Journal of Mathematical Biology最新文献

{"title":"A Ca²⁺ puff model based on integrodifferential equations.","authors":"Molly Hawker, Pengxing Cao, Ross A Kelly, James Sneyd, Ivo Siekmann","doi":"10.1007/s00285-025-02202-3","DOIUrl":"10.1007/s00285-025-02202-3","url":null,"abstract":"<p><p>The calcium signalling system is important for many cellular processes within the human body. Signals are transmitted within the cell by releasing calcium (Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> ) from the endoplasmic reticulum (ER) into the cytosol via clusters of Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> channels. Mathematical models of Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> release via inositol 1,4,5-trisphosphate receptors (IP₃R) are used to compute Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> transients in regions that are difficult to measure directly. In particular, accounting for the data on Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> puffs as stochastic Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> release events in models remains challenging. Parameterising Markov models for representing the IP₃R with steady-state single channel data obtained at fixed combinations of the ligands Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> and inositol-trisphosphate (IP₃) has previously been demonstrated to be insufficient. However, by extending an IP₃R model based on steady-state data with an integral term that incorporates the delayed response of the channel to varying Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> concentrations we succeed in generating realistic Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> puffs. By interpreting the integral term as a weighted average of Ca <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mrow><mn>2</mn> <mo>+</mo></mrow> </mmultiscripts> </math> concentrations that extend over a time interval of length  <math><mi>τ</mi></math> into the past we conclude that the IP₃R requires a certain amount of memory of past ligand concentrations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"43"},"PeriodicalIF":2.2,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11937165/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143711974","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":"Long-term behavior of stochastic SIQRS epidemic models.","authors":"Alexandru Hening, Dang H Nguyen, Trang Ta, Sergiu C Ungureanu","doi":"10.1007/s00285-025-02204-1","DOIUrl":"10.1007/s00285-025-02204-1","url":null,"abstract":"<p><p>In this paper we analyze and classify the dynamics of SIQRS epidemiological models with susceptible, infected, quarantined, and recovered classes, where the recovered individuals can become reinfected. We are able to treat general incidence functional responses. Our models are more realistic than what has been studied in the literature since they include two important types of random fluctuations. The first type is due to small fluctuations of the various model parameters and leads to white noise terms. The second type of noise is due to significant environment regime shifts in that can happen at random. The environment switches randomly between a finite number of environmental states, each with a possibly different disease dynamic. We prove that the long-term fate of the disease is fully determined by a real-valued threshold <math><mi>λ</mi></math> . When <math><mrow><mi>λ</mi> <mo><</mo> <mn>0</mn></mrow> </math> the disease goes extinct asymptotically at an exponential rate. On the other hand, if <math><mrow><mi>λ</mi> <mo>></mo> <mn>0</mn></mrow> </math> the disease will persist indefinitely. We end our analysis by looking at some important examples where <math><mi>λ</mi></math> can be computed explicitly, and by showcasing some simulation results that shed light on real-world situations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"41"},"PeriodicalIF":2.2,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143694292","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":"Attraction to equilibria in discrete population models with delayed feedbacks: stage-structure versus age-structure.","authors":"Hassan A El-Morshedy, Alfonso Ruiz-Herrera","doi":"10.1007/s00285-025-02200-5","DOIUrl":"10.1007/s00285-025-02200-5","url":null,"abstract":"<p><p>Time delays and stage structure are common features of most biological populations. This paper aims to describe the influence of these features through simple models. Regarding the role of time delays, we discuss the dynamical differences between populations where the main intraspecific competition episodes occur during the reproduction period or during a different one. The conclusion is that the second situation is generally more prone to generate long-term oscillations. Regarding the role of the stage structure, we show that the shape of the adult recruitment plays a key role. Particularly, adult recruitments associated with contest-type intraspecific competitions do not produce long-term oscillations. From a mathematical point of view, we offer two general criteria of global attraction in discrete systems valid for non-monotone models.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"40"},"PeriodicalIF":2.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11926005/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143671520","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":"Global dynamics of a fractional order SIRS epidemic model by the way of generalized continuous time random walk.","authors":"Zhaohua Wu, Yongli Cai, Zhiming Wang, Daihai He, Weiming Wang","doi":"10.1007/s00285-025-02201-4","DOIUrl":"10.1007/s00285-025-02201-4","url":null,"abstract":"<p><p>In this paper, we propose a novel fractional-order SIRS (frSIRS) model incorporating infection forces under intervention strategies, developed through the framework of generalized continuous-time random walks. The model is first transformed into a system of Volterra integral equations to identify the disease-free equilibrium (DFE) state and the endemic equilibrium (EE) state. Additionally, we introduce a new <math><mrow><mi>F</mi> <msup><mi>V</mi> <mrow><mo>-</mo> <mn>1</mn></mrow> </msup> </mrow> </math> method for calculating the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . Through several examples, we demonstrate the broad applicability of this <math><mrow><mi>F</mi> <msup><mi>V</mi> <mrow><mo>-</mo> <mn>1</mn></mrow> </msup> </mrow> </math> method in determining <math><msub><mi>R</mi> <mn>0</mn></msub> </math> for fractional-order epidemic models. Next, we establish that <math><msub><mi>R</mi> <mn>0</mn></msub> </math> serves as a critical threshold governing the model's dynamics: if <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> , the unique DFE is globally asymptotically stable; while if <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> , the unique EE is globally asymptotically stable. Furthermore, we apply our findings to two fractional-order SIRS (frSIRS) models incorporating infection forces under various intervention strategies, thereby substantiating our results. From an epidemiological perspective, our analysis reveals several key insights for controlling disease spread: (i) when the death rate is high, it is essential to increase the memory index; (ii) when the recovery rate is high, decreasing the memory index is advisable; and (iii) enhancing psychological or inhibitory effects-factors independent of the death rate, recovery rate, or memory index-can also play a critical role in mitigating disease transmission. These findings offer valuable insights into how the memory index influences disease outbreaks and the overall severity of epidemics.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"39"},"PeriodicalIF":2.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143598235","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":"wStri spread dynamics in Nilaparvata lugens via discrete mathematical models.","authors":"Bo Zheng, Huichao Yang, Saber Elaydi, Jianshe Yu","doi":"10.1007/s00285-025-02198-w","DOIUrl":"10.1007/s00285-025-02198-w","url":null,"abstract":"<p><p>Wolbachia, an intracellular bacterium, is well-known for inducing cytoplasmic incompatibility, which has become a promising and environmentally sustainable strategy for controlling pest populations. The strain wStri, specifically identified in Nilaparvata lugens (brown planthopper), has shown potential for such biocontrol applications. In this study, we develop a comprehensive discrete mathematical model to analyze the dynamics of wStri spread in a mixed population of wStri-infected, wLug-infected, and uninfected Nilaparvata lugens under both constant and periodically varying environmental conditions. Under a constant environment, the model identifies the critical threshold necessary for the successful establishment of wStri within the population. Our analysis reveals that the model exhibits a strong Allee effect, where a population must exceed a certain critical density-the Allee threshold-for the wStri strain to persist and spread. Below this threshold, the wStri strain is likely to be eliminated, failing in pest control efforts. When the environment varies periodically, the model transforms into a non-autonomous periodic discrete model, introducing additional complexity. In this scenario, we derive sufficient conditions that ensure the composition of finitely many Allee maps continues to function as an Allee map. Furthermore, we prove that a unique periodic orbit exists within such a periodic environment. This orbit is characterized as unstable and acts as a threshold, determining whether wStri will establish itself in the population or die out over time. The findings from this model provide critical insights into the conditions under which wStri can be effectively used to control Nilaparvata lugens, particularly in environments that are not constant but fluctuate periodically. These insights have significant implications for the practical deployment of Wolbachia-based biocontrol methods in pest management strategies.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"38"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143568772","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":"On the stochastic global dynamics of the delayed Nicholson's blowflies model.","authors":"Islam M Elbaz, M A Sohaly, H El-Metwally","doi":"10.1007/s00285-025-02199-9","DOIUrl":"10.1007/s00285-025-02199-9","url":null,"abstract":"<p><p>The well-known class of Nicholson's blowflies equations is considered under stochastic perturbations of the white noise type. We are concerned about the stability of the zero solution <math><msub><mi>x</mi> <mn>0</mn></msub> </math> which means the extinction of the species of Nicholson's blowflies, and the positive equilibrium <math><msup><mi>x</mi> <mo>∗</mo></msup> </math> which means their persistence. Using appropriate Lyapunov functionals, sufficient conditions of stochastic stability, uniform stability and stochastic global exponential mean-square stability are derived. Moreover, we develop a new way of constructing a delayed-deterministic system by Lyapunov functional that leads to the extinction in the sense of the mean-square. Areas of stability with some numerical simulations are given to illustrate our results.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"37"},"PeriodicalIF":2.2,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143537886","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 long-term effects of combination antiretroviral therapy of HIV infection: a modeling study.","authors":"Jing Cai, Jun Zhang, Kai Wang, Zhixiang Dai, Zhiliang Hu, Yueping Dong, Zhihang Peng","doi":"10.1007/s00285-025-02196-y","DOIUrl":"10.1007/s00285-025-02196-y","url":null,"abstract":"<p><p>Current HIV/AIDS treatments effectively reduce viral loads to undetectable levels as measured by conventional clinical assays, but immune recovery remains highly variable among patients. To assess the long-term treatment efficacy, we propose a mathematical model that incorporates latently infected CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cells and the homeostatic proliferation of CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cells. We investigate the dynamics of this model both theoretically and numerically, demonstrating that homeostatic proliferation can induce bistability, which implies that steady-state CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell count is sensitively affected by initial conditions. The model exhibits rich dynamics, including saddle node bifurcations, Hopf bifurcations, and saddle node bifurcations related to periodic orbits. The interplay between homeostatic proliferation and latent HIV infection significantly influences the model's dynamic behavior. Additionally, we integrate combination antiretroviral therapy (cART) into the model and fit the revised model to clinical data on long-term CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell counts before and after treatment. Quantitative analysis estimates the effects of long-term cART, revealing an increasing sensitivity of steady-state CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell count to drug efficacy. Correlation analysis indicates that the heightened activation of latently infected cells helps enhance treatment efficacy. These findings underscore the critical roles of CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell homeostatic proliferation and latently infected cell production in HIV persistence despite treatment, providing valuable insights for understanding disease progression and developing more effective therapies, potentially towards eradication.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"36"},"PeriodicalIF":2.2,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11872777/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143537869","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":"The power of Allee effects: inducing multistability and oscillations in a stoichiometric producer-herbivore system.","authors":"Zhiwei Zhu, Tao Feng","doi":"10.1007/s00285-025-02197-x","DOIUrl":"10.1007/s00285-025-02197-x","url":null,"abstract":"<p><p>Understanding producer-herbivore dynamics is fundamental for maintaining ecosystem stability and biodiversity. This study proposes a novel stoichiometric producer-herbivore model that incorporates positive density dependence induced by demographic factors. We conduct a rigorous mathematical analysis of the proposed model, covering well-posedness, nullcline analysis, and system stability. This analysis is expanded through numerical bifurcation analysis to explore the effects of critical biological parameters, including light intensity, on producer-herbivore interactions. Our findings reveal that variations in the severity of the Allee effect significantly influence these interactions, driving multistability and periodic oscillations. Severe Allee effects lead to complex dynamics, including four forms of bistability and three forms of tristability. Severe Allee effects can also lead to the extinction of both producer and herbivore populations due to positive density dependence. Intermediate levels of parameters such as light intensity, producer growth rate, herbivore loss rate, saturation levels of the Allee effect, total phosphorus, and sufficiently high production efficiency can lead to system instability and oscillations. Conversely, in scenarios with low-severity Allee effects, the system shows relatively simpler dynamics, with three types of bistability. Low producer growth rate and herbivore loss rate, moderate saturation levels of the Allee effect, light intensity, and sufficiently high herbivore production efficiency and total phosphorus levels can induce periodic oscillations. These findings emphasize the importance of managing Allee effect severity in conservation efforts to sustain biodiversity and prevent undesirable state transitions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"35"},"PeriodicalIF":2.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143517173","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":"Dynamics of an epidemic model arising in a spatial segregation control strategy.","authors":"Zhiguo Wang, Hua Nie, Sanyi Tang","doi":"10.1007/s00285-025-02195-z","DOIUrl":"10.1007/s00285-025-02195-z","url":null,"abstract":"<p><p>In this paper, we propose a free boundary problem to model the spread of an epidemic by introducing a spatial segregation control strategy. The model consists of two coupled reaction-diffusion equations along with an ordinary differential equation, while the free boundary is described by an integro-differential equation. The results reveal a trichotomy in which the epidemic can shrink, reach equilibrium, or expand spatially. Moreover, we establish the final size of the cumulative number of infected populations and characterize the threshold phenomenon of epidemic outbreak using the principal eigenvalue of an elliptic operator. Additionally, we apply this model to simulate the spatial spread of the COVID-19 epidemic in Xi'an, China, during 2021-2022. This study provides valuable model references for dynamically designing spatial isolation control strategies for newly emerging major infectious diseases.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"34"},"PeriodicalIF":2.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143505777","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":"Convective stability of the critical waves of an FKPP-type model for self-organized growth.","authors":"Florian Kreten","doi":"10.1007/s00285-025-02189-x","DOIUrl":"10.1007/s00285-025-02189-x","url":null,"abstract":"<p><p>We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the wave. The considered reaction-diffusion system was introduced by Hannezo et al. (Cell 171(1):242-255, 2017) in the context of branching morphogenesis: active, branching particles accumulate inactive particles, which do not react. Thus, the system features a continuum of steady state solutions, complicating the analysis. We adopt a result by Faye and Holzer (J Differ Equ 269(9):6559-6601, 2020) for proving the stability of the critical traveling waves, and modify the semi-group estimates to spaces with unbounded weights. We use a Feynman-Kac formula to get an exponential a priori estimate for the tail of the PDE, a novel and simple approach.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"33"},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11832597/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143442624","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}