Two-component systems (TCS) are signal transduction systems in bacteria and many other organisms that relay the sensory signal to genetic components. TCS consist of two proteins: a histidine kinase and a response regulator that the histidine kinase activates. This seemingly simple machinery can generate complex regulatory dynamics that enables the level of gene expression that matches the input signal:

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of fitter genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such

Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to encode structural information of the data. We show how these spectra can be used, in particular, in order to give an estimation of cellular redundancy, a novel

Emergency and establishment of variants of concern (VOC) impose significant challenges for the COVID-19 pandemic control specially when a large portion of the population has not been fully vaccinated. Here we develop a mathematical model and utilize this model to examine the impact of non pharmaceutical interventions, including the COVID-test (PCR, antigen and antibody test) and whole genome sequencing

Retrospective analyses of interventions to epidemics, in which the effectiveness of strategies implemented are compared to hypothetical alternatives, are valuable for performing the cost-benefit calculations necessary to optimize infection countermeasures. SIR (susceptible-infected-removed) models are useful in this regard but are limited by the challenge of deciding how and when to update the numerous

As the global climate changes, biological populations have to adapt in place or move in space to stay within their preferred temperature regime. Empirical evidence suggests that shifting speeds of temperature isoclines are location and elevation dependent and may accelerate over time. We present a mathematical tool to study transient behaviour of population dynamics within such moving habitats to discern

In mathematical phylogenetics, the Sackin index, measuring the sum of path lengths between leaves and the root, is one of the most frequently used measures of balance for phylogenetic trees. The uniform model, in which all rooted binary labeled trees for a given set of leaf labels are assumed to be equiprobable, is one of the most frequently used models for describing a probability distribution on

The climate change has the potential to dramatically affect species’ thermal physiology and may change the ecology and evolution of species’ lineages. In this work, we investigated the transition of dynamics in the heat shock response when the thermal stress approaches the upper thermal limits of species to understand how the climate change may affect the heat shock responses in ectotherms and endotherms

To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted – though with different timing and intensities – to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. In this article

Effects like selection in evolution as well as fertility inheritance in the development of populations can lead to a higher degree of asymmetry in evolutionary trees than expected under a null hypothesis. To identify and quantify such influences, various balance indices were proposed in the phylogenetic literature and have been in use for decades. However, so far no balance index was based on the number

Clostridioides difficile, formerly Clostridium difficile, is the leading cause of infectious diarrhea and one of the most common healthcare acquired infections in United States hospitals. C. difficile persists well in healthcare environments because it forms spores that can survive for long periods of time and can be transmitted to susceptible patients through contact with contaminated hands and fomites

The SARS-CoV-2 virus causing the global pandemic is a coronavirus with a genome of about 30Kbase length. The design of vaccines and choice of therapies depends on the structure and mutational stability of encoded proteins in the open reading frames(ORFs) of this genome. In this study, we computed, using Expectation Reflection, the genome-wide covariation of the SARS-CoV-2 genome based on an alignment

Population models are important tools for evaluating human impacts and potential management approaches on declining species. However, often studies are limited by constraints of the specific modeling approach. In this study we considered the persistence of a diamond-backed terrapin (Malaclemys terrapin) population using two distinct modeling approaches. Two of the models were deterministic matrix models

The Asian citrus psyllid (ACP) survival in the presence of contact insecticides may be through physiological adaptations or by behaviorally avoiding. Curiously, although the first alternative is the object of frequent attention, the second was often neglected, but both may lead to insecticide resistance. In this paper, we characterize the growth dynamics of ACP population using a novel impulsive differential

The spotted lanternfly (SLF) is an invasive pest that emerged in the US less than a decade ago. With few natural enemies and an ability to feed on a wide variety of readily available plants the population has grown rapidly. It is causing damage to a wide range of natural and economically important farmed plants and at present there is no known way to stop the growth and spread of the population. However

Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coronavirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining

The COVID-19 pandemic has challenged authorities at different levels of government administration around the globe. When faced with diseases of this severity, it is useful for the authorities to have prediction tools to estimate in advance the impact on the health system as well as the human, material, and economic resources that will be necessary. In this paper, we construct an extended Susceptib

The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use

Antibiotics are used extensively to control infections in humans and animals, usually by injection or a course of oral tablets. There are several methods by which bacteria can develop antimicrobial resistance (AMR), including mutation during DNA replication and plasmid mediated horizontal gene transfer (HGT). We present a model for the development of AMR within a single host animal. We derive criteria

We examine the problem of allocating a limited supply of vaccine for controlling an infectious disease with the goal of minimizing the effective reproduction number Re. We consider an SIR model with two interacting populations and develop an analytical expression that the optimal vaccine allocation must satisfy. With limited vaccine supplies, we find that an all-or-nothing approach is optimal. For

We developed a mathematical model to characterize how macular oxygenation may be affected by abnormalities in the retinal and choroidal oxygen supplies. The macular region is modeled as a layered structure including: ganglion cell and nerve fiber layers, inner plexiform layer, inner nuclear layer, outer plexiform layer, outer nuclear layer, inner segment of photoreceptors layer and retinal pigmented

The processes that determine the establishment of the complex morphology of neurons during development are still poorly understood. Here, we focus on the question how a difference in the length of neurites affects vesicle transport. We performed live imaging experiments and present a lattice-based model to gain a deeper theoretical understanding of intracellular transport in neurons. After a motivation

Beyond the reproductive system and reproductive behaviors, men and women exhibit major differences in many organ systems, including the anatomy of the brain, the activities of the stress and immune systems, and the metabolic and cardiovascular functions. A comprehensive understanding of the impact of these sex differences on health and disease is crucial to the development of effective sex-based therapies

With more than 1.7 million COVID-19 deaths, identifying effective measures to prevent COVID-19 is a top priority. We developed a mathematical model to simulate the COVID-19 pandemic with digital contact tracing and testing strategies. The model uses a real-world social network generated from a high-resolution contact data set of 180 students. This model incorporates infectivity variations, test sensitivities

We present a computational framework for analyzing and simulating mitochondrial ATP synthesis using basic thermodynamic and kinetic principles. The framework invokes detailed descriptions of the thermodynamic driving forces associated with the processes of the electron transport chain, mitochondrial ATP synthetase, and phosphate and adenine nucleotide transporters. Assembling models of these discrete

The sensitivity of cells to alterations in the microenvironment and in particular to external mechanical stimuli is significant in many biological and physiological circumstances. In this regard, experimental assays demonstrated that, when a monolayer of cells cultured on an elastic substrate is subject to an external cyclic stretch with a sufficiently high frequency, a reorganization of actin stress

Many physical phenomena in biology and physiology are described by mathematical models that comprise a system of initial value ordinary differential equations. Each differential equation may often be written as the sum of several terms, where each term represents a different physical entity. A wide range of techniques, ranging from heuristic observation to mathematically rigorous asymptotic analysis

Computational and mathematical models in biology rely heavily on the parameters that characterize them. However, robust estimates for their values are typically elusive and thus a large parameter space becomes necessary for model study, particularly to make translationally impactful predictions. Sampling schemes exploring parameter spaces for models are used for a variety of purposes in systems biology

About a year into the pandemic, COVID-19 accumulates more than two million deaths worldwide. Despite non-pharmaceutical interventions such as social distance, mask-wearing, and restrictive lockdown, the daily confirmed cases remain growing. Vaccine developments from Pfizer, Moderna, and Gamaleya Institute reach more than 90% efficacy and sustain the vaccination campaigns in multiple countries. However

When allocating limited vaccines to control an infectious disease, policy makers frequently have goals relating to individual health benefits (e.g., reduced morbidity and mortality) as well as population-level health benefits (e.g., reduced transmission and possible disease eradication). We consider the optimal allocation of a limited supply of a preventive vaccine to control an infectious disease

Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation

Understanding how environmental factors affect microbial survival is an important open problem in microbial ecology. Patterns of microbial community structure have been characterized across a wide range of different environmental settings, but the mechanisms generating these patterns remain poorly understood. Here, we use mathematical modelling to investigate fundamental connections between chemical

The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R0 is

Multistate statistical models are often used to characterize the complex multi-compartment progression of the disease such as cancer. However, the derivation of multistate transition kernels is often involved with the intractable convolution that requires intensive computation. Moreover, the estimation of parameters pertaining to transition kernel requires the individualized time-stamped history data

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death possibilities). We consider situations involving the application of social-distancing and other intervention measures in the time series

Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of

This study develops a novel model of a consumer-resource system with mobility included, in order to explain a novel experiment of competition between two breast cancer cell lines grown in 3D in vitro spheroid culture. The model reproduces observed differences in monoculture, such as overshoot phenomena and final size. It also explains both theoretically and through simulation the inevitable triumph

We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization.

For nearly eight decades the Luria–Delbrück protocol remains the preferred method for experimentally determining microbial mutation rates. However, earnest development and rigorous applications of statistical methods for mutation rate comparison using fluctuation assay data are a relatively recent phenomenon. While likelihood ratio tests tailored for the fluctuation protocol give investigators appropriate

The assessment and the management of the risks linked to insect pests can be supported by the use of physiologically-based demographic models. These models are useful in population ecology to simulate the dynamics of stage-structured populations, by means of functions (e.g., development, mortality and fecundity rate functions) realistically representing the nonlinear individuals physiological responses

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane

Phenomenological growth models (PGMs) provide a framework for characterizing epidemic trajectories, estimating key transmission parameters, gaining insight into the contribution of various transmission pathways, and providing long-term and short-term forecasts. Such models only require a small number of parameters to describe epidemic growth patterns. They can be expressed by an ordinary differential

The coffee berry borer (CBB, Hypothenemus hampei) is the most serious insect pest of coffee worldwide; understanding the dynamics of its reproduction is essential for pest management. The female CBB penetrates the coffee berry, eats the seed, and reproduces inside it. A mathematical model of the infestation progress of the coffee berry by the CBB during several coffee seasons is formulated. The model

For future application to studying regulation of microvascular oxygen delivery, a model is developed for O2 transport within an idealized volume of tissue, that is perfused by a continuous distribution of capillaries. Considering oxygen diffusion, convection, and consumption, an O2-dependent transfer term between the capillaries and tissue is used to extend previous single-compartment approaches to

The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency of treatments is subject to uncertainty. We consider two different regimes, or submodels, of the stochastic SIR model, where the population consists of three groups: susceptible, infected and recovered

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration.

The SARS-CoV-2 virus has spread across the world, testing each nation’s ability to understand the state of the pandemic in their country and control it. As we looked into the epidemiological data to uncover the impact of the COVID-19 pandemic, we discovered that critical metadata is missing which is meant to give context to epidemiological parameters. In this review, we identify key metadata for the

T cells protect the body from cancer by recognising tumour-associated antigens. Recognising these antigens depends on multiple factors, one of which is T cell avidity, i.e., the total interaction strength between a T cell and a cancer cell. While both high- and low-avidity T cells can kill cancer cells, durable anti-cancer immune responses require the selection of high-avidity T cells. Previous experimentation

Continuous-time stationary Markov jump processes among discrete sites are encountered in disparate biochemical ambits. Sites and connecting dynamical events form a ‘network’ in which the sites are the available system’s states, and the events are site-to-site transitions, or even neutral processes in which the system does not change site but the event is however detectable. Examples include conformational

Human movement is a key factor in infectious diseases spread such as dengue. Here, we explore a mathematical modeling approach based on a system of ordinary differential equations to study the effect of human movement on characteristics of dengue dynamics such as the existence of endemic equilibria, and the start, duration, and amplitude of the outbreak. The model considers that every day is divided

Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is to consider its ‘ancestral profile’ (the number of paths from each ancestral vertex to each leaf). In general, this information does not uniquely determine the underlying

In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell division on the lifetime risk of cancer, and report that symmetric division is more beneficial to delay the onset of cancer. The fate uncertainty of symmetric division

Understanding the way in which drug is released from drug carrying hydrogel based ophthalmic lenses aids in the development of efficient ophthalmic drug delivery. Various solute–polymer interactions affect solute diffusion within hydrogels as well as hydrogel–bulk partitioning. Additionally, surface modifications or coatings may add to resistance of mass transfer across the hydrogel interface. It is

Motivated by historical and present clinical observations, we discuss the possible unfavorable evolution of the immunity (similar to documented antibody-dependent enhancement scenarios) after a first infection with COVID-19. More precisely we ask the question of how the epidemic outcomes are affected if the initial infection does not provide immunity but rather sensitization to future challenges. We

Biodegradation is a pivotal natural process for elemental recycling and preservation of an ecosystem. Mechanistic modeling of biodegradation has to keep track of chemical elements via stoichiometric theory, under which we propose and analyze a spatial movement model in the absence or presence of bacterivorous grazing. Sensitivity analysis shows that the organic matter degradation rate is most sensitive

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from

Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous