The spread and control of antibiotic resistance is a major public health issue and challenge to address. This has driven a growing interest in bacteriophages, used alone or in combination with antibiotics to treat antibiotic-resistant biofilms. Evaluating the potential of phage therapy requires a detailed understanding of phages-microbes interactions, from their lytic activity to their capacity for transducing resistance genes. Mathematical models are a powerful tool to investigate specific aspects of these complex mechanisms, where a great number of biotic and abiotic interactions are involved. We present here a mathematical model exploring the role of phages in biofilm ecosystems and the potential of phage therapy to eliminate resistant bacterial populations. The model is formulated as a system of non-local partial differential equations in a one-dimensional, free-boundary domain. It incorporates all major routes of horizontal gene transfer - conjugation, natural transformation, and generalized transduction - along with selective pressure from metals and antibiotics, within a spatially structured, growing biofilm. Numerical simulations investigate the contribution of vertical and horizontal gene transfer, including generalized transduction, to the spread of plasmid-mediated resistance. We assess the potential of phage therapy, both as a stand-alone treatment and in combination with antibiotics, highlighting how phage-antibiotic synergy can substantially reduce the antibiotic concentration required to eradicate even resistant biofilms. The simulations reveal how phage predation contributes to selective pressure and shapes biofilm ecology.
Glaucoma is a group of diseases characterized by a degeneration of retinal ganglion cells (RGC) and is the second major cause of blindness worldwide. RGC vulnerability is thought to be the result of the interaction among mechanical, vascular, metabolic and neurodegenerative processes which progressively lead to RGC and optic nerve axon death. Clinical data show that glaucoma risk increases with age (A) and is higher in subjects with African-American (AA) than White-European (WE) descent. However, no quantitative mechanistic framework currently explains how A, race and ethnicity (χ) interact with cellular metabolism to influence RGC vulnerability, limiting our ability to predict which individuals are at highest risk or to identify metabolic pathways to be targeted therapeutically. To fill this gap, we propose a differential model of how the concentration of RGC mitochondria (MITO) metabolism products vary with time, A and χ. We represent the MITO synthase rate of adenosine triphosphate (ATP) as an exponentially decaying function of A and define the metabolic efficiency ηMITO as the ratio of the stationary ATP concentration and its reference value. Simulation results indicate that ηMITO decreases with A, with a maximum decrease of 37.84% and 32.4% for AA and WE subjects, respectively. Model predictions are consistent with clinical observations indicating higher glaucoma prevalence and severity in older individuals and in specific population groups, and strengthen the view of glaucoma as a multifactorial neurodegenerative disease in which metabolic vulnerability may represent one contributing pathway.
Individuals experience varying selective pressures as they pass through different classes, defined by developmental stage, age, physiological condition, or spatial location. Adaptive Dynamics models predict the long-term evolutionary dynamics of class-structured populations, but there is a trade-off when using the two forms of the selection gradient. The determinant-form - defined by the derivative of the determinant of the class transition rate matrix - has an explicit formula but lacks a biological interpretation. Alternatively, the reproductive-value-weighted-form (RVW-form) has a clear biological interpretation, but the reproductive values do not have explicit formulas outside of special cases. In this study, I show that the determinant-form is a sum of class-mediated indirect effects of selection, where for each indirect effect, selection alters the transition rate for a particular class and changes in that rate propagate through the population and indirectly affect the density of that class. I also show how to compute the reproductive values from minors of the population's transition rate matrix. Those minors represent the total effects between classes and can be visualized as pathways through a population's life cycle graph, mirroring classical results for discrete-time stage-structured models. To illustrate the utility of these results, I analyze a model of virulence evolution in an environmentally transmitted parasite, yielding novel predictions about how density-dependent host mortality and trait-dependent decay rates affect predictions related to the Curse of the Pharaoh hypothesis. I also analyze a model of the evolution of lysis and lysogeny, which helps clarify how host density and parasite life-history traits affect viral evolution.
Size is an important trait among marine phytoplankton as it influences a vast range of physiological, ecological, and evolutionary processes. For Trichodesmium, a cyanobacterial diazotroph important for the global nitrogen cycle, size is a flexible trait that can change because of its ability to form colonies. Trichodesmium colonies can persist from 10 µm to greater than 1 mm in the natural environment. Despite this known ability, we still do not know whether a maximum size limit exists for Trichodesmium colonies and, more importantly, whether any mechanisms regulate this limit. In this paper, we use a theoretical metabolic model to investigate the role of two factors known to influence Trichodesmium colony size: carbon dioxide and light availability. The greater the availability of carbon dioxide or the average light availability, the greater the potential colony size of Trichodesmium. Carbon limitations have a much stronger effect on colony sizes than light limitations. Higher respiratory costs, perhaps due to higher water temperatures, do not appear to limit maximum colony sizes unless they consume nearly all the carbon that is fixed. Our theoretical model highlights several scenarios that likely assert some control over the ecology of Trichodesmium in the global ocean. It also implies that natural colonies must have mechanisms to escape from carbon limitations. To achieve sizes like 1 mm, Trichodesmium colonies must be highly porous (>91%) or live in environments with a nutrient flux 12 times greater than what molecular diffusion can provide.
Remote digital symptom monitoring systems (rSMS) have been increasingly used in recent years to monitor symptoms, health-related quality of life, and other patient-reported outcomes in lung cancer. Previous studies have demonstrated variability in study design, types of rSMS, and outcomes used to assess benefits for patients and health care systems. However, there remains a lack of synthesized evidence pertaining to the similarities and differences among rSMS, including their theoretical underpinnings, key functional components, and reported benefits and limitations. This review aims to identify and synthesize existing research to map the current landscape of rSMS in lung cancer, including the theoretical foundations for its development and implementation, as well as its types, applications, and outcomes. This scoping review followed the Joanna Briggs Institute scoping review framework and adhered to the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) guidelines. A comprehensive literature search was conducted from database inception to October 16, 2025, across 7 English-language databases and 3 Chinese-language databases (CNKI, WanFang, and SinoMed). Eligible studies were peer-reviewed original research articles examining rSMS among adults with lung cancer. Data were independently screened and extracted by 2 reviewers, with discrepancies resolved by a third reviewer. Quantitative data were extracted using a standardized form and synthesized descriptively. Content analysis was performed to analyze the qualitative data. A total of 41 studies involving 11,765 patients and 85 health care providers were included. Twelve studies focused exclusively on advanced-stage lung cancer. Participants were generally middle-aged to older adults (mean ages 51-74 y), with male participants typically comprising 30% to 50% across studies. Most studies were conducted in the United States (n=19). We identified 32 patient-reported outcome measures that were used either as core rSMS components or as study outcomes. Four common functional modules were observed across rSMS: data collection, data analysis, response systems, and patient education. Qualitative evidence was limited; the most frequently reported benefit was the promotion of patient-centered care. Health care providers raised concerns about uncertain effectiveness and increased workload. This scoping review highlights the promising role of rSMS in lung cancer care and provides a structured map of current evidence. It adds to prior literature in 3 ways. First, it summarizes how and how often theoretical frameworks are reported and applied in rSMS development and implementation. Second, it synthesizes and categorizes four common functional modules across systems. Third, it differentiates measures embedded as rSMS components from those used as evaluation outcomes. These contributions clarify current practices and methodological gaps and underscore the importance of theory-informed design, functional clarity, and stakeholder engagement in the development of patient-centered, clinically meaningful, and sustainable rSMS platforms.
This commentary highlights the influenza model of Arino et al. (2008), emphasizing its analytical framework for evaluating vaccination, antiviral treatment, and behavioral withdrawal. Its simplicity and tractability illustrate the lasting value of deterministic compartmental models in understanding epidemic control.
The high heterogeneity of lung adenocarcinoma (LUAD) is largely due to its complex tumor immune microenvironment (TIME). Cancer-associated fibroblasts (CAFs) are a core matrix component of TIME. However, their functional heterogeneity and the specific molecular mechanisms driving tumor progression have not been fully elucidated. In addition, the role of nuclear receptor NR2F2 in tumor development is still controversial. This study integrated scRNA-seq data from the GEO database with RNA-seq data from TCGA and GEO and then performed multiple levels of validation through in vitro experiments. We adopted a systematic computational biology strategy and analyzed the cellular composition, interaction networks and functional states of cancer-associated fibroblasts (CAFs) in lung adenocarcinoma using Seurat, CellChat, and AUCell. According to the marker genes of key CAF subgroup, prognostic risk models were constructed through LASSO-Cox regression and validated in an independent cohort (GSE72094). Afterwards, we carried out in vitro experiments and validated the biological role of NR2F2 through a coculture system. Functional validation was conducted through siRNA knockdown, plasmid overexpression, CCK-8 assay, EdU labeling, and Transwell experiments. We noticed the CAF - 2 subgroup, characterized by the highest level of TGF - β signaling activation, sends various signals to different cell types. We constructed and verified a consistent prognostic signature made of 16 genes using the LASSO-Cox method. This model can effectively assess the risk of LUAD patients. The prognosis in high-risk group is worse. And we also do some analysis to find out that risk score is highly associated with immunosuppressive TME and high expressions of PD - L1. We have found in our further study that the expression of NR2F2 in CAF is associated with the promoting of matrix remodeling and metabolic reprogramming. From the coculture system and in vitro functional experiments, overexpression of NR2F2 in CAFs enhanced tumor cell proliferation and invasion, whereas knockdown of NR2F2 attenuated these malignant phenotypes. Using single-cell RNA sequencing data, we identified a CAF subgroup with the most active TGF-β signaling. Based on the marker genes of the subgroup, we constructed and validated an effective prognostic model, then we further screened and confirmed NR2F2 as a major pro-tumorigenic regulator from this feature gene set through single cell and transcriptome data as well as in vitro experiments. NR2F2 promotes malignant remodeling of TIME by synergistically enhancing TGF-β signaling and EMT processes. Our study provides not only a solid theoretical foundation but also a therapeutic target to explore new therapeutic options targeting the CAFs-TGF-β-EMT axis.
In temperate regions, respiratory virus epidemics recur on a yearly basis, primarily during the winter season. This is believed to be induced by seasonal forcing, where the rate at which the virus can be transmitted varies cyclically across the course of each year. Seasonal epidemics can place substantial burden upon the healthcare system, with large numbers of infections and hospitalisations occurring across a short time period. However, the interactions between seasonal forcing and the factors necessary for epidemic resurgence - such as waning immunity, antigenic variation or demography - remain poorly understood. In this manuscript, we examine how the dynamics of antibody waning and antigenic variation can shape the seasonal recurrence of epidemics. We develop a novel susceptible-infectious-susceptible (SIS) immuno-epidemiological model of respiratory virus spread, where the susceptible population is stratified by their antibody level against the currently circulating strain of the virus, with this decaying as both antibody waning and antigenic drift occur. In the absence of seasonal forcing, we demonstrate the existence of two Hopf bifurcations over the effective antibody decay rate, with associated periodic model solutions. When seasonal forcing is introduced, we identify complex interactions between the strength of forcing and the effective antibody decay rate, yielding myriad dynamics including multi-year periodicity, quasiperiodicity and chaos. The timing and magnitude of seasonal epidemics is highly sensitive to this interaction, with the distribution of infection timing (by time of year) varying substantially across the parameter space. Finally, we show that seasonal forcing can produce resonant damping resulting in a cumulative infection incidence that is less than would otherwise be observed.
Maximum swimming speeds increase with animal length up to about the size of wahoo or tuna, but increase little more beyond that: even the great whales do not appear much faster. Here, the scaling of top swimming speeds is considered in terms of meeting the power demands with muscle power and work. The power required to provide thrust to overcome drag scales with area (the square of length). Without other constraints, muscle power capacity would be proportional to volume (the cube of length) meaning that bigger animals should be able to swim faster - which they do, up to a limit. However, the capacity for muscle to produce work over a contraction is also limited, and animals are hindered in that they can contract locomotor muscles only once per gait cycle. Larger animals have lower frequency oscillations of their propulsive fins or flukes, presumably due to the geometric requirements of high hydrodynamic efficiency; and a reduction in efficiency equates to a loss of thrust for a given power supply at a given speed. It is proposed that, above a certain size - very approximately a length of 1 m - top speed does not increase with size because of the limited capacity of muscle to produce mechanical work, the geometry of hydrodynamic efficiency, and the resulting decrease in contraction frequency. However, a similar constant top speed limit is also predicted if cavitation - a phenomenon that damages propellers and would presumably hurt or injure fish or whales - is to be avoided.
The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of n individuals has been considered by several authors (Stadler in Journal of Theoretical Biology 261(1):58-66, 2009: Williams et al in Nature 602 (7895):162-168, 2022: Mitchell et al in Nature 606(7913):343-350, 2022: Johnson et al in Bioinformatics 39(9):btad561, 2023). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, Johnson et al Bioinformatics 39(9):btad561, 2023) proposed an analytical method for estimating the growth rate using the theory of coalescent point processes, which has comparable accuracy to more computationally intensive methods when the sample size n is large. We use a similar approach to obtain an estimate of the growth rate that is not based on the assumption that n is large. We demonstrate, through simulations using the R package cloneRate, that our estimator of the growth rate performs well in comparison with previous approaches when n is small.
Magnetic microporous organic network (MMON) materials have attracted extensive attention in sample pretreatment for their excellent adsorption performance and rapid magnetic separation. In this study, a series of novel core-shell structured MMON materials were synthesized by selecting two types of monomers and adjusting the molar ratio of monomers to magnetic spheres. Through pore structure design and theoretical calculations, the molecular sizes of two steroid hormones (progesterone and 17α-hydroxyprogesterone) were determined to be approximately 1.04-1.12 nm, while the pore size of C3C4-type MMON was approximately 1.47 nm, whose suitable pore size enabled efficient adsorption of the target analytes. Furthermore, the amino-carboxyl dual-functionalized magnetic microporous organic network (C3C4-NH2-COOH) was chosen as an effective adsorbent and exhibited rapid magnetic response, good thermal and chemical stability. Under the optimal conditions, the developed MSPE-UPLC-MS/MS method offered a low detection limit (0.5 pg mL-1), a wide linear range (1.0-1000.0 pg mL-1) and a rapid pretreatment process (less than 25 min). The method was successfully applied to the enrichment and determination of trace progesterone and 17α-hydroxyprogesterone in complex samples, with concentrations ranging from 0.062 to 19.19 ng mL-1 in serum and from 0.83 to 2.67 ng mL-1 in milk. Combined with density functional theory calculations and instrumental characterization, hydrogen bonding, π-π and hydrophobic interactions were involved in the extraction mechanism. This study achieved controllable synthesis of MMONs by regulating their pore size, shell thickness, and functional groups. Furthermore, it expanded the application of MMONs as adsorbents in the fields of food safety and early disease diagnosis.
Systems of oligonucleotide chemical replicator molecules provide some of the finest, empirically realizable models of prebiotic evolution. Yet, a full understanding of their eco-evolutionary implications is hampered by conflicting assumptions, modeling strategies, and therefore predictions in the literature. Here we construct a model of these systems that accounts for the reversible association of templates and copies, ultimately leading to self-inhibition and sub-exponential growth. We show that, contrary to predictions from simplified model descriptions, there are well-defined limits on the attainable diversity of different replicator species. We also demonstrate that increasing the overall concentration of the system increases diversity, but counterintuitively, an analogous increase in the available resource concentration has the opposite effect. Most notably, if an exponentially-growing replicator is also present in the system, it absorbs any increase in the total replicator concentration, while the concentrations of the sub-exponential replicators remain unchanged. In the context of prebiotic evolution, this means that in high-concentration local environments, an exponential replicator can reach disproportionately high concentrations even if its copying rate is lower than that of the sub-exponential replicators. In a variable environment, this can lead to the eventual stochastic extinction of its competitors, with the exponentially growing species taking over the community.
The interplay between tumor cells and macrophages plays a central regulatory role in cancer progression. In this study, we developed a mathematical model that incorporates tumor cells, M1-type macrophages, M2-type macrophages and an M3-type macrophage population characterized by dual phenotypic features. First, we analyzed the fundamental mathematical properties of the model and derived the conditions under which the system attains a tumor-free equilibrium or a coexistence state of tumor and immune cells. Second, global sensitivity analysis revealed that key parameters governing macrophage polarization and intercellular communication vary dynamically during tumor development. Bifurcation analysis further identified the polarization rate of M1-type macrophages (κ) and the baseline level of resting macrophages (M0) as critical determinants of the system's dynamical behavior. Notably, using approximate Bayesian computation for parameter inference and dynamic simulations, the model successfully recapitulated the evolutionary trajectories of eight tumor samples. The results demonstrate that lower tumor burden is significantly associated with higher M1-type macrophage infiltration and delayed peak time of M3-type macrophage activation. Moreover, survival analysis indicated that both enhanced M1-type macrophage infiltration and delayed peak time of M3-type macrophage activation are correlated with longer survival time. In summary, this study provides a theoretical framework for understanding the dynamic mechanisms underlying tumor-macrophage interactions and proposes two model-derived parameters as candidate prognostic markers: the level of M1-type macrophage infiltration and the peak time of M3-type macrophage activation. These predictions, while grounded in the model, require further experimental and clinical validation.
Cell differentiation is a pivotal evolutionary transition underlying multicellular complexity. Irreversible differentiation - a process in which cells permanently lose plasticity to become specialized types - is hypothesized to emerge predominantly in large, cell-rich organisms. However, the causal relationship between organismal size and the evolutionary origins of this extreme developmental commitment in multicellular organisms remains unclear. Here, by integrating developmental dynamics into a mathematical model, inspired by volvocine algae, we demonstrate that extreme irreversible differentiation (where all cell types exhibit irreversibility) most robustly evolves in intermediately sized multicellularity. This reveals a non-monotonic dependence of cell fate determinism on an organismal scale. Specifically, increasing organismal size initially promotes extreme irreversible differentiation by enhancing the selective advantages of cellular division of labor. Beyond a critical size threshold, however, further expansion destabilizes this extreme irreversibility due to its decreasing differentiation advantages compared with reversible differentiation. Counterintuitively, smaller organisms establish cellular irreversibility at earlier developmental stages than larger organisms. Our framework identifies an evolutionary double-edged sword: while body size expansion initially facilitates extreme differentiation irreversibility, it ultimately leads to its collapse. These results establish quantitative links between organismal dimensions and cell fate determinism, explaining the size-dependent evolution of developmental strategies in simple multicellular systems.
It is well established that hunting cooperation among predators can significantly influence the dynamic behavior of predator-prey interactions. In this paper, we present a qualitative analysis of a basic predator-prey model with hunting cooperation, including the existence and local stability of all feasible equilibria, and the global dynamics under certain conditions. Explicit expressions of the corresponding conditions are provided through ingenious and technical deduction. The obtained theoretical results reveal the effects of both the strength of hunting cooperation and the basic reproduction number on the population dynamics. Combining the qualitative analysis with quantitative analysis, we demonstrate the distribution of all possible asymptotic states of the model and give the corresponding biological interpretations. Notably, beyond the Allee effect and collapse in predators reported in existing works, we identify and discuss novel phenomena such as the inverse Allee effect and relaxation oscillations. These findings are instrumental for understanding predator-prey interactions with hunting cooperation and mitigating the risk of predator extinction.
Mathematical models are often used to predict the impact of infectious disease interventions. Most models, however, neglect how the intervention might influence patterns of contact within the population, and consequently change the dynamics of the epidemic. Here we introduce a mathematical model of disease transmission where contact rates change in response to a vaccination campaign. We explore two scenarios: homogeneous mixing, where contact rates increase uniformly across the population as vaccination coverage increases, and heterogeneous mixing, where the probability of contact depends on the vaccination statuses of the two individuals involved. We derive the effective reproduction number as a function of vaccine coverage and its transmission-blocking effectiveness, and show the conditions under which an increase in vaccination coverage leads to a growing number of infections. The model is then parameterised using United Kingdom COVID-19 data between 2020 and 2022 and vaccine-dependent contact rates are estimated using contact survey data. We observe that contact increases concordantly with vaccination coverage. Implementing this relationship in the model, we infer that the epidemiological impact of the rising contact rate was tempered by a mixing structure where contacts predominantly involve at least one vaccinated individual.
This paper presents the study of a DNA replication model grounded in the biochemical kinetics of DNA polymerases, which copy each DNA strand into a reverse-complement strand, except for rare point-like mutations caused by nucleotide substitution errors. Numerical simulations of many successive replications, starting from an arbitrary initial DNA sequence, show that the fractions of mono- and oligonucleotides converge toward compliance with Chargaff's second parity rule. The theoretical framework developed for this multireplication process demonstrates that the near-equalities of reverse-complement nucleotide fractions arise from two key features: (1) the dominant role of reverse complementarity in replication kinetics and (2) the low intrinsic error rate of DNA polymerases. Together, these two features yield a robust mechanistic basis for Chargaff's second parity rule. These considerations explain the existence of deviations with respect to the predictions of models assuming no-strand-bias conditions.
Oncolytic virotherapy, which employs genetically engineered viruses to target cancer cells and stimulate anti-tumour immune response, has emerged as a promising therapeutic strategy. In our previous work, we developed a stochastic agent-based model elucidating the spatial dynamics of infected and uninfected cells within solid tumours. Building upon this foundation, we present a novel stochastic agent-based model to describe the intricate interplay between the virus and the immune system; the agents' dynamics are coupled with a balance equation for the concentration of the chemoattractant that guides the movement of immune cells. To better understand the macroscopic behavior, we derive a formal continuum limit of the model and compare it quantitatively to the individual-based simulations in two spatial dimensions. Furthermore, we describe the travelling waves of the three populations, with the uninfected proliferative cells trying to escape from the infected cells while immune cells infiltrate the tumour. Simulations show a good agreement between agent-based approaches and numerical results for the continuum model. In certain parameter regimes, both the agent-based and continuum models exhibit oscillatory behavior, echoing Hopf bifurcations seen in non-spatial analogues. However, divergences between the models in specific cases highlight the critical role of stochasticity. Notably, we find that a premature immune response may undermine therapeutic efficacy, emphasising the importance of timing and modulation in combined immunovirotherapy approaches. This further suggests the importance of clinically improving the modulation of the immune response according to the tumour's characteristics and to the immune capabilities of the patients.
Islands are often regarded as "natural laboratories" for biology, and this applies also to ecological interactions between species that co-occur on islands. Mutualistic interactions, the association between organisms of two different species in which each benefits, should have important effects on the ability of species to establish, speciate or persist on islands. However, while island biogeography models increasingly incorporate the dynamics of biotic interactions in island ecosystems, current approaches do not consider the complexities introduced by mutualistic relationships, e.g., mutualism-driven immigration, cospeciation between mutualistic partners, dynamic formation and loss of mutualistic links. Here we present a new simulation model of island biogeography that explicitly includes mutualistic interactions and their influence on biodiversity at macroevolutionary scales. With this approach, we aim to better understand the effect of mutualism on insular diversity patterns over macroevolutionary time. Our model shows how mutualism influences species immigration, diversification and persistence through its effects on species-level processes. Strong mutualism is associated with higher species richness and more connected communities, while networks with weak or absent mutualism remain fragmented, with many species failing to establish interactions. By extending classical island biogeography to include ecological interaction networks, our study offers a new theoretical lens on how mutualism can influence biodiversity patterns and network structures in insular systems over evolutionary timescales.
Despite extensive studies of single hair-bundle dynamics, comparatively little attention has been paid to the collective dynamics arising in coupled hair-bundle systems. In this work, we investigate the collective dynamics of coupled hair bundles using a simplified dimensionless mechanical model that captures the essential nonlinear features of hair-bundle activity. We focus on two physically motivated interaction mechanisms: elastic and viscous coupling between neighboring bundles. The stability of synchronized motion is first analyzed using the master stability function framework and complemented by extensive numerical simulations. Our results demonstrate that within the present model, viscous coupling is significantly more effective than elastic coupling in promoting stable synchronization across a wide range of system parameters. Beyond complete synchronization, the network exhibits a variety of complex collective states, including non-stationary chimera patterns and clustered dynamics with distinct dynamical behaviors. Finally, we establish the occurrence of coherence resonance in the network, showing that an intermediate level of noise can enhance temporal regularity in the absence of external periodic forcing. These findings provide new insights into the mechanisms governing collective phenomena in interacting hair-bundle systems.