Mathematical Biosciences最新文献

{"title":"Computing the extinction path for epidemic models","authors":"Damian Clancy,&nbsp;John J.H. Stewart","doi":"10.1016/j.mbs.2025.109454","DOIUrl":"10.1016/j.mbs.2025.109454","url":null,"abstract":"<div><div>In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may have been limited by the practical difficulties of implementation. It is necessary to compute a trajectory of a (high dimensional) dynamical system, the ‘extinction path’, and this trajectory is maximally sensitive to small perturbations, making numerical computation challenging. The purpose of this paper is to make this methodology more accessible. Our method to achieve this is to present four computational algorithms, with associated Matlab code, together with discussion of various ways in which the algorithms may be tuned to achieve satisfactory convergence. One of the four algorithms is standard in this context, although we are able to somewhat enhance previously available code; the use of the three other algorithms in this context is novel. We illustrate our methods using three standard infectious disease models. Our results demonstrate that for each such model, our algorithms are able to improve upon previously available results.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"386 ","pages":"Article 109454"},"PeriodicalIF":1.9,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144001173","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":"Sustainability & social segmentation in social media contagion: A mathematical and computational study on dual effects of individual needs & peer influence","authors":"Dibyajyoti Mallick ,&nbsp;Priya Chakraborty ,&nbsp;Sayantari Ghosh","doi":"10.1016/j.mbs.2025.109451","DOIUrl":"10.1016/j.mbs.2025.109451","url":null,"abstract":"<div><div>Addiction to internet-based social media has increasingly emerged as a critical social problem, especially among young adults and teenagers. Based on multiple research studies, excessive usage of social media may have detrimental psychological and physical impacts. In this study, we are going to explore mathematically the dynamics of social media addiction behavior and explore the determinants of compulsive use of social media from the dual perspectives of individual needs or <em>cravings</em> and peer-related factors or <em>peer pressure</em>. The theoretical analysis of the model without the peer pressure effect reveals that the associated addiction-free equilibrium is globally stable whenever a certain threshold, known as the addictive-generation number, is less than unity and unstable when the threshold is greater than unity. We observed how introduction of peer influence adds a sustainability to the dynamics, and causes a multistability, through which addiction-contagion can proliferate, even below the designated critical threshold. Using simulations over model networks, we demonstrate our finding, even in the presence of social heterogeneity. Finally, we use the reaction–diffusion approach to investigate spatio-temporal dynamics in a synthetic society, in the form of a 2D lattice. Instead of a fast convergence to the steady states, we observe a long transient of social clustering and segmentation, represented by spatio-temporal pattern formation. Our model illustrates how the peer influence factor plays a crucial role and concludes that it is required to consider the peer factors while formulating specific strategies that could be more effective against this addiction and its potential adverse outcomes.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109451"},"PeriodicalIF":1.9,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936415","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 COVID-19 based on spontaneous individual behaviors of vaccination","authors":"Yunsu Zhou ,&nbsp;Xianning Liu ,&nbsp;Yangjiang Wei","doi":"10.1016/j.mbs.2025.109452","DOIUrl":"10.1016/j.mbs.2025.109452","url":null,"abstract":"<div><div>As the <span><math><mrow><mi>C</mi><mi>O</mi><mi>V</mi><mi>I</mi><mi>D</mi></mrow></math></span>-19 vaccine becomes widely available, human self-protection awareness is gradually weakening. However, the epidemic still continue to erupt repeatedly in various areas. Therefore, it is necessary to reveal the relationship between vaccination and individual spontaneous behaviors and their impact on the epidemic. Based on an <span><math><mrow><mi>S</mi><mi>V</mi><mi>E</mi><mi>I</mi><mi>R</mi></mrow></math></span> epidemic dynamical model, a novel imitation dynamics model is established by integrating the dynamic changes of individual spontaneous behaviors before and after vaccination. Unvaccinated people are more likely to choose long-term individual spontaneous behavior change strategies to reduce the risk of infection. While the vaccinated individuals are more likely to choose multiple, short-term strategies of individual spontaneous behavior changes. In the case of low vaccine protective efficacy, the changes of individual spontaneous behavior will drive several small-scale outbreaks at the same time. Besides, when the value of <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is 4.5 and vaccination rate is 0.45, keeping the vaccine protection efficacy above 76.3% can not only complement the epidemic recurrence caused by behavioral changes, but also effectively reduce the epidemic peak and therefore quickly control the epidemic. Our results reveal the underlying mechanisms between vaccination, vaccine protection efficacy, individual spontaneous behaviors of the two groups of people and the <span><math><mrow><mi>C</mi><mi>O</mi><mi>V</mi><mi>I</mi><mi>D</mi></mrow></math></span>-19 epidemic. Vaccination and its protective efficacy effectively have a reciprocal effect with individual behavior changes, so as to control the epidemic quickly and effectively.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109452"},"PeriodicalIF":1.9,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917203","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 pattern formation in the thermodynamically-consistent variational Gray-Scott model","authors":"Wenrui Hao ,&nbsp;Chun Liu ,&nbsp;Yiwei Wang ,&nbsp;Yahong Yang","doi":"10.1016/j.mbs.2025.109453","DOIUrl":"10.1016/j.mbs.2025.109453","url":null,"abstract":"<div><div>In this paper, we explore pattern formation in a four-species variational Gary-Scott model, which includes all reverse reactions and introduces a virtual species to describe the birth–death process in the classical Gray-Scott model. This modification transforms the classical Gray-Scott model into a thermodynamically consistent closed system. The classical two-species Gray-Scott model can be viewed as a subsystem of the variational model in the limiting case when the small parameter <span><math><mi>ϵ</mi></math></span>, related to the reaction rate of the reverse reactions, approaches zero. We numerically explore pattern formation in this physically more complete Gray-Scott model in one spatial dimension, using non-uniform steady states of the classical model as initial conditions. By decreasing <span><math><mi>ϵ</mi></math></span>, we observed that the stationary patterns in the classical Gray-Scott model can be stabilized as the transient states in the variational model for a significantly small <span><math><mi>ϵ</mi></math></span>. Additionally, the variational model admits oscillating and traveling-wave-like patterns for small <span><math><mi>ϵ</mi></math></span>. The persistent time of these patterns is on the order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. We also analyze the energy stability of two uniform steady states in the variational Gary-Scott model for fixed <span><math><mi>ϵ</mi></math></span>. Although both states are stable in a certain sense, the gradient flow type dynamics of the variational model exhibit a selection effect based on the initial conditions, with pattern formation occurring only if the initial condition does not converge to the boundary steady state, which corresponds to the trivial uniform steady state in the classical Gray-Scott model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109453"},"PeriodicalIF":1.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936852","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":"Exploring the spatio–temporal dynamics in activator–inhibitor systems through a dual approach of analysis and computation","authors":"Vincent Nandwa Chiteri ,&nbsp;Victor Ogesa Juma ,&nbsp;James Mariita Okwoyo ,&nbsp;Stephen Kibet Moindi ,&nbsp;Kudzanayi Zebedia Mapfumo ,&nbsp;Anotida Madzvamuse","doi":"10.1016/j.mbs.2025.109449","DOIUrl":"10.1016/j.mbs.2025.109449","url":null,"abstract":"<div><div>Real–world mathematical models often manifest as systems of non-linear differential equations, which presents challenges in obtaining closed-form analytical solutions. In this paper, we study the diffusion-driven instability of an activator–inhibitor–type reaction–diffusion (RD) system modeling the GEF–Rho–Myosin signaling pathway linked to cellular contractility. The mathematical model we study is formulated from first principles using experimental observations. The model formulation is based on the biological and mathematical assumptions. The novelty is the incorporation of Myo9b as a GAP for RhoA, leading to a new mathematical model that describes Rho activity dynamics linked to cell contraction dynamics. Assuming mass conservation of molecular species and adopting a quasi-steady state assumption based on biological observations, model reduction is undertaken and leads us to a system of two equations. We adopt a dual approach of mathematical analysis and numerical computations to study the spatiotemporal dynamics of the system. First, in absence of diffusion, we use a combination of phase-plane analysis, numerical bifurcation and simulations to characterize the temporal dynamics of the model. In the absence of spatial variations, we identified two sets of parameters where the model exhibit different transition dynamics. For some set of parameters, the model transitions from stable to oscillatory and back to stable, while for another set, the model dynamics transition from stable to bistable and back to stable dynamics. To study the effect of parameter variation on model solutions, we use partial rank correlation coefficient (PRCC) to characterize the sensitivity of the model steady states with respect to parameters. Second, we extend the analysis of the model by studying conditions under which a uniform steady state becomes unstable in the presence of spatial variations, in a process known as Turing diffusion–driven instability. By exploiting the necessary conditions for diffusion–driven instability and the sufficient conditions for pattern formation we carry out, numerically, parameter estimation through the use of mode isolation. To support theoretical and computational findings, we employ the pdepe solver in one-space dimension and the finite difference method in two–space dimension.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109449"},"PeriodicalIF":1.9,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908190","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":"Mathematical modeling of neuroblast migration toward the olfactory bulb","authors":"Daniel Acosta-Soba ,&nbsp;Carmen Castro ,&nbsp;Noelia Geribaldi-Doldán ,&nbsp;Francisco Guillén-González ,&nbsp;Pedro Nunez-Abades ,&nbsp;Noelia Ortega-Román ,&nbsp;Patricia Pérez-García ,&nbsp;J. Rafael Rodríguez-Galván","doi":"10.1016/j.mbs.2025.109446","DOIUrl":"10.1016/j.mbs.2025.109446","url":null,"abstract":"<div><div>This article is devoted to the mathematical modeling of the migration of neuroblasts, precursor cells of neurons, along the Rostral Migratory Stream (RMS), the pathway they usually follow before maturing. According to our model, this way is determined mainly by attraction forces to the olfactory bulb, and also by the heterogeneous mobility of neuroblasts in different regions of the brain. Carefully identifying them as solutions to partial differential equations allows us to determine the movement of neuroblasts along the RMS in a realistic fashion. For solving the equations we develop numerical schemes where the application of novel discontinuous Galerkin methods allows to maintain the properties of the continuous model such as the maximum principle. We present some successful computer tests including parameter adjustment to fit real data from rodent brains.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109446"},"PeriodicalIF":1.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908189","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":"Impact of heterogeneity on infection probability: Insights from single-hit dose–response models","authors":"Francisco J. Pérez-Reche","doi":"10.1016/j.mbs.2025.109447","DOIUrl":"10.1016/j.mbs.2025.109447","url":null,"abstract":"<div><div>The process of infection of a host is complex, influenced by factors such as microbial variation within and between hosts as well as differences in dose across hosts. This study uses dose–response and within-host microbial infection models to delve into the impact of these factors on infection probability. It is rigorously demonstrated that within-host heterogeneity in microbial infectivity enhances the probability of infection. The effect of infectivity and dose variation between hosts is studied in terms of the expected value of the probability of infection. General analytical findings, derived under the assumption of small infectivity, reveal that both types of heterogeneity reduce the expected infection probability. Interestingly, this trend appears consistent across specific dose–response models, suggesting a limited role for the small infectivity condition. Additionally, the vital dynamics behind heterogeneous infectivity are investigated with a within-host microbial growth model which enhances the biological significance of single-hit dose–response models. Testing these mathematical predictions inspire new and challenging laboratory experiments that could deepen our understanding of infections.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109447"},"PeriodicalIF":1.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894599","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 roles of continuous and discontinuous proliferations on hepatitis B virus infection","authors":"Rupchand Sutradhar,&nbsp;D.C. Dalal","doi":"10.1016/j.mbs.2025.109448","DOIUrl":"10.1016/j.mbs.2025.109448","url":null,"abstract":"<div><div>The proliferation of both uninfected and infected hepatocytes, as well as the recycling effects of rcDNA-containing capsids are two key mechanisms playing significant roles in the persistence and clearance of hepatitis B virus (HBV) infection. In this study, the temporal dynamics of this viral infection is investigated through two intercellular mathematical models considering proliferation of both types of hepatocytes (uninfected and infected) and recycling effects of capsids. Both models are formulated on the basis of a key finding in the existing literature: mitosis of an infected hepatocytes yields in two uninfected progenies. In the first model (defined by P-model), we examine the continuous proliferation (which occur continuously), while the second one (defined by M-model) deals with the discontinuous proliferation (happen when the concentration of liver cells decreases to less than 70% of its initial concentration). The proposed models are calibrated with the experimental data obtained from an adult chimpanzee. Results of this study suggest that when both hepatocytes proliferate with equal rate, proliferation helps the individual in a rapid recovery from the acute infection whereas in case of chronic infection, the severity of the infection increases. On the other hand, if the infected hepatocytes proliferate at a different rate that of uninfected hepatocytes, the proliferation of uninfected hepatocytes contributes to increase the infection, but the proliferation of infected hepatocytes acts to reduce the infection from the long-term perspective. The global sensitivity analysis also shows the same results. Furthermore, it is also observed that the differences between the outcomes of continuous and discontinuous proliferations are significant and noteworthy.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109448"},"PeriodicalIF":1.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876819","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":"Dynamical differences in rod and cone photoresponses","authors":"Miguel Castillo García,&nbsp;Eugenio Urdapilleta","doi":"10.1016/j.mbs.2025.109445","DOIUrl":"10.1016/j.mbs.2025.109445","url":null,"abstract":"<div><div>Understanding how photoreceptor cells respond to light is crucial for comprehending the intricacies of vision. These cells, known as rods and cones, play a pivotal role as they convert light into electrical signals that the brain can interpret. If these cells share this exquisite machinery, how can photoresponses be so different? In this work, we study the factors influencing the dynamics of photoreceptor responses. Based on a detailed model of the underlying biochemical steps, we analyzed the impact of various processes on the response, with particular emphasis on the cyclase feedback. Our study focused on the transition between monophasic and biphasic regimes in photoreceptor responses. Critically, the influence of intracellular messengers’ turnover rates, such as for Ca²⁺ and cGMP, initial concentrations, maximum currents, and the modulation by other parameters was studied in depth. By analyzing both dark-adapted and light-adapted responses for rods and cones, we highlighted the importance of Ca²⁺ concentration and the cGMP turnover in darkness to determine bi- or mono-phasic responses. Through this systematic exploration, we aimed to provide valuable insights about the underlying mechanisms driving the dynamic behavior of photoresponses and to answer why similar experiments give rise to different dynamical behaviors.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109445"},"PeriodicalIF":1.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143842539","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":"Biological pattern formation in cell dynamics under cross-diffusion: An Isogeometric analysis perspective","authors":"Ilham Asmouh","doi":"10.1016/j.mbs.2025.109444","DOIUrl":"10.1016/j.mbs.2025.109444","url":null,"abstract":"<div><div>This note presents an efficient numerical method based on isogeometric analysis (IgA) and an operator splitting approach for solving nonlinear reaction–diffusion systems with cross-diffusion. Such problems are often used in mathematical modeling of developmental biology and are subject to highly rigid reactive and diffusive terms. Similarly, the interactions between substances produce complex morphologies (Roth, 2011) <span><span>[1]</span></span>. In this note we present two different types of solutions. Mainly, the Turing patterns and the traveling waves, which are a direct result of the presence of linear diffusion and/or cross-diffusion in the dynamical system. To deal with the multiphysical nature of the nonlinear system, we propose a time-splitting method. The spatial discretization is performed using IgA-based Non-Uniform Ratinal B-spline (NURBS) functions, where the semidiscrete problem is integrated using an implicit scheme. The nonlinear terms are treated by an adaptive fourth-order Runge–Kutta method. The well-known FitzHugh–Nagumo and Gray–Scott models are used to study the performance of the new method. The results obtained demonstrate the ability of our algorithm to accurately maintain the shape of the solution in the presence of complex patterns arising from biological cells on complex geometries. Furthermore, the energy dissipation in the Allen-Cahn equation is analyzed and the new method clarifies the effect of the geometry on the formed patterns and on the energy decay for the considered benchmarks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"384 ","pages":"Article 109444"},"PeriodicalIF":1.9,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830344","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}