Mathematical Biosciences最新文献

{"title":"Modeling spike frequency adaptation through higher-order fractional leaky integrate and fire model","authors":"Yash Vats ,&nbsp;Mani Mehra ,&nbsp;Dietmar Oelz","doi":"10.1016/j.mbs.2025.109548","DOIUrl":"10.1016/j.mbs.2025.109548","url":null,"abstract":"<div><div>Spike frequency adaptation is a key characteristic of spiking neurons. To examine this form of adaptation, we introduce a higher-order fractional leaky integrate and fire model. In this model, the exponent of the fractional derivative can range from one (representing an ordinary first order derivative) to two. In this regime, the impact of the past membrane potential on the present potential is inhibitory leading to spike frequency adaptation. We also analyze spike frequency adaptation in response to noisy input current and show that spike frequency adaptation is reinforced as the intensity of noisy input increases.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109548"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145305091","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":"The cumulative lethal rate of repeated spraying of pesticides and its applications","authors":"Zhigang Liu ,&nbsp;Bo Zheng ,&nbsp;Jia Li ,&nbsp;Jianshe Yu","doi":"10.1016/j.mbs.2025.109562","DOIUrl":"10.1016/j.mbs.2025.109562","url":null,"abstract":"<div><div>Due to the presence of residual effects of pesticides, repeated spraying of pesticides has a cumulative lethal effect on pests which has not been clearly expounded in the existing literature. In this paper, we start by depicting the cumulative lethal rate of pests caused by repeated pesticide spraying. Although the cumulative lethal rate function is complex, our analysis gives an integral invariant of the cumulative killing-rate function, which plays a crucial role in the dynamical analysis of the Logistic single-population growth model that we preferred as a direct application, and helps us obtain a complete dynamical conclusion including the existence, uniqueness and stability of periodic solutions. We derive a threshold of pesticide spraying period for the eventual extinction of the pest population. By combining our theoretical findings and numerical simulations, in accordance with the frequency and cumulative killing-rate function of pesticide spraying, pesticide spraying strategies can be determined to achieve effective pest control within a predetermined time.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109562"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363825","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":"Resilience in a modified Leslie–Gower model with dual Allee effects and cooperative hunting","authors":"Gourav Mandal ,&nbsp;Lakshmi Narayan Guin ,&nbsp;Santabrata Chakravarty ,&nbsp;Renji Han","doi":"10.1016/j.mbs.2025.109563","DOIUrl":"10.1016/j.mbs.2025.109563","url":null,"abstract":"<div><div>The present study is devoted to the precise characterization of dynamic transitions within a continuous two-dimensional ecological framework, induced by a bifurcation module. This investigation aims to enhance our understanding of ecological evolution by disentangling the individual and interactive influences of the double Allee effect and hunting cooperation. Dynamics of all non-negative equilibria are investigated to disclose the degenerate nature of them. Bifurcation points are systematically identified, as their determination is critical for devising strategies aimed at stabilizing ecological systems or averting species extinction, particularly within networks influenced by dual Allee effects and cooperative predation. Both local and global bifurcation analyses, distinguished by the number of relevant parameters and the qualitative behaviour have been explored to capture the system’s intricate dynamics. A comprehensive overview of current numerical bifurcation analysis techniques and their ecological applications is provided. Emphasis is placed on the computational challenges encountered in detecting extinction-driven bifurcations and in identifying diverse attractor landscapes and phase transitions. Particular attention has been given to the numerical difficulties posed by both weak and strong forms of the Allee effect, and potential resolutions to these methodological bottlenecks are proposed. Through this structured analysis, an in-depth understanding of species interaction dynamics within bifurcation-driven ecological models is sought, aiming to elucidate complex behaviours that are often obscured in conventional studies of large bifurcating ecological networks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109563"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145318944","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":"A mathematical study of anti-VEGF and cytotoxic therapies of cancer with optimal control","authors":"Shikun Li ,&nbsp;Xiaoming Zheng ,&nbsp;Ling Xue ,&nbsp;Kun Zhao","doi":"10.1016/j.mbs.2025.109542","DOIUrl":"10.1016/j.mbs.2025.109542","url":null,"abstract":"<div><div>This work studies two cancer treatments, anti-angiogenic therapy and chemotherapy, with a novel mathematical model and the associated optimal control problem. The model includes tumor cells, endothelial cells, immune cells, and Vascular Endothelial Growth Factor (VEGF), where the anti-angiogenic therapy only targets VEGF and the chemotherapy kills all cells indiscriminately. The optimal control problem minimizes the tumor burden and drug toxicity over a set of time-variant drug doses. The mathematical analysis shows the existence of the positive invariant set of the model over all the therapeutic strategies, the stability of multiple steady state solutions, as well as the existence and uniqueness of the optimal control solutions. The analysis and simulations lead to several significant findings. First, all the steady states with the vanished tumor are unstable under the anti-VEGF therapy, which confirms its limited efficacy as observed in clinics. Second, the Hopf bifurcation appears in each treatment approach with a common feature: the system exhibits periodic oscillations at low drug doses and transitions to a stable coexistence state at higher drug doses. Third, the optimal treatment strategy involves a delicate combination of both treatment types. This strategy is particularly effective when the anti-VEGF drug has a high binding affinity to VEGF molecules, and the chemotherapy drug has a small killing rate of immune cells and large killing rates of endothelial cells and tumor cells.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109542"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145182294","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":"A mathematical model for cancer dynamics with treatment and saboteur bacteria","authors":"Anna Geretovszky ,&nbsp;Gergely Röst","doi":"10.1016/j.mbs.2025.109541","DOIUrl":"10.1016/j.mbs.2025.109541","url":null,"abstract":"<div><div>We construct a mathematical model of cancer dynamics with chemotherapeutic treatment, in the presence of bacteria that are capable of metabolizing the chemotherapeutic drug, hence sabotaging the treatment. We investigate the possibility of complementing the cancer treatment with antibiotic drugs, thus eradicating the bacteria or at least mitigating their negative impact on the prospects of therapy. Our model is a nonlinear system of four differential equations, for which we perform a complete analysis, explicitly characterizing the four possible outcomes, depending on whether the cancer cells or the bacteria become extinct or persist. Global stability results are proven by the iterative application of a comparison principle, and a bifurcation diagram is created to show the transitions between scenarios with respect to the controllable parameters. We apply our model to an experiment on mice with colon cancer and the drug Gemcitabine.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109541"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159542","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":"CAR T-cell and oncolytic virus dynamics and determinants of combination therapy success for glioblastoma","authors":"Martina Conte ,&nbsp;Agata Xella ,&nbsp;Ryan T. Woodall ,&nbsp;Kevin A. Cassady ,&nbsp;Sergio Branciamore ,&nbsp;Christine E. Brown ,&nbsp;Russell C. Rockne","doi":"10.1016/j.mbs.2025.109531","DOIUrl":"10.1016/j.mbs.2025.109531","url":null,"abstract":"<div><div>Glioblastoma is a highly aggressive and treatment-resistant primary brain cancer. While chimeric antigen receptor (CAR) T-cell therapy has demonstrated promising results in targeting these tumors, it has not yet been curative. An innovative approach to improve CAR T-cell efficacy is to combine them with other immune modulating therapies. In this study, we investigate <em>in vitro</em> combination of IL-13R<span><math><mi>α</mi></math></span>2 targeted CAR T-cells with an oncolytic virus (OV) and study the complex interplay between tumor cells, CAR T-cells, and OV dynamics with a novel mathematical model. We fit the model to data collected from experiments with each therapy individually and in combination to reveal determinants of therapy synergy and improved efficacy. Our analysis reveals that the virus bursting size is a critical parameter in determining the net tumor infection rate and overall combination treatment efficacy. Moreover, the model predicts that administering the oncolytic virus simultaneously with, or prior to, CAR T-cells could maximize therapeutic efficacy.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109531"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145082921","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":"A new optimized regularized Stokeslet model reveals the effects of multicellular protozoan colony configuration on hydrodynamic performance","authors":"Hongfei Chen ,&nbsp;Tom Hata ,&nbsp;Ricardo Cortez ,&nbsp;Hoa Nguyen ,&nbsp;M.A.R. Koehl ,&nbsp;Lisa Fauci","doi":"10.1016/j.mbs.2025.109519","DOIUrl":"10.1016/j.mbs.2025.109519","url":null,"abstract":"<div><div>Many microbial eukaryotes have unicellular life stages, but can also form multicellular colonies. We explored hydrodynamic consequences of colony morphology, which affects swimming and flux of prey-carrying water to cells in a colony, using the choanoflagellate, <em>Choanoeca flexa</em>, which forms cup-like colonies that can turn inside-out so flagella line the cup’s interior or cover its outside surface. Detailed hydrodynamic models incorporating cell morphologies are not feasible for colonies with many cells. Therefore, we designed a reduced model of each cell using regularized-force-dipoles with parameters optimized (by selecting the regularized delta function from a given class) to match the flow-field of a detailed model of a cell. Calculated swimming speeds and water flux to flagella-in colonies match those measured for living <em>C. flexa</em>. For a given shape (flat bowls, hemispheres, spherical cups) of flagella-in colony, models showed that swimming speed and water flux towards the colony increases with cell density, although flux per cell is independent of density. Denser packing of cells at the front of flagella-in colonies increases swimming speed and flux to cells at all positions in the colonies. Flagella-in colonies swim more slowly, but produce higher water flux per cell than do flagella-out colonies of the same configuration, suggesting that flagella-out colonies are better swimmers, whereas flagella-in colonies are better feeders. A model flagella-out colony with morphology matched to a real <em>C. flexa</em> requires a flagellar force 5–10 times greater than that for flagella-in colonies to achieve the measured swimming speed, suggesting flagella beat differently on flagella-out colonies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109519"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144984281","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":"Employing nullclines to balance treatment efficacy and neurotoxicity for sustained tumor control","authors":"Lois C. Okereke ,&nbsp;Ernesto A.B.F. Lima ,&nbsp;Anna G. Sorace ,&nbsp;Thomas E. Yankeelov","doi":"10.1016/j.mbs.2025.109535","DOIUrl":"10.1016/j.mbs.2025.109535","url":null,"abstract":"<div><div>There is increasing interest in identifying therapeutic regimens capable of maintaining tumor burden within well-defined size boundaries with constraints on the amount and frequency of drugs on a patient-specific basis. We have developed coupled systems of ordinary differential equations (ODEs) capturing the temporal dynamics of tumor burden, treatment effects due to cytotoxic drugs, and neurotoxicity. The models account for tumor cell proliferation and phenotypic heterogeneity, drug availability due to continuous or impulsive drug delivery, drug-induced apoptosis and microglia activation. We utilize nullclines of the system to derive effective dose ranges that stabilize tumor burden and mitigate neurotoxicity. Our results generate bounded treatment regimens that can be validated in the experimental setting. We found that for tumors with a proliferation saturation index (i.e., pre-treatment volume to carrying capacity ratio) between 0.10 and 0.30, containing the tumor in the sense of RECIST can yield up to a 51.8% reduction in drug concentration when compared with regimens designed for tumor eradication. <em>In silico</em> experiments using data from a breast cancer study demonstrate that the nullcline-derived treatments maintained stable disease in the tumors with neurotoxicity maintained below the desired threshold. The methodology developed in this study provides a theoretical formalism to potentially explain several preclinical and clinical observations indicating that low dose therapy can stabilize tumor growth and result in an enhanced quality of life. Importantly, our model identified quantitative biologic indices that can offer practical guidance to the design of personalized regimens that balance treatment efficacy and toxicity.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109535"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145056604","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":"Spatio-temporal modeling and analysis of two HIV strain infections via demographic–geographic data","authors":"Peng Wu ,&nbsp;Tong Chen ,&nbsp;Shigui Ruan","doi":"10.1016/j.mbs.2025.109539","DOIUrl":"10.1016/j.mbs.2025.109539","url":null,"abstract":"<div><div>The emergence of drug resistance poses a significant challenge to the clinical treatment of HIV/AIDS, making the spread of drug-resistant strains among the infected population a key focus in the monitoring and control of HIV/AIDS. In this paper, we construct a reaction–diffusion model with two HIV strains (drug-sensitive and drug-resistant) to study the spatio-temporal dynamics of HIV/AIDS transmission. With spatial heterogeneity, we derive the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and show that it is a threshold for the outbreak of the disease; that is, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span> the disease will eventually die out, while when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> the disease is uniformly persistent. In particular, when the model parameters are independent of the space variable, global stability of the infection equilibrium is proven by constructing an appropriate Lyapunov functional. In the numerical simulation part, we discuss the traveling wave phenomenon of HIV/AIDS infection in the population under different diffusion forms and different initial value distributions. We combine the population statistical data, geographical data, and data of different strain infection cases in Zhejiang Province, China, and simulate the spatial spread of HIV/AIDS in Zhejiang Province through the finite element method with the aid of COMSOL Multiphysics software. This provides a new perspective to analyze the impact of dispersal on the spatio-temporal transmission of HIV/AIDS. Numerical simulations show that: (i) High adherence to treatment can effectively reduce the proportion of acquired drug-resistant cases among the total number of cases; (ii) The form of population diffusion has a huge impact on the spatio-temporal transmission of HIV/AIDS, which means that population movement will be one of the important contents of HIV/AIDS prevention and monitoring; (iii) Ignoring the differences in population movement will misjudge the overall trend of HIV/AIDS in the region, so the differences in spatial diffusion in HIV/AIDS prevention and control cannot be ignored.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109539"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145208794","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":"Nucleation feedback can drive establishment and maintenance of biased microtubule polarity in neurites","authors":"Hannah G. Scanlon ,&nbsp;Gibarni Mahata ,&nbsp;Anna C. Nelson ,&nbsp;Scott A. McKinley ,&nbsp;Melissa M. Rolls ,&nbsp;Maria-Veronica Ciocanel","doi":"10.1016/j.mbs.2025.109538","DOIUrl":"10.1016/j.mbs.2025.109538","url":null,"abstract":"<div><div>The microtubule cytoskeleton is comprised of dynamic, polarized filaments that facilitate transport within the cell. Polarized microtubule arrays are key to facilitating cargo transport in long cells such as neurons. Microtubules also undergo dynamic instability, where the plus and minus ends of the filaments switch between growth and shrinking phases, leading to frequent microtubule turnover. Although microtubules often completely disassemble and new filaments nucleate, microtubule arrays have been observed to both maintain their biased orientation throughout the cell lifetime and to rearrange their polarity as an adaptive response to injury. Motivated by cytoskeleton organization in neurites, we propose a spatially-explicit stochastic model of microtubule arrays and investigate how nucleation of new filaments could generate biased polarity in a simple linear domain. Using a continuous-time Markov chain model of microtubule growth dynamics, we model and parameterize two experimentally-validated nucleation mechanisms: nucleation feedback, where the direction of filament growth depends on existing microtubule content, and a checkpoint mechanism, where microtubules that nucleate in a direction opposite to the majority experience frequent catastrophe. When incorporating these validated mechanisms into the spatial model, we find that nucleation feedback is sufficient to establish biased polarity in neurites of different lengths, and that the emergence and maintenance of biased polarity is relatively stable in spite of stochastic fluctuations. This work provides a framework to study the relationship between microtubule nucleation and polarity, and could extend to give insights into mechanisms that drive the formation of polarized filament arrays in other biological settings.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109538"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145139810","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}