Under the assumption of the autopilot model, after antigen stimulation ex- ceeds 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 pro- liferation 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 regu- latory 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 effec- tively. 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-β, thus inhibiting the unregulated immune response.

During infectious disease outbreaks, the dissemination of information and the dynamic adjustment of intervention strategies trigger psychological and behav- ioral 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 dif- ferent 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 dif- ferent 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 ad- vantages and limitations. Finally, we summarize the key findings and outline several promising directions for future research.

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 af- fects 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 pro- vided in each case to illustrate the impact on the mosquito control.

Vegetation patterns are a hallmark of ecosystem self-organization, emerg- ing from the intrinsic dynamics of nonlinear feedback mechanisms and spatiotem- poral interactions. This review systematically explores and examines the structural characteristics of these patterns, the phenomena of multistability, and their implica- tions for ecosystem stability through the lens of mathematical modeling and dynam- ical 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 tran- sitions among uniform vegetation, patterned states, and bare soil under environmen- tal 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 ecolog- ical 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.

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 math- ematical modeling to investigate these ecological challenges. Building on our previ- ous models of green sea turtle population dynamics, we develop a sex-structured and stage-structured life history model that integrates temperature-dependent sex deter- mination 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 repro- ductive number, which accounts for both thermal and environmental influences. Ad- ditionally, 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 re- sults illustrate how climate change and deteriorating environmental conditions shape the long-term viability of green sea turtle populations.

In this paper, a juvenile-adult population model incorporating seasonal suc- cession 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 cor- responding 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 prin- cipal eigenvalue, we establish sufficient conditions for population persistence and ex- tinction. 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 unfavor- able season can trigger a critical transition from population persistence to extinction.

Understanding phenotypic differences at the cell level is critical for com- prehending the underlying pathogenesis of related complex diseases. However, the biological variations are obscured by batch effects, posing a challenge for integrat- ing 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 condi- tion-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 integrat- ing datasets with two or more conditions and different batch sources. scFLASH can enhance the gene expression profiles and identify the condition-related cell subpopu- lations, facilitating downstream analyses and offering biological insights into the cel- lular mechanisms of disease pathology.