{"title":"Switch-like Behavior in the Heme Receptor for Vibrio Vulnificus.","authors":"Kathryn S Lynch, James P Keener","doi":"10.1007/s11538-025-01505-2","DOIUrl":"10.1007/s11538-025-01505-2","url":null,"abstract":"<p><p>Switch-like behavior and bistability are important features in gene regulatory networks, allowing cells to distinguish between changing environments and express certain genes only under the appropriate conditions. Vibrio vulnificus, an opportunistic Gram-negative marine pathogen, has iron as a limiting growth factor. When inside a human host, this bacteria utilizes heme as a source of iron, necessitating the ability to turn this heme acquisition system off and on in response to environmental pressures. As establishment of infection depends on V. vulnificus's ability to change from a marine to human environment, the ability to switch on the heme-intake system is an important part of establishment of initial infection. In particular, the protein HupA is a key part of the bacteria's heme importation complex, and is regulated primarily by a divergently transcribed protein, HupR. The dynamics of this regulation result in a genetic switch, allowing the bacteria to differentiate between high iron or high heme environments, determining which source of iron should be used. Bifurcation analysis of this network uncovers a saddle-node bifurcation, which encodes this switch-like behavior into the regulation of the heme transport system and allows different levels of expression for HupA depending on external concentrations of heme and iron. The influences of other parameters in this system are also investigated; in particular, promoter leakage is found to be required to enable this bistability, indicating the importance of imperfect regulation in a cell's ability to respond to the environment.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"125"},"PeriodicalIF":2.2,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12335394/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144803580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pattern Formation Driven by Nonlocal Perception in a Delayed Pine Wilt Disease Model with Top-Hat Kernel.","authors":"Jia Li, Yuting Ding, Yongli Song","doi":"10.1007/s11538-025-01504-3","DOIUrl":"10.1007/s11538-025-01504-3","url":null,"abstract":"<p><p>Nonlocal perception plays a crucial role in studying animal cognitive movement modeling. In this paper, the impact of nonlocal perception on pattern formation is analyzed, and it is applied to study the control of pine wilt disease. It turns out that perceptual movement can provide a theoretical scientific basis for the multi-point outbreaks and spatiotemporal aggregation of pine wilt disease. For the top-hat kernel, we concentrate on the joint effect of perception scale and delay on the stability, and find that Turing-Hopf bifurcation occurs due to their interaction. Besides, the patterns near the bifurcation points are simulated in detail by adopting parameters with actual biological meaning, which are selected by analyzing real data, and diverse complicated spatiotemporal patterns are obtained, such as peak alternating periodic patterns and spatiotemporal aggregation patterns. Finally, we demonstrate that the artificial release of the parasitic natural enemy of the pest can drive the populations to reach stability in the form of the steady state or periodic solutions. The obtained results not only well explain the transmission mechanism of pine wilt disease, but also contribute to the study of biological phenomena such as the formations of flocks and swarms.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"126"},"PeriodicalIF":2.2,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144803579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling the Impact of Phenotypic Heterogeneity on Cell Migration: A Continuum Framework Derived from Individual-Based Principles.","authors":"Rebecca M Crossley, Philip K Maini, Ruth E Baker","doi":"10.1007/s11538-025-01502-5","DOIUrl":"10.1007/s11538-025-01502-5","url":null,"abstract":"<p><p>Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration in the local environment, which is coarse-grained from an underlying individual-based model that captures the dynamics of cell migration that are influenced by the phenotype of the cell, such as random movement, proliferation, phenotypic transitions, and interactions with the local environment. The resulting, flexible, and general model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. We showcase the utility of the generalised framework in three biological scenarios: range expansion; cell invasion into the extracellular matrix; and T cell exhaustion. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence migration patterns, a phenomenon that would be computationally very expensive to explore using an individual-based model alone. This framework provides a versatile and robust tool for understanding the role of phenotypic heterogeneity in collective cell migration, with potential applications in optimising therapeutic strategies for diseases involving cell migration.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"123"},"PeriodicalIF":2.2,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12334544/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144798217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francisco Antônio Bezerra Coutinho, Marcos Amaku, Fernanda Castro Boulos, José Alfredo de Sousa Moreira, Eliana Nogueira Castro de Barros, Esper Georges Kallas, Eduardo Massad
{"title":"Estimating the Size of the Aedes Mosquitoes' Population Involved in Outbreaks of Dengue and Chikungunya Using a Mathematical Model.","authors":"Francisco Antônio Bezerra Coutinho, Marcos Amaku, Fernanda Castro Boulos, José Alfredo de Sousa Moreira, Eliana Nogueira Castro de Barros, Esper Georges Kallas, Eduardo Massad","doi":"10.1007/s11538-025-01489-z","DOIUrl":"10.1007/s11538-025-01489-z","url":null,"abstract":"<p><p>Aedes aegypti continues to cause many cases of dengue, chikungunya and Zika fever in affected areas of the tropical world. After being eradicated from Brazil in the decades of 1940 and 1950, Aedes aegypti returned with full force in the early 1970s. Knowing the total number of mosquitoes transmitting Aedes-borne infections is crucial for quantifying the intensity of transmission of these infections. In this paper, we propose a model to estimate the distribution of the number of Aedes mosquitoes' populations during an outbreak of either dengue or chikungunya. The model assumes that the mosquitoes' distribution follows a Gaussian Mesa Function (GMF), which has 5 parameters and allows for variable asymmetry. These 5 parameters are adjusted so that they fit indirectly, from a modified Ross‒Macdonald model, the incidence of dengue or chikungunya infections (see main text). Therefore, the observed incidence becomes a function of the parameters of the GMF. We illustrate the model with dengue and chikungunya data from 5 cities in the state of Minas Gerais in the southeastern region of Brazil for the 2023-2024 transmission season. The model shows that it is possible to estimate the size of the mosquitoes' population from incidence data, circumventing the logistic hurdles involved in the actual counting of mosquitoes. This is the most important practical contribution of this paper. The paper also contains several theoretical innovations, such as a modification of the Ross‒Macdonald model, which is usually presented for a constant mosquitoes' population, which, of course, is very unrealistic.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"124"},"PeriodicalIF":2.2,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12334540/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144803578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Practical Identifiability in a Viscoelastic Respiratory Model for Mechanical Ventilation.","authors":"A E Cerdeira, N N Lam, S Hamis, P D Docherty","doi":"10.1007/s11538-025-01497-z","DOIUrl":"10.1007/s11538-025-01497-z","url":null,"abstract":"<p><p>Mechanical ventilation is a life support system for patients with acute respiratory distress syndrome (ARDS). As part of strategies to protect the lung during ventilation, plateau pressure can be determined via an end-inspiratory pause; however, there is no agreed-upon pause duration in medical protocols. Mechanical ventilation can be modelled using the Viscoelastic model (VEM) for respiration. The identification of static compliance is of clinical interest, as it can be used to estimate plateau pressure. Practical identifiability analysis quantifies the confidence with which model parameters can be estimated from finite, noisy data. This paper evaluates the robustness of plateau pressure estimates in clinical data by analysing practical identifiability of the VEM identified in data with varying durations of end expiratory pauses. Profile likelihood and Hamiltonian Monte Carlo (HMC) simulations were used to determine estimation robustness. The methods were applied to mechanical ventilation data from a previous ARDS study. Profile likelihood and HMC showed strong agreement in both parameter estimates and identifiability results with similar confidence distributions. Both methods demonstrated a loss of parameter robustness that would preclude clinical utility when the end expiratory pause was reduced. By quantifying the confidence in parameter estimation and finding trade-offs in parameters that may be previously unknown when parameters are estimated, the methods give insight into the certainty of the estimate and parameter behaviours, even when the model fits the data well.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"122"},"PeriodicalIF":2.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12328475/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144793549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pattern dynamics analysis and application of West Nile virus spatiotemporal models based on higher-order network topology.","authors":"Linhe Zhu, Tongtong Zheng","doi":"10.1007/s11538-025-01501-6","DOIUrl":"10.1007/s11538-025-01501-6","url":null,"abstract":"<p><p>The higher-order network structure characterized by hypergraphs or simplicial complexes has become a research hotspot in network space. In this paper, a simplicial complex is used to describe the multivariate interaction between populations, and the reaction diffusion equation in higher-order organization is established. Under certain constraints, the Turing instability condition of the system is derived. Then, the advection mechanism is introduced to construct a reaction-diffusion model with directional migration mechanism, and the pattern dynamics of the reaction-diffusion-advection equation is systematically analyzed on two-dimensional torus and triangular lattice networks. In addition, in the numerical simulation part, it is found that the spatial density distribution in the stable patterns of the two populations is anti-phase. At the same time, we verify that the diffusion of the population depends on the topological structure and coupling, and conclude that the higher-order interaction on the triangular lattice network has a greater influence on the Turing instability than the higher-order Erdos-Renyi (ER) network. In the system process of simulating the existence of advection mechanism, the triangular lattice network will increase the spatial heterogeneity of the pattern due to the existence of directional migration mechanism. In the absence of diffusion, the increase of directional movement intensity will also cause Turing instability. Finally, the reaction-diffusion model in higher-order organization is applied to practice, and the validity of the model is verified.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"121"},"PeriodicalIF":2.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144759250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tomas Ferreira Amaro Freire, Sten Madec, Erida Gjini
{"title":"Unpacking fitness differences between two invaders in a multispecies context.","authors":"Tomas Ferreira Amaro Freire, Sten Madec, Erida Gjini","doi":"10.1007/s11538-025-01491-5","DOIUrl":"10.1007/s11538-025-01491-5","url":null,"abstract":"<p><p>Ecosystems are constantly exposed to newcoming strains or species. Which newcomer will be able to invade a resident multi-species community depends on the invader's relative fitness. Classical fitness differences between two growing strains are measured using the exponential model. Here we complement this approach, developing a more explicit framework to quantify fitness differences between two co-invading strains, based on the replicator equation. By assuming that the resident species' frequencies remain constant during the initial phase of invasion, we are able to determine the invasion fitness differential between the two strains, which drives growth rate differences post-invasion. We then apply our approach to a critical current global problem: invasion of the gut microbiota by antibiotic-resistant strains of the pathobiont Escherichia coli, using previously-published data. Our results underscore the context-dependent nature of fitness and demonstrate how species frequencies in a host environment can explicitly modulate the selection coefficient between two strains. This mechanistic framework can be augmented with machine-learning algorithms and multi-objective optimization to predict relative fitness in new environments, to steer selection, and design strategies to lower resistance levels in microbiomes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"120"},"PeriodicalIF":2.2,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12296887/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144728091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
U J Giménez-Mujica, J Velázquez-Castro, A Anzo-Hernández, I Barradas
{"title":"Final size index-driven strategies for cost-effective epidemic management in metapopulation.","authors":"U J Giménez-Mujica, J Velázquez-Castro, A Anzo-Hernández, I Barradas","doi":"10.1007/s11538-025-01500-7","DOIUrl":"10.1007/s11538-025-01500-7","url":null,"abstract":"<p><p>Designing effective control strategies for managing epidemics in metapopulations, where human mobility plays a critical role, is essential for public health policies. In this paper, we propose a novel methodology for efficiently distributing control resources by considering both the epidemiological response of each region and the cost of implementing a control strategy to reduce contact rates within a given patch. Specifically, using the SEIR (Susceptible-Exposed-Infectious-Recovered) model to describe the epidemic process in each patch of the metapopulation, we derive a mathematical expression for the epidemic's final size in each patch, which measures the total number of individuals that become infected by the end of the epidemic. By solving this expression with an interactive approach, we guarantee computational efficiency even in large and highly connected metapopulations. Based on the final size of each patch, we propose an index to guide the control strategy efficiently. We compare this approach with other intuitive strategies, such as allocating all control resources to the most affected patch or distributing resources homogeneously. Our findings suggest that allocating control resources proportionally to the final size index best allocates resource returns across multiple zones. This strategy results in similar epidemic trajectories across regions, prevents resource concentration in a few areas, maintains lower local peaks, and ensures a more balanced epidemic impact across the metapopulation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"119"},"PeriodicalIF":2.2,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144717593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling the effects of a Shock-and-Kill Treatment for HIV: Latency-Reversing Agents and Natural Killer Cells.","authors":"Guyue Liu, Suli Liu, Chiyu Zhang, Xu Chen, Wenxuan Li, Huilai Li","doi":"10.1007/s11538-025-01498-y","DOIUrl":"10.1007/s11538-025-01498-y","url":null,"abstract":"<p><p>Despite the substantial success of combination antiretroviral therapy (ART) in suppressing HIV replication, achieving a complete cure remains challenging due to the persistence of viral reservoirs. The use of latency-reversing agents (LRAs) combined with natural killer (NK) cells in a \"shock-and-kill\" strategy has been experimentally confirmed as an effective approach to reducing reservoirs. Here, we utilized an HIV infection mathematical model that incorporates both 'virus-cell' and 'cell-cell' infection modes to assess the dynamic synergy of ART, LRAs, and NK cells. Model calibration was performed using experimental viral load data from HIV-1-infected humanized mice, employing Bayesian inference and an affine-invariant ensemble Markov Chain Monte Carlo (MCMC) sampling algorithm. Our findings validate the established understanding of HIV pathogenesis: post-treatment viral rebound is significantly influenced by the size of the viral reservoir, and 'cell-cell' transmission accounts for more than half of infections. Our findings also highlight the crucial role of natural killer (NK) cell-mediated immune responses in influencing interindividual variability in therapeutic responses to HIV. Comparative analysis of therapeutic strategies reveals that tripartite regimens combining ART with LRAs and NK cells demonstrate enhanced antiviral efficacy and accelerated treatment timelines. There is a key parameter region of the tripartite regimens therapy that will lead to an HIV cure. These insights collectively reinforce the immunotherapeutic potential of NK cells modulation and provide a mechanistic basis for optimizing combination therapies in eradication strategies.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"116"},"PeriodicalIF":2.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144706399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evaluating the Intensity of a Potential Yellow Fever Outbreak During an International Trading Event: a Case Study on Canton Fair.","authors":"Yining Chen, Yufeng Wang, Jianshe Yu, Jianhong Wu","doi":"10.1007/s11538-025-01484-4","DOIUrl":"10.1007/s11538-025-01484-4","url":null,"abstract":"<p><p>We evaluate the risk of yellow fever outbreaks in a major trade event, with a case study of Canton Fair (Guangzhou, China), caused by case importation at different stages of the trade event. Our baseline model is a standard vector-borne disease transmission dynamics system, but we incorporate the division of a calendar year into favorable and unfavorable seasons based on impacts of different climatic conditions (temperature in particular) on mosquito population dynamics. We also incorporate square-waves to describe scenarios of case importation. We then use this periodic switching model to inform the potential of outbreaks and intensity of outbreaks due to case importation in different periods in relation to the two seasons. Our results show that importation of cases (even with a single case introduced) in the favorable season can induce a large outbreak in the local population in the host city, and the intensity of outbreak depends on the total number of imported cases (up to a level, when local transmission dominates). We also incorporate the public health interventions-isolation and emergency vaccination-to the model to provide quantitative information for the event organizer and public health decision makers for the preparedness and rapid response to the outbreak induced by case importation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 9","pages":"117"},"PeriodicalIF":2.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144706398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}