different external temperature stimuli. The results show that the SUMOylated HSF1 levels agree closely with the experimental findings. This demonstrates the validity of this nonlinear dynamic model for the important role of SUMOylation in response to heat shock.

A viral strain may infect a host, proliferate rapidly, become controlled by immune reactions, and eventually be eliminated from the body. The virulence, or the magnitude of harm to the host due to infection, depends on the abundance and duration of the viral strain in the body, and the importance of the damaged tissue of the host. In this study, we investigated how the cumulative viral load (time-integral of the number of infected cells) depends on various factors, such as the viral growth rate, the effectiveness of immune cells to kill infected cells, speed of immune activation, formation of memory cells, and longevity of immune cells. In addition, viruses may produce a mutant with different antigen types, escape the immune reaction targeting the original type, and inflate virulence. We succeeded in deriving simple and explicit formulas of the virulence in four different parameter regions. We found that, in some parameter region, enhancing memory cells is very effective in suppressing virulence, but direct activation of immune effector cells is not effective; while the opposite is the case in other regions. The result could be important in designing drug suppressing virus effectively. Additionally, we discussed the reported correlation between virulence and molecular evolution rate.

The mammalian adaptive immune system has evolved over millions of years to become an incredibly effective defense against foreign antigens. The adaptive immune system's humoral response creates plasma B cells and memory B cells, each with their own immunological objectives. The affinity maturation process is widely viewed as a heuristic to solve the global optimization problem of finding B cells with high affinity to the antigen. However, memory B cells appear to be purposely selected earlier in the affinity maturation process and have lower affinity. We propose that this memory B cell selection process may be an approximate solution to two optimization problems: optimizing for affinity to similar antigens in the future despite mutations or other minor differences, and optimizing to warm start the generation of plasma B cells in the future. We use simulations to provide evidence for our hypotheses, taking into account data showing that certain B cell mutations are more likely than others. Our findings are consistent with memory B cells having high-affinity to mutated antigens, but do not provide strong evidence that memory B cells will be more useful than selected naive B cells for seeding the secondary germinal centers.

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.

We study the evolution of virulence of an endemic pathogen in response to healthcare interventions which affect host recovery and pathogen transmission. By anticipating the evolutionary response of the pathogen we may develop effective long-term management strategies for controlling the impact of the endemic on the society. To that end, we use standard Adaptive Dynamics techniques in an SIS model. The recovery rate and the transmission rate, both of which can be affected by healthcare interventions, are used as evolutionary control variables. The effect of interventions may be density-independent (self-help based on healthcare instructions) or density-dependent (when assistance of a healthcare worker is required). We consider the evolutionary response of the pathogen both to abrupt changes and to gradual changes in the level of healthcare intervention. Healthcare intervention is optimised for three alternative objectives: minimisation of virulence, minimisation of the probability that an infected individual dies of the disease, and total eradication of the endemic. We find that the optimal strategy may depend on the objective. High levels of healthcare intervention may eradicate the pathogen, but this option may not be available for budgetary reasons or otherwise. Counterintuitively, to minimise virulence, one should keep healthcare interventions at a minimum, while to minimise the probability for an infected individual to die of the disease, both low and high levels of healthcare intervention suffice. Changes in the level of healthcare intervention should be implemented fast (not gradually) in order to avoid sudden changes in pathogen evolution and the possible emergence of multiple simultaneously coexisting pathogen strains.

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often become increasingly complicated to interpret. To tackle this problem, we introduce persistent homology as a rigorous framework that can be used to both define and compute higher-order features of data in a manner which is invariant to parameter choices, robust to noise, and independent of human observation. Our work demonstrates its relevance for spatial games by showing how topological features of simulation data that persist over different spatial scales reflect the stability of strategies in 2D lattice games. To do so, we analyze the persistent homology of scenarios from two games: a Prisoner's Dilemma and a SIRS epidemic model. The experimental results show how the method accurately detects features that correspond to real aspects of the game dynamics. Unlike other tools that study dynamics of spatial systems, persistent homology can tell us something meaningful about population structure while remaining neutral about the underlying structure itself. Regardless of game complexity, since strategies either succeed or fail to conform to shapes of a certain topology there is much potential for the method to provide novel insights for a wide variety of spatially extended systems in biology, social science, and physics.

With an increasingly elderly population globally, the impacts of cerebrovascular diseases, such as stroke and dementia, become increasingly significant. Haemorrhagic transformation (HT) is one of the most common complications of ischaemic stroke that is caused by dysfunction of endothelial cells in the blood-brain barrier (BBB) and that can be exacerbated by thrombolytic therapy. Recent studies also suggest that HT can lead to an increase in intracranial pressure (ICP) and result in capillary compression. The aim of this study is to develop a mathematical model that can be used to simulate the consequence of HT over a range of vasculature length scales. We use a 2D vasculature model to investigate the severity of HT with different vascular geometry. The resulting model shows that the haematoma radius is approximately constant across different length scales (100-1000μm) and in good agreement with the available experimental data. In addition, this study identified that the effects of capillary compression do appear to have a significant impact on the leakage fraction of blood and hence act to restrain the development of a haematoma.

Butterfly wing color patterns are a representative model system for studying biological pattern formation, due to their two-dimensional simple structural and high inter- and intra-specific variabilities. Moreover, butterfly color patterns have demonstrated roles in mate choice, thermoregulation, and predator avoidance via disruptive coloration, attack deflection, aposematism, mimicry, and masquerade. Because of the importance of color patterns to many aspects of butterfly biology and their apparent tractability for study, color patterns have been the subjects of many attempts to model their development. Early attempts focused on generalized mechanisms of pattern formation such as reaction-diffusion, diffusion gradient, lateral inhibition, and threshold responses, without reference to any specific gene products. As candidate genes with expression patterns that resembled incipient color patterns were identified, genetic regulatory networks were proposed for color pattern formation based on gene functions inferred from other insects with wings, such as Drosophila. Particularly detailed networks incorporating the gene products, Distal-less (Dll), Engrailed (En), Hedgehog (Hh), Cubitus interruptus (Ci), Transforming growth factor-β (TGF-β), and Wingless (Wg), have been proposed for butterfly border ocelli (eyespots) which helps the investigation of the formation of these patterns. Thus, in this work, we develop a mathematical model including the gene products En, Hh, Ci, TGF-β, and Wg to mimic and investigate the eyespot formation in butterflies. Our simulations show that the level of En has peaks in the inner and outer rings and the level of Ci has peaks in the inner and middle rings. The interactions among these peaks activate cells to produce white, black, and yellow pigments in the inner, middle, and outer rings, respectively, which captures the eyespot pattern of wild type Bicyclus anynana butterflies. Additionally, our simulations suggest that lack of En generates a single black spot and lack of Hh or Ci generates a single white spot, and a deficiency of TGF-β or Wg will cause the loss of the outer yellow ring. These deficient patterns are similar to those observed in the eyespots of Vanessa atalanta, Vanessa altissima, and Chlosyne nycteis. Thus, our model also provides a hypothesis to explain the mechanism of generating the deficient patterns in these species.

Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R0 varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

Species competition takes place in a fluctuating environment, so the selective forces on different populations vary through time. In many realistic situations the mean fitness and the amplitude of its temporal variations are abundance-dependent. Here we present a theory of two-species competition with abundance-dependent stochastic fitness variations and solve for the chance of ultimate fixation, the time to absorption and the time to fixation. We then examine the ability of this two-species system to serve as an effective model for high-diversity assemblages and to account for the presence of an intra-specific differential response to environmental variations. The effective model is shown to capture the main features of competition between composite populations.

Vaccination remains a critical element in the eventual solution to the COVID-19 public health crisis. Many vaccines are already being mass produced and supplied in many countries. However, the COVID-19 vaccination programme will be the biggest in history. Reaching herd immunity will require an unprecedented mass immunisation campaign that will take several months and millions of dollars. Using different network models, COVID-19 pandemic dynamics of different countries can be recapitulated such as in Italy. Stochastic computational simulations highlight that peak epidemic sizes in a population strongly depend on the network structure. Assuming a vaccine efficacy of at least 80% in a mass vaccination program, at least 70% of a given population should be vaccinated to obtain herd immunity, independently of the network structure. If the vaccine efficacy reports lower levels of efficacy in practice, then the coverage of vaccination would be needed to be even higher. Simulations suggest that the "Ring of Vaccination" strategy, vaccinating susceptible contact and contact of contacts, would prevent new waves of COVID -19 meanwhile a high percent of the population is vaccinated.

The depolarization of the postsynaptic membrane potential in neuromuscular junction, which is conducted by the (stochastic) opening of nicotinic acetylcholine (nACh) receptors distributed in postsynaptic folds, is an inevitable stage in transmitting the electric signals from neural ends to muscle fibers. To perform this work, free energy must be dissipated. Being the first step in understanding the speech-accuracy-energy trade-off, we calculate the energy dissipation of a tiny membrane system that contains a single nACh receptor, i which firstly the stationary distribution of voltage is calculated based on our new method on solving the high-dimensional ODEs with variable coefficients. The ratio of the extent of depolarized-potential to the dissipated power is used to characterize the energy consuming efficiency of the system.

We develop new equations for the eco-evolutionary dynamics of populations and their traits. These equations resolve the change in the phenotypic differentiation within a population, which better estimates how the variance of the trait distribution changes. We note that traits may be bounded, assume they may be described by beta distributions with small variances, and develop a coupled ordinary differential equation system to describe the dynamics of the total population, the mean trait value, and a measure of phenotype differentiation. The variance of the trait in the population is calculated from its mean and the population's phenotype differentiation. We consider an example of two competing plant populations to demonstrate the efficacy of the new approach. Each population may trade-off its growth rate against its susceptibility to direct competition from the other population. We create two models of this system: a population model based on our new eco-evolutionary equations; and a phenotype model, in which the growth or demise of each fraction of each population with a defined phenotype is simulated as it interacts with a shared limiting resource and its competing phenotypes and populations. Comparison of four simulation scenarios reveals excellent agreement between the predicted quantities from both models: total populations, the average trait values, the trait variances, and the degree of phenotypic differentiation within each population. In each of the four scenarios simulated, three of which are initially subject to competitive exclusion in the absence of evolution, the populations adapt to coexist. One population maximises growth and dominates, while the other minimises competitive losses. These simulations suggest that our new eco-evolutionary equations may provide an excellent approximation to phenotype changes in populations.

Colonization of the water column by animals occurred gradually during the early Palaeozoic. However, the morphological and functional changes that took place during this colonization are poorly understood. The fossil record provides clear evidence of animals that were well adapted for swimming near the seafloor or in the open ocean, but recognising transitional forms is more problematic. Trilobites are a good model to explore the colonization of marine ecosystems. Here, we use computational fluid dynamics (CFD) to test between competing functional hypotheses in the Ordovician trilobite Placoparia. The CFD simulations exhibits hydrodynamics that promote detachment from the seafloor but also promote return to the seafloor following detachment, this is compatible with hopping locomotion. The results suggest that Placopara was not able to swim, but its hydrodynamics allowed it to hop long distances. This is consistent with the fossil record, as some ichnofossils show evidence of hopping. This type of locomotion could be useful to avoid predators as an escape mechanism. In addition, CFD simulation shows how the morphology of Placoparia is adapted to protect anterior appendices of the trunk and generate a ventral vortex that send food particles directly to the trilobite mouth. Adaptations in Placoparia allowed the first steps to evolved a new ecological habitat and consequently nektonization during the GOBE.

Is population-level heterogeneity a reflection of distinct subpopulations, exhibiting different metabolic functions, or dynamic metabolism of individuals within the population? This fascinating question has remained a subject of great interest in studying metabolic specialization in microorganisms. The Crabtree effect - i.e., the ability of some microorganisms to switch from respiration to fermentation in the presence of oxygen - is an appropriate case study to address the aforementioned question. Game-theoretical approaches have been routinely used to examine and explain the way a microorganism, such as yeast, would switch between the two ATP-producing pathways, i.e., respiration and fermentation. Here we attempt to explain the switch between respiration and fermentation in yeast by constructing a simple metabolic switch. We then utilize an individual-based model, in which each individual is equipped with all the relevant chemical reactions, to see how cells equipped with such metabolic switch would behave in different conditions. We further investigate our proposed metabolic switch using the game-theoretical approach. Based on this model, we postulate that the population-level metabolic heterogeneity in microorganisms can simply arise from individuals utilizing a mixed strategy.

Sudden shifts in vaccine uptake, vaccine opinion, and infection incidence can occur in coupled behaviour-disease systems going through a bifurcation as the perceived risk of the vaccine increases. Literature shows that such regime shifts are sometimes foreshadowed by early warning signals (EWS). We propose and compare the performance of various measures of network structure as potential EWS indicators of epidemics and changes in population vaccine opinion. We construct a multiplex model coupling transmission of a vaccine-preventable childhood infectious disease and social dynamics concerning vaccine opinion. We find that the modularity of pro- and anti-vaccine network communities perform well as EWS, as do several measures of the number and size of opinion-based communities, and the size of pro-vaccine echo chambers. The number of opinion changes also gives early warnings, although the clustering coefficient and metrics concerning anti-vaccine echo chambers provide little warning. Stronger social norms are found to compromise the ability of all EWS metrics to provide advance warning. These exploratory results suggest that EWS indicators based on the network structure of online social media communities might assist public health preparedness by providing early warning of potential regime shifts.

Allocating limit medicine resources by mathematical modeling to control spreading of epidemic diseases is a very promising approach. Especially, how to use the existing partial data to efficiently control epidemic diseases is a interesting problem. When an epidemic disease is spreading, it is very urgent and essential to build a prediction and control model based on the real-time and partial data in order that decision makers find and implement the optimal strategy timely. In this paper, we developed a new framework for solving the problem. Our nonlinear model predictive control (NMPC) based on a discrete time susceptible-infected-removed dynamics (SIR) gave an attempt that aims at timely dealing with the condition. Our NMPC model minimizes the total number of infectious cases and the total cost, with the treatment beds capacity constraints and other constraints, especially, with a state observer based on the system output which can be sampled more easily and more accurately. Our control policy can be updated timely according to the current statistical data because our NMPC is a kind of closed-loop control algorithm based on our observer. We also presented some theoretical results on the state observer. Finally, we gave a numerical example to illustrate our algorithm.

Seed germination is the primary stage of growth in a seed. A wealth of experiments exist in literature to support the existence of correlation between seed germination to the electric and magnetic fields. This becomes more important as researchers have suggested to develop technologies to build ecologically clean and environment-friendly solutions to agricultural practices. Although the literature supports the existence of seed germination acceleration, the lack of a definite causal theory has been observed by numerous researchers over decades. After considering all the existing experimental data, we have formulated a causal theory to explain the factors influencing seed germination around high voltage DC transmission lines. This work opens new avenues of research in this field.

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.

While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses geometry to show that, holding order and richness constant, the families of divergence-based evenness measures nest. This property allows them to be ranked based on their reactivity to changes in relatively even assemblages or changes in relatively uneven ones. We establish this ranking and explore how the distance-based measures relate to it for both order q = 2 and q = 1. We also derive a new family of distance-based measures that captures the angular distance between the vector of relative abundances and a perfectly even vector and is highly reactive to changes in even assemblages. Finally, we show that if we only require evenness to be a divergence, then any smooth, monotonically increasing function of diversity can be made into an evenness measure. A deeper understanding of how to measure evenness will require empirical or theoretical research that uncovers which kind of divergence best reflects the underlying concept.

Arbuscular mycorrhizal (AM) fungi play a key role in determining ecosystem functionality. Understanding how diversity in the fungal community affects plant productivity is therefore an important question in ecology. Current research has focused on understanding the role of functional complementarity in the fungal community when the host plant faces multiple stress factors. Fewer studies, however, have investigated how variation in traits affecting nutrient exchange can impact the plant growth dynamics, even in the absence of environmental stressors. Combining experimental data and a mathematical model based on ordinary differential equations, we investigate the role played by carbon sink strength on plant productivity. We simulate and measure plant growth over time when the plant is associated with two fungal isolates with different carbon sink strength, and when the plant is in pairwise association with each of the isolates alone. Overall, our theoretical as well as our experimental results show that co-inoculation with fungi with different carbon sink strength can induce positive non-additive effects (or synergistic effects) in plant productivity. Fungi with high carbon sink strength are able to quickly establish a fungal community and increase the nutrient supply to the plant, with a consequent positive impact on plant growth rate. On the other side, fungi with low carbon sink strength inflict lower carbon costs to the host plant, and support maximal plant productivity once plant biomass is large. As AM fungi are widely used as organic fertilizers worldwide, our findings have important implications for restoration ecology and agricultural management.

We model the population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV -2), a causative agent of COVID-19 disease, poses a significant threat to public health. Since its outbreak in December 2019, Wuhan, China, extensive collection of diverse data from cell culture and animal infections as well as population level data from an ongoing pandemic, has been vital in assessing strategies to battle its spread. Mathematical modelling plays a key role in quantifying determinants that drive virus infection dynamics, especially those relevant for epidemiological investigations and predictions as well as for proposing efficient mitigation strategies. We utilized a simple mathematical model to describe and explain experimental results on viral replication cycle kinetics during SARS-CoV-2 infection of animal and human derived cell lines, green monkey kidney cells, Vero-E6, and human lung epithelium cells, A549-ACE2, respectively. We conducted cell infections using two distinct initial viral concentrations and quantified viral loads over time. We then fitted the model to our experimental data and quantified the viral parameters. We showed that such cellular tropism generates significant differences in the infection rates and incubation times of SARS-CoV-2, that is, the times to the first release of newly synthesised viral progeny by SARS-CoV-2-infected cells. Specifically, the rate at which A549-ACE2 cells were infected by SARS-CoV-2 was 15 times lower than that in the case of Vero-E6 cell infection and the duration of latent phase of A549-ACE2 cells was 1.6 times longer than that of Vero-E6 cells. On the other hand, we found no statistically significant differences in other viral parameters, such as viral production rate or infected cell death rate. Since in vitro infection assays represent the first stage in the development of antiviral treatments against SARS-CoV-2, discrepancies in the viral parameter values across different cell hosts have to be identified and quantified to better target vaccine and antiviral research.