Bulletin of Mathematical Biology最新文献_第2页

A Mathematical Exploration of SDH-b Loss in Chromaffin Cells.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-13 DOI: 10.1007/s11538-025-01427-z

Elías Vera-Sigüenza, Himani Rana, Ramin Nashebi, Ielyaas Cloete, Katarína Kl'uvčková, Fabian Spill, Daniel A Tennant

{"title":"A Mathematical Exploration of SDH-b Loss in Chromaffin Cells.","authors":"Elías Vera-Sigüenza, Himani Rana, Ramin Nashebi, Ielyaas Cloete, Katarína Kl'uvčková, Fabian Spill, Daniel A Tennant","doi":"10.1007/s11538-025-01427-z","DOIUrl":"10.1007/s11538-025-01427-z","url":null,"abstract":"The succinate dehydrogenase (SDH) is a four-subunit enzyme complex (SDH-a, SDH-b, SDH-c, and SDH-d) central to cell carbon metabolism. The SDH bridges the tricarboxylic acid cycle to the electron transport chain. A pathological loss of the SDH-b subunit leads to a cell-wide signalling cascade that shifts the cell's metabolism into a pseudo-hypoxic state akin to the so-called Warburg effect (or aerobic glycolysis). This trait is a hallmark of phaeochromocytomas, a rare tumour arising from chromaffin cells; a type of cell that lies in the medulla of the adrenal gland. In this study, we leverage the insights from a mathematical model constructed to underpin the metabolic implications of SDH-b dysfunction in phaeochromocytomas. We specifically investigate why chromaffin cells seemingly have the ability to maintain electron transport chain's Complex I function when confronted with the loss of the SDH-b subunit while other cells do not. Our simulations indicate that retention of Complex I is associated with cofactor oxidation, which enables cells to manage mitochondrial swelling and limit the reversal of the adenosine triphosphate synthase, supporting cell fitness, without undergoing lysis. These results support previous hypotheses that point to mitochondrial proton leaks as a critical factor of future research. Moreover, the model asserts that control of the proton gradient across the mitochondrial inner membrane is rate-limiting upon fitness management of SDH-b deficient cells.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"53"},"PeriodicalIF":2.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11906556/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143623523","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}

引用次数: 0

Characterization of the Long-distance Dispersal Kernel of White-Tailed Deer and Evaluating its Impact on Chronic Wasting Disease Spread in Wisconsin. 白尾鹿长距离传播内核的特征及其对威斯康星州慢性消耗性疾病传播的影响评估。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-13 DOI: 10.1007/s11538-024-01394-x

Mennatallah Gouda, Jim Powell, W Jacob McClure, Daniel P Walsh, Daniel Storm

{"title":"Characterization of the Long-distance Dispersal Kernel of White-Tailed Deer and Evaluating its Impact on Chronic Wasting Disease Spread in Wisconsin.","authors":"Mennatallah Gouda, Jim Powell, W Jacob McClure, Daniel P Walsh, Daniel Storm","doi":"10.1007/s11538-024-01394-x","DOIUrl":"10.1007/s11538-024-01394-x","url":null,"abstract":"Chronic wasting disease (CWD) is a fatal neurodegenerative disease infecting cervids. It is highly contagious and caused by misfolded prions that propagate via templated conformational conversion of the cervid's normal prion protein. Prevalence of CWD in free-ranging deer in North America is mostly low, but in some regions local prevalence has reached 80%. CWD prions can be transmitted via direct contact with infected individuals or indirectly through the environment. Infected individuals shed prions through feces, urine, saliva or carcasses, and prions have long environmental persistence. Long-distance dispersal of infected deer poses a significant risk for CWD spread. We propose an integrodifference equation (IDE) model to capture CWD dynamics and the consequences of long-distance dispersal behavior in white-tailed deer (WTD, Odocoileus virginianus). A diffusion-settling model characterizes long-distance dispersal kernels, accommodating hypothetical dispersal behaviors through time-dependent settling rate functions. Three new closed-form dispersal kernels are approximated using Laplace's method and parameterized with GPS location data collected from WTD in Wisconsin, USA. Settling rates reflecting ongoing sensitivity to stimuli which prompt deer to disperse from their natal home range give the most supported long-distance dispersal kernel. Impact of long-distance dispersal on CWD spread is quantified using the IDE model. At high population densities, long-distance dispersal can magnify CWD spread by a factor of four. At lower population densities single infected individuals cannot initiate an outbreak, but CWD may still spread due to the accumulation of environmental hazard from prions behind the wave of invasion, possibly presenting substantial management challenges.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"52"},"PeriodicalIF":2.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143623671","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}

引用次数: 0

Exploring the Evolution of Altruistic Punishment with a PDE Model of Cultural Multilevel Selection.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-03-12 DOI: 10.1007/s11538-025-01422-4

Daniel B Cooney

{"title":"Exploring the Evolution of Altruistic Punishment with a PDE Model of Cultural Multilevel Selection.","authors":"Daniel B Cooney","doi":"10.1007/s11538-025-01422-4","DOIUrl":"10.1007/s11538-025-01422-4","url":null,"abstract":"Two mechanisms that have been used to study the evolution of cooperative behavior are altruistic punishment, in which cooperative individuals pay additional costs to punish defection, and multilevel selection, in which competition between groups can help to counteract individual-level incentives to cheat. Boyd, Gintis, Bowles, and Richerson have used simulation models of cultural evolution to suggest that altruistic punishment and pairwise group-level competition can work in concert to promote cooperation, even when neither mechanism can do so on its own. In this paper, we formulate a PDE model for multilevel selection motivated by the approach of Boyd and coauthors, modeling individual-level birth-death competition with a replicator equation based on individual payoffs and describing group-level competition with pairwise conflicts based on differences in the average payoffs of the competing groups. Building off of existing PDE models for multilevel selection with frequency-independent group-level competition, we use analytical and numerical techniques to understand how the forms of individual and average payoffs can impact the long-time ability to sustain altruistic punishment in group-structured populations. We find several interesting differences between the behavior of our new PDE model with pairwise group-level competition and existing multilevel PDE models, including the observation that our new model can feature a non-monotonic dependence of the long-time collective payoff on the strength of altruistic punishment. Going forward, our PDE framework can serve as a way to connect and compare disparate approaches for understanding multilevel selection across the literature in evolutionary biology and anthropology.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"51"},"PeriodicalIF":2.0,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143613490","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}

引用次数: 0

Epidemiological Dynamics in Populations Structured by Neighbourhoods and Households.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-27 DOI: 10.1007/s11538-025-01426-0

Abby Barlow, Sarah Penington, Ben Adams

{"title":"Epidemiological Dynamics in Populations Structured by Neighbourhoods and Households.","authors":"Abby Barlow, Sarah Penington, Ben Adams","doi":"10.1007/s11538-025-01426-0","DOIUrl":"10.1007/s11538-025-01426-0","url":null,"abstract":"Epidemiological dynamics are affected by the spatial and demographic structure of the host population. Households and neighbourhoods are known to be important groupings but little is known about the epidemiological interplay between them. In order to explore the implications for infectious disease epidemiology of households with similar demographic structures clustered in space we develop a multi-scale epidemic model consisting of neighbourhoods of households. In our analysis we focus on key parameters which control household size, the importance of transmission within households relative to outside of them, and the degree to which the non-household transmission is localised within neighbourhoods. We construct the household reproduction number <math><mmultiscripts><mi>R</mi> <mrow><mrow></mrow> <mo>∗</mo></mrow> <mrow></mrow></mmultiscripts> </math> over all neighbourhoods and derive the analytic probability of an outbreak occurring from a single infected individual in a specific neighbourhood. We find that reduced localisation of transmission within neighbourhoods reduces <math><mmultiscripts><mi>R</mi> <mrow><mrow></mrow> <mo>∗</mo></mrow> <mrow></mrow></mmultiscripts> </math> when household size differs between neighbourhoods. This effect is amplified by larger differences between household sizes and larger divergence between transmission rates within households and outside of them. However, the impact of neighbourhoods with larger household sizes on an individual's risk of infection is mainly limited to the individuals that reside in those neighbourhoods. We consider various surveillance scenarios and show that household size information from the initial infectious cases is often more important than neighbourhood information while household size and neighbourhood localisation influences the sequence of neighbourhoods in which an outbreak is observed.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"50"},"PeriodicalIF":2.0,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11868190/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143522736","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}

引用次数: 0

An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains. 增长的一维域上反应-扩散模式的尖峰自复制和尖峰成核的渐近分析。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-24 DOI: 10.1007/s11538-025-01418-0

Chunyi Gai, Edgardo Villar-Sepúlveda, Alan Champneys, Michael J Ward

{"title":"An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains.","authors":"Chunyi Gai, Edgardo Villar-Sepúlveda, Alan Champneys, Michael J Ward","doi":"10.1007/s11538-025-01418-0","DOIUrl":"10.1007/s11538-025-01418-0","url":null,"abstract":"In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a one-dimensional finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinct bifurcation mechanisms can occur which generate spike patterns of increased spatial complexity as the domain half-length L slowly increases; so-called spike nucleation and spike self-replication. Self-replication is found to occur via the passage beyond a saddle-node bifurcation point that can be predicted through linearization around the inner spike profile. In contrast, spike nucleation occurs through slow passage beyond the saddle-node of a nonlinear boundary-value problem defined in the outer region away from the core of a spike. Here, by treating L as a static parameter under the Lagrangian framework, precise conditions are established within the semi-strong interaction asymptotic regime to determine which occurs, conditions that are confirmed by numerical simulation and continuation. For the Schnakenberg and Brusselator RD models, phase diagrams in parameter space are derived that predict whether spike self-replication or spike nucleation will occur first as L is increased, or whether no such instability will occur. For the Gierer-Meinhardt model with a non-trivial activator background, spike nucleation is shown to be the only possible spike-generating mechanism. From time-dependent PDE numerical results on an exponentially slowly growing domain, it is shown that the analytical thresholds derived from the asymptotic theory accurately predict critical values of L where either spike self-replication or spike-nucleation will occur. The global bifurcation mechanism for transitions to patterns of increased spatial complexity is further elucidated by superimposing time-dependent PDE simulation results on the numerically computed solution branches of spike equilibria in which L is the primary bifurcation parameter.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"48"},"PeriodicalIF":2.0,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481833","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}

引用次数: 0

EAD Mechanisms in Hypertrophic Mouse Ventricular Myocytes: Insights from a Compartmentalized Mathematical Model.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-24 DOI: 10.1007/s11538-025-01423-3

Dilmini Warnakulasooriya, Vladimir E Bondarenko

{"title":"EAD Mechanisms in Hypertrophic Mouse Ventricular Myocytes: Insights from a Compartmentalized Mathematical Model.","authors":"Dilmini Warnakulasooriya, Vladimir E Bondarenko","doi":"10.1007/s11538-025-01423-3","DOIUrl":"10.1007/s11538-025-01423-3","url":null,"abstract":"Transverse aortic constriction (TAC) is one of the experimental mouse models that are designed to investigate cardiac hypertrophy and heart failure. Most of the studies with this model are devoted to the stage of developed heart failure. However, several studies of the early stages (hypertrophy after 1 week of TAC) of this disease found significant changes in the β-adrenergic system, electrical activity, and Ca2+ dynamics in mouse ventricular myocytes. To provide a quantitative description of cardiac hypertrophy, we developed a new compartmentalized mathematical model of hypertrophic mouse ventricular myocytes for the early stage after the TAC procedure. The model described the changes in cell geometry, action potentials, [Ca2+]i transients, and β1- and β2-adrenergic signaling systems. We also showed that the hypertrophic myocytes demonstrated early afterdepolarizations (EADs) upon stimulation with isoproterenol at relatively long stimulation periods. Simulation of the hypertrophic myocyte activities revealed that the synergistic effects of the late Na+ current, the L-type Ca2+ current, and the T-type Ca2+ current were responsible for the initiation of EADs. The mechanisms of EAD and its suppression were investigated and sensitivity analysis was performed. Simulation results obtained with the hypertrophic cell model were compared to those from the normal ventricular myocytes. The developed mathematical model can be used for the explanation of the existing experimental data, for the development of the models for other hypertrophic phenotypes, and to make experimentally testable predictions of a hypertrophic myocyte's behavior.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"49"},"PeriodicalIF":2.0,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481835","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}

引用次数: 0

modelSSE: An R Package for Characterizing Infectious Disease Superspreading from Contact Tracing Data. modelSSE：从接触追踪数据描述传染病超级传播特征的 R 软件包。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-21 DOI: 10.1007/s11538-025-01421-5

Shi Zhao, Zihao Guo, Kai Wang, Shengzhi Sun, Dayu Sun, Weiming Wang, Daihai He, Marc Kc Chong, Yuantao Hao, Eng-Kiong Yeoh

{"title":"modelSSE: An R Package for Characterizing Infectious Disease Superspreading from Contact Tracing Data.","authors":"Shi Zhao, Zihao Guo, Kai Wang, Shengzhi Sun, Dayu Sun, Weiming Wang, Daihai He, Marc Kc Chong, Yuantao Hao, Eng-Kiong Yeoh","doi":"10.1007/s11538-025-01421-5","DOIUrl":"10.1007/s11538-025-01421-5","url":null,"abstract":"Infectious disease superspreading is a phenomenon where few primary cases generate unexpectedly large numbers of secondary cases. Superspreading, is frequently documented in epidemiology literature, and is considered a consequence of heterogeneity in transmission. Since understanding the risks of superspreading became a rising concern from both statistical modelling and public health aspects, the R package modelSSE provides comprehensive analytical tools to characterize transmission heterogeneity. The package modelSSE integrates recent advances in statistical methods, such as decomposition of reproduction number, for modelling infectious disease superspreading using various types and sources of contact tracing data that allow models to be grounded in real-world observations. This study provided an overview of the theoretical background and implementation of modelSSE, designed to facilitate learning infectious disease transmission, and explore novel research questions for transmission risks and superspreading potentials. Detailed examples of classic, historical infectious disease datasets are given for demonstration and model extensions.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"47"},"PeriodicalIF":2.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143467161","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}

引用次数: 0

Influence of Contact Lens Parameters on Tear Film Dynamics.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-19 DOI: 10.1007/s11538-025-01425-1

Darshan Ramasubramanian, José Luis Hernández-Verdejo, José Manuel López-Alonso

{"title":"Influence of Contact Lens Parameters on Tear Film Dynamics.","authors":"Darshan Ramasubramanian, José Luis Hernández-Verdejo, José Manuel López-Alonso","doi":"10.1007/s11538-025-01425-1","DOIUrl":"10.1007/s11538-025-01425-1","url":null,"abstract":"This study employs a computational model to simulate the dynamics of tear fluid and tear film in conjunction with contact lens motion, examining the interplay between diverse contact lens characteristics-such as material, design, and dimensions-and key ocular factors like dry eye conditions, corneal size, and blink rate. These interactions are critical for customising lens fit to maximise wearer comfort. Utilising optical measurements from a single participant, the study integrates data on tear meniscus size, blink velocity, and palpebral fissure height with sixteen different contact lens parameters, including Young's modulus, thickness, diameter, and curvature. Correlation analyses were conducted to determine the impact of these parameters on the dynamics of the tear fluid and overall tear film. Results show that the diameter and Young's modulus of the contact lens significantly influence pre-lens tear film thickness, with robust, statistically significant correlations. In contrast, lens thickness and base curve showed minimal impact, as evidenced by weak and non-significant correlations. These findings underscore the critical roles of lens diameter and Young's modulus in enhancing the stability and distribution of tear fluid, thereby improving wearer comfort and advancing contact lens design.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"45"},"PeriodicalIF":2.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143448181","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}

引用次数: 0

Unveiling the Negative Synergistic Effect of Wall Shear Stress and Insulin on Endothelial NO Dynamics by Mathematical Modeling.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-19 DOI: 10.1007/s11538-025-01424-2

Yu-Yuan Zhang, Yong-Jiang Li, Xu-Qu Hu, Chun-Dong Xue, Shen Li, Zheng-Nan Gao, Kai-Rong Qin

{"title":"Unveiling the Negative Synergistic Effect of Wall Shear Stress and Insulin on Endothelial NO Dynamics by Mathematical Modeling.","authors":"Yu-Yuan Zhang, Yong-Jiang Li, Xu-Qu Hu, Chun-Dong Xue, Shen Li, Zheng-Nan Gao, Kai-Rong Qin","doi":"10.1007/s11538-025-01424-2","DOIUrl":"10.1007/s11538-025-01424-2","url":null,"abstract":"Diabetic vascular complications (DVCs) are diabetes-induced vascular dysfunction and pathologies, leading to the major causes of morbidity and mortality in millions of diabetic patients worldwide. DVCs are provoked by endothelial dysfunction which is closely coordinated with two important hallmarks: one is the insufficient insulin secretion or insulin resistance, and another is the decrease in intracellular nitric oxide (NO) influenced by dynamic wall shear stress (WSS). Although the intracellular NO dynamics in endothelial cells (ECs) is crucial for endothelial function, the regulation of NO production by dynamic WSS and insulin is still poorly understood. In this study, we have proposed a mathematical model of intracellular NO production in ECs under the stimulation of dynamic WSS combined with insulin. The model integrates simultaneously the biochemical signaling pathways of insulin and the mechanotransduction pathways induced by dynamic WSS. The accuracy and reliability of the model to quantitatively describe NO production in ECs were compared and validated with reported experimental data. According to the validated model, inhibition of protein kinase B (AKT) phosphorylation and Ca2+ influx by dynamic oscillatory WSS disrupts the dual nature of endothelial nitric oxide synthase (eNOS) enzyme activation. This disruption leads to the decrease in NO production and the bimodal disappearance of NO waveforms. Moreover, the results reveal that dynamic WSS combined with insulin promote endothelial NO production through negative synergistic effects, which is resulted from the temporal differences in mechanical and biochemical signaling. In brief, the proposed model elucidates the mechanism of NO generation activated by dynamic WSS combined with insulin, providing a potential target and theoretical framework for future treatment of DVCs.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 4","pages":"46"},"PeriodicalIF":2.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143448184","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}

引用次数: 0

Correction to: Combining Mechanisms of Growth Arrest in Solid Tumours: A Mathematical Investigation.

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-02-12 DOI: 10.1007/s11538-024-01382-1

Chloé Colson, Helen M Byrne, Philip K Maini

引用次数: 0