Advancing the Frontiers of Mathematical Life Sciences CSIAM Transactions on Life Sciences is an innovative, interdisciplinary journal dedicated to fostering the integration of applied mathematics and life sciences. As the boundaries between these fields continue to blur, the need for sophisticated mathematical models, computational techniques, and quantitative frameworks in understanding biological complexity has never been greater. Our journal aspires to become a leading publication at this intersection, serving as a premier platform for researchers worldwide to share their most novel, impactful, and rigorous scientific contributions. A Unique Platform for Interdisciplinary Research The journal welcomes high-quality, original research that harnesses mathematical principles, computational methods, and analytical techniques to address fundamental and applied questions in the life sciences. We seek to bridge the gap between mathematics and real-world biological phenomena, emphasizing the role of mathematical modeling, algorithmic innovation, and data-driven approaches in tackling complex biological systems. Our goal is to facilitate knowledge exchange between mathematicians, biologists, physicists, engineers, and medical researchers, fostering interdisciplinary collaboration that drives scientific discovery.
Effectively Preserving Biological Variations in Multi-Batch and Multi-Condition Single-Cell Data Integration
Understanding phenotypic differences at the cell level is critical for comprehending the underlying pathogenesis of related complex diseases. However, the biological variations are obscured by batch effects, posing a challenge for integrating multi-batch and multi-condition single-cell datasets. Here, we present scFLASH, a deep learning-based model specially designed to explore single-cell biological variations while correcting undesired batch effects. scFLASH employs a conditional variational autoencoder with adversarial training to separate biological variations from technical noise and introduces a penalized condition classifier to preserve condition-specific biological signals. Through comprehensive benchmarking evaluations, scFLASH shows superior integration performances compared to other state-of-the-art methods. Applied to datasets such as Alzheimer’s disease, COVID-19, and diabetes, we demonstrate that scFLASH is applicable to various scenarios, effectively integrating datasets with two or more conditions and different batch sources. scFLASH can enhance the gene expression profiles and identify the condition-related cell subpopulations, facilitating downstream analyses and offering biological insights into the cellular mechanisms of disease pathology.
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Vegetation Patterns: Structures and Dynamics
Vegetation patterns are a hallmark of ecosystem self-organization, emerging from the intrinsic dynamics of nonlinear feedback mechanisms and spatiotemporal interactions. This review systematically explores and examines the structural characteristics of these patterns, the phenomena of multistability, and their implications for ecosystem stability through the lens of mathematical modeling and dynamical systems theory. In particular, reaction-diffusion models serve as a key analytical tool, revealing how local positive feedback and non-local negative feedback drive self-organized spatial structures via Turing bifurcation. Bifurcation theory and potential landscape analysis further elucidate ecosystem multistability, quantifying critical transitions among uniform vegetation, patterned states, and bare soil under environmental conditions. Advances in spatial metrics, including traditional statistical measures (e.g. variance, autocorrelation) and emerging complexity-based indicators (e.g. hyper-uniformity, spatial permutation entropy) provide robust methods for detecting ecological functional shifts and early-warning signs of regime shifts. Additionally, restoration strategies grounded in structural optimization, such as optimal control theory, offer a theoretical framework for vegetation pattern reconstruction and stability regulation, particularly in arid and semi-arid regions. Future research should integrate multiscale modeling and interdisciplinary approaches to deepen our understanding of vegetation structure-function relationships. Such efforts will yield both theoretical insights and practical solutions for mitigating global ecological degradation and climate change.
Mathematical Modeling of Green Sea Turtle Population Dynamics Under Environmental and Thermal Constraints
Global warming and deteriorating environmental conditions have raised concerns about the persistence of green sea turtle populations, whose reproduction is governed by temperature-dependent sex determination. This study employs mathematical modeling to investigate these ecological challenges. Building on our previous models of green sea turtle population dynamics, we develop a sex-structured and stage-structured life history model that integrates temperature-dependent sex determination and ecological viability, offering a mechanistic framework for understanding green sea turtle population dynamics under climate and environmental stress. Our findings reveal that population dynamics are governed by an Allee-adjusted reproductive number, which accounts for both thermal and environmental influences. Additionally, we conduct a global stability analysis of the collapsed equilibrium using the singular perturbation approach, offering insights into long-term population viability. While additional parameter validation is necessary for definitive conclusions, our results illustrate how climate change and deteriorating environmental conditions shape the long-term viability of green sea turtle populations.
Evolutionary Stability in Stochastic Environments
Evolutionary stability (or evolutionarily stable strategy) is the core concept of evolutionary game theory. Although evolutionary game theory has achieved great success in evolutionary biology, economics and social science, etc. over the past forty years, how to understand the impact of environmental stochastic fluctuations on the evolutionary stability is still one of the most challenging issues in evolutionary game theory. This paper mainly introduces the recent advances in the study of stochastic evolutionary stability and stochastic Nash equilibrium within the framework of stochastic evolutionary game dynamics. These studies may provide a possible way to better understand the complexity of evolutionary game dynamics in real world situations.
Co-Evolution of Behavior Change and Infectious Disease Transmission Dynamics: A Modelling Review
During infectious disease outbreaks, the dissemination of information and the dynamic adjustment of intervention strategies trigger psychological and behavioral changes among individuals, which significantly influence disease transmission. Mathematical models have played a crucial role in analyzing the interplay between behavioral changes and disease spread. In this review, we revisit research studies that model behavioral changes during epidemics and classify the literature based on different modeling approaches. Specifically, we categorize these models into three main types: (1) modifying the incidence function to incorporate behavior-driven changes, including a novel approach that utilizes neural networks to describe the incidence rate; (2) introducing additional compartments to represent subpopulations with different behaviors; and (3) employing game-theoretic modeling to study the interactions between infectious disease dynamics and behavioral changes. In the game-theoretic framework, we also examine how key epidemiological metrics – such as the peak size and peak time of the first wave, as well as the final epidemic size – are affected when behavioral changes are incorporated into the classic SIR model. For each category, we introduce the classical modeling frameworks and their extensions, analyzing their advantages and limitations. Finally, we summarize the key findings and outline several promising directions for future research.
On a Juvenile-Adult Model: The Effects of Seasonal Succession and Harvesting Pulse
In this paper, a juvenile-adult population model incorporating seasonal succession and pulsed harvesting is developed. The seasonal succession captures the cyclical change between favorable and unfavorable environmental conditions, while the pulsed harvesting represents a periodic human intervention, targeting the adult population exclusively during favorable seasons. The principal eigenvalue for the corresponding linearized system is defined and its dependence on both the intensity of the harvesting pulses and the duration of the unfavorable season is analyzed. Explicit expressions and analysis of the principal eigenvalue for a logistic model extended with seasonal succession and pulsed harvesting are provided specifically. Based on the principal eigenvalue, we establish sufficient conditions for population persistence and extinction. Numerical simulations are conducted to validate these analytical results. Our findings demonstrate that higher harvesting intensity during the favorable season is detrimental to species survival. Furthermore, extending the duration of the unfavorable season can trigger a critical transition from population persistence to extinction.
Effect of Interspecific Mosquito Competition on Mosquito Suppression with Sterile Mosquitoes
In the interactive dynamical models, we include two different competing wild mosquito species and sterile mosquitoes which are the same type as one of the competing wild mosquitoes. We study the dynamics of the interspecific competition models in different circumstances. We explore how the interspecific competition affects the wild mosquito control with releases of sterile mosquitoes and establish a new release threshold based on the effect of the competition. Numerical examples are provided in each case to illustrate the impact on the mosquito control.
Global Dynamics of a Threshold Control Discrete Population Model with Allee Effects
This paper investigates a threshold control discrete population model with Allee effects, characterized by density-dependent growth functions separated at a critical population threshold. The model captures diverse ecological scenarios through simple switching mechanisms while maintaining biological realism. We overcome analytical challenges in piecewise systems by developing a complete classification of five distinct dynamics, revealing how critical transitions emerge at specific parameter boundaries. One key theoretical contribution identifies the precise conditions generating persistent oscillations, a counterintuitive result demonstrating how discontinuous switching can sustain periodic behavior despite monotonic growth functions. These findings provide actionable conservation strategies, including extinction prevention protocols and sustainable harvesting policies. The framework offers both theoretical advances in piecewise dynamical systems and practical tools for ecological management, with potential applications in species conservation and ecosystem restoration.
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Determine Vaccination Priority in a Population of Partially Overlapping Groups
Personal diverse interests and many group interactions naturally create partially overlapping groups within a population. Those who belong to multiple groups play a crucial role in spreading of infectious diseases across the whole population. We develop an algorithm to decompose the microscopic overlap structure of groups with representing a population of partially overlapping groups as a hypergraph of partially overlapping hyperedges, and characterize it using a newly defined overlap matrix. We formulate a specific multi-group SIR epidemic model, and address a one-time preventive vaccine allocation problem aimed at effectively reducing the basic reproduction number. By leveraging perturbation theory, we derive a principled ranking index to measure the vaccination priority of different groups, and establish a ranking vaccination strategy, which usually outperforms random vaccination strategies as verified by a series of numerical examples. These results offer a theoretical foundation for public health decision-making to develop effective vaccination allocation plans.
Mathematical Analysis of a Predator-Prey System with Adaptive Prey Motion
A mathematical model is proposed that describes the adaptive spatial movement of prey towards higher population density to reduce predation risk. The model admits the increased nonlinearity and the global existence of solutions of the system is established in Sobolev space through analytical estimates. The conditions for the Turing instability from a coexistence steady state are obtained, and sharp conditions for the asymptotical stability of the positive equilibrium in a large region are established with the help of a Lyapunov function. Numerical simulations are presented to support the theoretical results and demonstrate the versatility of spatial models.
Ideal Free Distribution of Multiple Species in a Time-Periodic and Patchy Habitat
Dispersal strategies that lead to the ideal free distribution (IFD) were shown to be evolutionarily stable in various ecological models. In this paper, we investigate this phenomenon in time-periodic environments where $N$ species – identical except for dispersal strategies – compete. We extend the notions of IFD and joint IFD, previously established in spatially continuous models, to time-periodic and spatially discrete models and derive sufficient and necessary conditions for IFD to be feasible. Under these conditions, we demonstrate two competitive advantages of ideal free dispersal: if there exists a subset of species that can achieve a joint IFD, then the persisting collection of species must converge to a joint IFD for large time; if a unique subcollection of species achieves a joint IFD, then that group will dominate and competitively exclude all the other species. Furthermore, we show that ideal free dispersal strategies are the only evolutionarily stable strategies. Our results generalize previous work by construction of Lyapunov functions in multi-species, time-periodic setting.
Stability and Persistence of an Age Structured Epidemic Model with Mutation and Vaccination
In this paper, we propose an age-structured epidemic model with strain mutation and age-based vaccination. We define the reproduction numbers of both the original and mutant strains ($R_{0}^{1}$ and $R_{0}^{2}$). If the reproduction number $R_{0} < 1$, the disease-free steady state is locally asymptotically stable. If the reproduction number $R_{0}^{2} > 1$, there exists a dominant steady state of the mutant strain. Conditions for local stability of this dominant steady state are also obtained. If both reproduction numbers $R_{0}^{1}$ and $R_{0}^{2}$ are greater than 1, a coexistence steady state may occur. Finally, the uniform persistence of the disease described by our age-structured model is strictly proved when the reproduction number $R_{0}^{1} > 1.$ By using the data of the COVID-19 epidemic in Wuhan and the theoretical results obtained in this paper, some numerical calculations are carried out to demonstrate the effect of the age-based vaccination strategy.
Modeling Effects of ${\rm T}$ Cell Exhaustion on the Dynamics of Chronic Viral Infection
During chronic viral infection, sustained antigen stimulation leads to exhaustion of virus-specific ${\rm CD}8^+$ ${\rm T}$ cells, characterized by elevated expression of inhibitory receptors and progressive functional impairment, including loss of cytokine production, reduced cytotoxicity, and diminished proliferative capacity. In this paper, to investigate how ${\rm T}$ cell exhaustion influences viral persistence, we developed a within-host mathematical model integrating viral infection dynamics with adaptive immune responses. The model demonstrates three non-trivial equilibria: infection-free equilibrium ($S_1$), uncontrolled-infection state ($S_2$), and immune-controlled equilibrium ($S_3$). Through dynamical systems analysis, we established the local stability of all states ($S_1$-$S_3$) and prove global stability for both $S_1$ (complete viral clearance) and $S_2$ (chronic infection). Notably, the system exhibits Hopf bifurcations at $S_2$ and $S_3$, with distinct critical thresholds governing oscillatory dynamics. Numerical simulations reveal that successful immune-mediated control of viral load and infected cell levels requires maintenance of low ${\rm CD}8^+$ ${\rm T}$ cell exhaustion rates.
Revisiting Hopf Bifurcation in Single-Species Models with Time Delays
Hopf bifurcation in delay differential equations has been a central topic in the study of complex dynamical behaviors in biological and ecological systems. In this review, we revisit Hopf bifurcation phenomena in single-species models that incorporate time delays, emphasizing recent progress in both ordinary and partial differential equation frameworks. We present a comprehensive overview of classic and contemporary models, such as Wright’s equation, Nicholson’s blowflies equation, and diffusive logistic models, highlighting criteria for local and global bifurcations, the geometric and analytical methods used to determine critical values, and the stability of emerging periodic solutions. The review also covers structured models with age, stage, advection, and spatial effects, as well as equations with multiple delays. Through this survey, we aim to consolidate theoretical insights and provide a unified understanding of delay-induced oscillations in population models, laying the groundwork for future developments in delay-driven dynamics.
A Brucellosis Model with Different Clinical Symptoms and a Time Delay Representing Incubation Period: Global Dynamics and Data Fitting
Brucellosis is a significant zoonotic disease that has a high incidence rate in sheep, particularly in the Inner Mongolia region of China. To better investigate its transmission dynamics, this paper proposes a sheep brucellosis model incorporating acute and chronic infections, a saturated incidence rate describing environmental transmission and a time delay representing the incubation period. By constructing Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: If $\mathcal{R}_0<1,$ the brucellosis always dies out; if $\mathcal{R}_0>1,$ a unique endemic equilibrium exists and is globally asymptotically stable. Using data of sheep brucellosis cases in Inner Mongolia from 2016 to 2020, unknown parameters and the basic reproduction number $(\mathcal{R}_0=1.544)$ are estimated via the Markov chain Monte Carlo method. Numerical simulations show that reducing the transmission rate of acutely infected sheep while increasing the culling rate of symptomatic infected sheep is the most effective strategy to control the spread of brucellosis in Inner Mongolia. Notably, decreasing the proportion of acutely infected sheep or increasing acute-to-chronic conversion rate may lead to a significant short-term increase in chronically infected sheep.
The Dynamics of CD4+ T Cell Proliferation in Autopilot Model
Under the assumption of the autopilot model, after antigen stimulation exceeds a threshold, the proliferation and effector function of CD4+ T cells are self-sustained and do not need further antigen stimulation. However, CD4+ T cell proliferation is driven by their production of IL-2, which then binds to cells and triggers proliferation. Without regulation, this autocrine process forms a positive feedback loop that causes uncontrolled proliferation. This study mathematically modeled the regulatory mechanisms of the CD4+ T cell response after infection, focusing on the role of IL-2 self-regulation and Treg in this mechanism. We performed a phase-space analysis to study the long-term behavior of the proliferation process. Our results show that IL-2 self-regulation alone is not sufficient to fully inhibit CD4+ T cell response, and that the involvement of Treg cells is essential to regulate the immune response effectively. In particular, when the rate of CD4+ T cell proliferation is controlled by the rate of IL-2-mediated CD4+ T cell removal, Treg cells control CD4+ T cell proliferation by releasing immunosuppressive cytokines such as IL-10 and TGF-$\beta$, thus inhibiting the unregulated immune response.
A Two-Patch Epidemic Model with Prevalence-Dependent Contact Patterns and Migration Rates
We consider a two-patch Susceptible-Infected-Recovered epidemic model that incorporates awareness-driven behavioural changes in both contact and mobility patterns. Individuals modify their behaviour in response to a perceived risk of infection, which is modelled through two awareness variables that depend either on the current or past disease prevalence in each patch. We qualitatively analyse the model through stability and bifurcation theory and derive threshold conditions that determine the existence and stability of the biologically relevant equilibria. We find that awareness-induced behavioural changes in contact and mobility can destabilise mixed equilibria – where the disease persists in one patch only – and contribute to the emergence of stable co-endemic states. When awareness depends on past epidemic values, the stability analysis shows that mixed equilibria may lose stability via Hopf bifurcations, depending on the sign of some awareness-related parameters. Finally, the impact of the behaviour-related parameters on the epidemic dynamics is investigated through numerical simulations.
Dynamics of Coral-Algae Phase Shifts via Ecological Stoichiometric Approach
Coral reefs have evolved over hundreds of millions of years and are now considered one of the most critical yet vulnerable ecosystem on earth. Environmental changes, including variations in light availability, nutrient levels, and fishing pressure, can significantly impact the health of coral reefs, potentially leading to ecosystem degradation. A coral-macroalgae-herbivorous fish model is developed based on ecological stoichiometry to investigate the dynamics of coral-algae phase shifts. The positivity, invariance, and dissipativity of the model are carefully established, the existence and stability of equilibria are rigorously demonstrated, and rich dynamics such as bistability and various types of periodic oscillations are numerically explored. Furthermore, the effects of environmental factors (e.g., light intensity, nutrient levels, and fishing pressure) on the system’s dynamics are investigated. The main findings highlight that environmental variations are key drivers of ecological phase transitions in coral reef ecosystems, providing more insights into the mechanisms underlying coral-algae dynamics and offering implications for the sustainable management of coral reefs.
Exploring the Impact of Media Coverage and Limited Medical Resources on Influenza Transmission Dynamics: Insights from a Mathematical Modeling Study
Changes in personal protective behaviors driven by media influence contribute to epidemic prevention and control, whereas limited medical resources constrain the effectiveness of such interventions. In this study, we propose a novel influenza transmission model with the media impact and limited medical resources. Theoretical and numerical analyses reveal some complex nonlinear dynamics, including saddle node bifurcations, forward and backward bifurcations, and both subcritical and supercritical Hopf bifurcations. Besides, two types of bistable scenarios are identified: bistability of a disease-free equilibrium and an endemic equilibrium, and bistability of two different endemic equilibria. In addition, we fit the model to the monthly new influenza reported case data from August 2023 to October 2024 in Jiangsu, China, where the fitting results successfully capture the observed epidemic trends. The estimated basic reproduction number $\mathcal{R}_0=1.2183>1$ implies sustained transmission. Finally, sensitivity analysis suggests that effectively controlling influenza transmission can be achieved by decreasing the population input rate, transmission rate, awareness loss rate, and medical saturation constant, as well as increasing the awareness transmission rate, media response intensity, and maximum recovery rate. These findings highlight the critical role of combining public awareness initiatives with enhanced medical resource allocation to strengthen influenza prevention and control efforts.
Dynamics and Optimal Control of a Size-Structured Influenza Model Linking Within-Host and Between-Host
Multi-scale models improve the prediction of key epidemic factors and disease prevalence by capturing the interaction between individual immune responses and the spread of diseases among the population, helping to implement targeted control strategies for disease management. In this paper, we develop a novel size-structured influenza model based on the nested rules, aiming to explore how the replication of influenza virus affects its transmission at a population level. We calculate the basic reproduction numbers separately at the individual and population levels and rigorously prove the conditions under which the feasible equilibrium exists and is stable. Then, by evaluating the effectiveness of four measures consisting of individual antiviral treatment and population vaccination, we can determine an optimal treatment to minimize both the influenza cases and the total expenditure on influenza prevention. Numerical results reveal the complex interactions between the two interventions and the progression of the epidemic.
Stochastic Dynamics Between HIV-1 Latent Infection and cART Efficacy Within the Brain Microenvironment
We develop a stochastic human immunodeficiency virus type 1 (HIV-1) infection model to analyze combination antiretroviral therapy (cART) dynamics in the brain microenvironment, explicitly accounting for two infected cell states: (1) productively infected and (2) latently infected populations. The model introduces two key epidemiological thresholds $- \ \overline{\mathcal{R}}_{c1} $ (productive infection) and $ \overline{\mathcal{R}}_{c2}$ (latent infection) $-$ and defines the stochastic control reproduction number as $ \overline{\mathcal{R}}_c = \max\{\overline{\mathcal{R}}_{c1}, \overline{\mathcal{R}}_{c2}\} $. Our analysis reveals three distinct dynamical regimes: (1) viral extinction $(\overline{\mathcal{R}}_c<1):$ the infection clears exponentially with probability one; (2) latent reservoir dominance $( \overline{\mathcal{R}}_c = \overline{\mathcal{R}}_{c2} >1):$ the system almost surely converges to a purely latent state, characterizing stable viral reservoir formation; (3) persistent productive infection $( \overline{\mathcal{R}}_c = \overline{\mathcal{R}}_{c1} > 1):$ the infection persists indefinitely with a unique stationary distribution, for which we derive the exact probability density function. And numerical simulations validate these theoretical predictions, demonstrating how environmental noise critically modulates HIV-1 dynamics in neural reservoirs. Our results quantify the stochastic balance between productive infection, latency establishment, and cART efficacy, offering mechanistic insights into viral persistence in the brain.
Invasion Dynamics of Alien Mussels: A Mussel-Algae Model with Time Delay in Filter Feeding and Environmental Variability
The dynamic behavior of alien mussels interacting with algae after arriving in a new environment has long been a focus of invasion ecology research. This paper extends and analyzes a classical mussel-algae model by incorporating a time delay in mussel filter feeding and accounting for environmental variability. We theoretically study the stochastic dynamics, including the global existence and uniqueness of the positive solution, the existence of a unique stationary distribution, and mussel extinction, using tools from stochastic analysis. Furthermore, we derive an explicit expression for the probability density function around the quasi-stable equilibrium by solving the corresponding Fokker-Planck equation. Our theoretical and numerical results indicate that: (a) larger environmental disturbances or artificial removal can effectively prevent the survival of alien mussels in novel habitats, (b) a decreased filter feeding rate leads to an accelerated extinction rate of mussels, and (c) an increased consumption constant $c$ decelerates the transition rate of mussels from the initial state to the extinction state, as analyzed through the mean first passage time of mussels. These findings highlight the complex interaction between intrinsic and extrinsic factors in influencing the invasion dynamics of alien mussels.
On a Cross-Diffusive SIS Epidemic Model with Singular Sensitivity
This work introduces a repulsive chemotaxis susceptible-infected-susceptible (SIS) epidemic model with logarithmic sensitivity and with mass-action transmission mechanism, in which the logarithmic sensitivity assumes that the chemotactic migration of susceptible populations is suppressed by large density of infected individuals while the biased movement is strongly sensitive to a density variation of small infected population. Under suitable regular assumption on the initial data, we firstly assert the global existence and boundedness of smooth solutions to the corresponding no-flux initial boundary value problem in the spatially one-dimensional setting. Second, we investigate the effect of strong chemotaxis sensitivity on the dynamics of solutions through extensive numerical simulations. Our numerical study suggests that although this chemotaxis model includes an unbounded force of infection, the blow-up of solutions cannot occur in two dimensions, which remains to be analytically verified. Moreover, the numerical studies on the asymptotic profiles of the endemic equilibrium indicate that the susceptible populations move to low-risk domains whereas infected individuals become spatially homogeneous when the repulsive-taxis coefficient is large. Furthermore, simulations performed in the one- and two-dimensional cases find that rich patterns, like periodic peaks, structured holes, dots and round circles, may arise at intermediate times, but eventually are smoothed out, and that clusters of infection can emerge in a heterogeneous environment. Additionally, our numerical simulations suggest that the susceptible population with larger chemosensitivity, tends to respond better to the infected population, revealing the effect of strong chemotaxis sensitivity coefficient on the dynamics of the disease.
Integrating Gene Regulatory Network Dynamics with Heterogeneous Stem Cell Regeneration
Stem cell regeneration is crucial for development and maintaining tissue homeostasis in self-renewing tissues. The dynamics of gene regulatory networks (GRNs) play a vital role in regulating stem cell renewal and differentiation. However, integrating the quantitative dynamics of GRNs at the single-cell level with population-level stem cell regeneration poses significant challenges. This study presents a computational framework that links GRN dynamics to stem cell regeneration through an inheritance function. This function captures epigenetic state transitions during cell division in heterogeneous stem cell populations. Our model derives this function using a hybrid approach that integrates cross-cell-cycle GRN dynamics, effectively connecting cellular-level GRN structures with population-level regeneration processes. By incorporating GRN structure directly into stem cell regeneration dynamics, this framework simulates cross-cell-cycle gene regulation using individual-cell-based models. The scheme is adaptable to various GRNs, providing insights into the relationship between gene regulatory dynamics and stem cell regeneration. Additionally, we propose a future perspective that integrates single-cell ribonucleic acid sequencing data, GRN analysis, and cell regeneration dynamics using AI-driven tools to enhance the precision of regenerative studies.
Patterns of Transmission Dynamics of Severe Fever with Thrombocytopenia Syndrome Virus in Dalian: Roles of Systemic, Co-Feeding, and Transovarial Routes
Severe fever with thrombocytopenia syndrome (SFTS) is an emerging tick-borne zoonotic disease caused by severe fever with thrombocytopenia syndrome virus. In recent years, there has been an increasing number of human SFTS cases in central and northeast China. In the study region, Dalian, the number of human cases in years between 2011 and 2019 exhibited recurrent patterns in synchrony with the seasonal temperature variation. Here, we develop a transmission dynamics model to incorporate contact characteristics of animal and human hosts from published literature, and fit the model to historical temperature and human incidence data in our study region to analyze trends in human SFTS incidence and the time trends of SFTS prevalence within the natural tick-host cycle. Our analysis highlights the contributions of the systemic, co-feeding, and transovarial transmission routes, and provides insights for cost-effective public health interventions targeted to reducing transmission in these coexisting transmission pathways.
Modeling the Spatial Motion of Chromatin and the Whole Process of Gene Transcription
Biological experiments have verified that chromatin organization has importance influence on gene expression, but the conventional models of gene expression neglect this influence, in particular the effect of enhancer-promoter (E-P) communication on gene expression. Here we first review properties of the classical Rouse model that is a quite accurate description of chromatin as confirmed by microscopy experiments. Second, we extend this model to the polymer models with long-range interactions so that they include E-P communications that are typically long-range interactions. We also carry out theoretical analysis for the extended models. Third, we establish mathematical models for the whole process of gene transcription, which consider connections between upstream chromatin dynamics and downstream promoter kinetics. These connections consider two possible ways of regulation: The one via E-P encounter probability and the other via E-P spatial distance, both supported by a different experimental measurement. These models lay solid foundations not only for the deep study of gene-expression dynamics but also for the statistical inference of experimental data.
Basic Reproduction Number of Infectious Disease in Heterogeneous Environment: A Scoping Review
This paper overviews the recent advances how spatial-temporal heterogeneity affects the spread of epidemic diseases from the perspective of basic reproduction number. First part focuses upon the theoretical studies and applications of seasonal effects on infectious invasion. Then the investigations are introduced to demonstrate the role of spatial structure and spatial contact patterns in the prevention of disease outbreaks. Suggestions are presented for potential future researches.
Mathematical Modeling of Tumor-Immune Interactions: Methods, Applications, and Future Perspectives
Mathematical oncology is a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. Tumor-immune interactions play a crucial role in cancer biology, influencing tumor progression and the effectiveness of immunotherapy and targeted treatments. However, studying tumor dynamics in isolation often fails to capture the complex interplay between cancer cells and the immune system, which is critical to disease progression and therapeutic efficacy. Mathematical models that incorporate tumor-immune interactions offer valuable insights into these processes, providing a framework for analyzing immune escape, treatment response, and resistance mechanisms. In this review, we provide an overview of mathematical models that describe tumor-immune dynamics, highlighting their applications in understanding tumor growth, evaluating treatment strategies, and predicting immune responses. We also discuss the strengths and limitations of current modeling approaches and propose future directions for the development of more comprehensive and predictive models of tumor-immune interactions. We aim to offer a comprehensive guide to the state of mathematical modeling in tumor immunology, emphasizing its potential to inform clinical decision-making and improve cancer therapies.
Stability Analysis of an SIS Epidemic Model in Heterogeneous Environment
This paper studies an susceptible-infected-susceptible reaction-diffusion model in spatially heterogeneous environment proposed in [Allen et al., Discrete Contin. Dyn. Syst., 21, 2008], where the existence and uniqueness of the endemic equilibrium are established and its stability is proposed as an open problem. However, till now, there is no progress in the stability analysis except for special cases with either equal diffusion coefficients or constant endemic equilibrium. In this paper, we demonstrate the first criterion in determining the stability of the non-constant endemic equilibrium with different diffusion coefficients. Thanks to this criterion, when one of the diffusion rates is small or large, the impact of spatial heterogeneity on the stability can be characterized based on the asymptotic behavior of the endemic equilibrium.
Multiple Stable Traveling Wave Profiles of a System of Conservation Laws Arising from Chemotaxis
In this paper, we establish the existence and nonlinear stability of a hyperbolic system of conservation laws derived from a repulsive singular chemotaxis model. By the phase plane analysis alongside Poincaré-Bendixson theorem, we first prove that this hyperbolic system admits three different types of traveling wave profiles, which are explicitly illustrated with numerical simulations. Then using a unified weighted energy estimates and technique of taking anti-derivatives, we prove that all types of traveling wave profiles, including non-monotone pulsating wave profiles, are nonlinearly and asymptotically stable if the initial data are small perturbations with zero mass from the spatially shifted traveling wave profiles.