Mathematical Biosciences最新文献

{"title":"The effects of tritiated water on competitive outcomes of two Daphnia species in lakes: A reaction–diffusion tritium-taxis model","authors":"Xiaoshuang Li ,&nbsp;Hua Nie ,&nbsp;Xiao Yan","doi":"10.1016/j.mbs.2025.109420","DOIUrl":"10.1016/j.mbs.2025.109420","url":null,"abstract":"<div><div>The discharge of nuclear-contaminated water, particularly tritiated water (HTO), poses a significant global environmental challenge due to its potential negative impacts on ecosystems. To examine how such discharges influence the competitive dynamics between two Daphnia species in lake environments, we develop a spatiotemporal competition model that incorporates a tritium-taxis term. Our findings indicate that a moderate HTO input rate, combined with varying radiosensitivity between the species, can reverse the competitive outcomes between the two species. Specifically, species with lower radiosensitivity to HTO may compensate for competitive disadvantages, potentially enhancing biodiversity, or conversely, gain a competitive edge, which could reduce biodiversity. Moreover, a low HTO removal rate can lead to bistability or tristability in the system, while strong tritium-taxis promotes the development of spatially heterogeneous patterns. This study underscores the importance of considering the indirect effects of moderate HTO input and species-specific radiosensitivity, which can result in counterintuitive ecological dynamics.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"383 ","pages":"Article 109420"},"PeriodicalIF":1.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143598670","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":"Role of non-exponential reversal times in aggregation models of bacterial populations","authors":"Michael Batista ,&nbsp;Patrick Murphy ,&nbsp;Oleg A. Igoshin ,&nbsp;Misha Perepelitsa ,&nbsp;Ilya Timofeyev","doi":"10.1016/j.mbs.2025.109418","DOIUrl":"10.1016/j.mbs.2025.109418","url":null,"abstract":"<div><div>Individual bacteria typically follow somewhat simple rules of motion, but collective behavior can exhibit complex behavioral patterns. For instance, the formation and dispersal of aggregates of reversing bacteria in biofilms are primarily driven by coordinated motion among cells. Many mathematical models of aggregation assume that cells have no memory, e.g., the time between their behavior changes, such as direction reversals, is exponentially distributed. However, in practice, the distribution is quite distinct from exponential. Therefore, in this paper, we analyze numerically the importance of non-exponential reversal times in 1D agent-based and kinetic models of aggregation. In particular, we consider these models in a practical parameter regime by fitting a Gamma distribution to represent the run times of myxobacteria and study their collective behavior with exponential and non-exponential reversal times. We demonstrate that non-exponential reversal times aid aggregation and result in tighter aggregates. We compare and contrast the behavior of agent-based and kinetic models that consider aggregation driven by chemotaxis. Thus, incorporating non-exponential reversal times into models of aggregation can be particularly important for reproducing experimental data, such as aggregate persistence and dispersal. These results provide a simple example of how the existence of memory helps bacteria coordinate their behaviors.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"383 ","pages":"Article 109418"},"PeriodicalIF":1.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143588891","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":"Mechanistic models are hypotheses: A perspective","authors":"John W Glasser ,&nbsp;Zhilan Feng","doi":"10.1016/j.mbs.2025.109419","DOIUrl":"10.1016/j.mbs.2025.109419","url":null,"abstract":"<div><div>Science involves perceiving patterns (events that are repeated) in observations, hypothesizing causal explanations (underlying processes), and testing them. Mathematical models either describe or provide explanations for patterns. The equations of descriptive models have convenient mathematical properties while those of mechanistic ones correspond to processes. The parameters of descriptive models are fit to observations by choosing values that minimize discrepant predictions. Because mechanistic models are hypotheses about the processes underlying patterns, their parameters should not be fit, but rather, should be based insofar as possible on first principles or estimated independently. The precision of mathematics facilitates comparing the predictions of mechanistic models to the patterns that they purport to explain and, until concordant, identifying and remedying the cause(s) of disparities.</div><div>The findings and conclusions in this report are those of the authors and do not necessarily represent official positions of the Centers for Disease Control and Prevention or National Science Foundation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"383 ","pages":"Article 109419"},"PeriodicalIF":1.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143545259","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 modeling study of the effectiveness of contact tracing in reducing the spread of infectious diseases with incubation period","authors":"Mohamed Ladib ,&nbsp;Cameron J. Browne ,&nbsp;Hayriye Gulbudak ,&nbsp;Aziz Ouhinou","doi":"10.1016/j.mbs.2025.109415","DOIUrl":"10.1016/j.mbs.2025.109415","url":null,"abstract":"<div><div>In this work, we study an epidemic model with demography that incorporates some key aspects of the contact tracing intervention. We derive generic formulae for the effective reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> when contact tracing is employed to mitigate the spread of infection. The derived expressions are reformulated in terms of the initial reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> (in the absence of tracing), the number of traced cases caused by a primary untraced reported index case, and the average number of secondary cases infected by traced infectees during their infectious period. In parallel, under some restrictions, the local stability of the disease-free equilibrium is investigated. The model was fitted to data of Ebola disease collected during the 2014–2016 outbreaks in West Africa. Finally, numerical simulations are provided to investigate the effect of key parameters on <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span>. By considering ongoing interventions, the simulations indicate whether contact tracing can suppress <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> below unity, as well as identify parameter regions where it can effectively contain epidemic outbreaks when applied with a given level of efficiency.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"383 ","pages":"Article 109415"},"PeriodicalIF":1.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143532276","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":"Bifurcations of higher codimension in a Leslie–Gower predator–prey model with Holling II functional response and weak Allee effect","authors":"Zhenliang Zhu ,&nbsp;Qun Zhu ,&nbsp;Lingling Liu","doi":"10.1016/j.mbs.2025.109405","DOIUrl":"10.1016/j.mbs.2025.109405","url":null,"abstract":"<div><div>A Leslie-type predator–prey system with Holling II functional response and weak Allee effect in prey is analyzed deeply in this paper. Through rigorous analysis, the system can undergo a series of bifurcations such as cusp type nilpotent bifurcation of codimension 4 and a degenerate Hopf bifurcation of codimension up to 3 as the parameters vary. Compared with the system without Allee effect, it can be concluded that weak Allee effect can induce more abundant dynamics and bifurcations, in particular, the increase in the number of equilibria and the appearance of multiple limit cycles. Moreover, when the intensity of predation is too high, the prey affected by the weak Allee effect will also become extinct, and eventually lead to the collapse of the system. Finally, we present some numerical simulations by MATCONT to illustrate the existence of bifurcations and some phase portraits of the system.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109405"},"PeriodicalIF":1.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520541","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 trade-offs in drug administration for cancer treatment: A multi-criteria optimisation approach","authors":"Maicon de Paiva Torres ,&nbsp;Fran Sérgio Lobato ,&nbsp;Gustavo Barbosa Libotte","doi":"10.1016/j.mbs.2025.109404","DOIUrl":"10.1016/j.mbs.2025.109404","url":null,"abstract":"<div><div>This study addresses the combination of immunotherapy and chemotherapy in cancer treatment, recognising its promising effectiveness but highlighting the challenges of complex interactions between these therapeutic modalities. The central objective is to determine guidelines for the optimal administration of drugs, using an optimal control model that considers interactions in tumour dynamics, including cancer cells, the immune system, and therapeutic agents. The optimal control model is transformed into a multi-objective optimisation problem with treatment constraints. This is achieved by introducing adjustable trade-offs, allowing personalised adaptations in drug administration to achieve an optimal balance between established objectives. Various optimisation problems are addressed, considering two and three simultaneous objectives, such as optimising the number of cancer cells and the density of effector cells at the final treatment time. The diverse combinations presented reflect the model’s flexibility in the face of multi-objective optimisation, providing a range of approaches to meet specific medical needs. The analysis of Pareto optimal fronts in <em>in silico</em> investigation offers an additional resource for decision-makers, enabling a more effective determination of the optimal administration of cytotoxic and immunotherapeutic agents. By leveraging an optimal control model, we have demonstrated the effectiveness of considering interactions in tumour dynamics, including the integration of immunotherapy and chemotherapy. Our findings underscore the importance of tailored treatment plans to achieve optimal outcomes, showcasing the versatility of our approach in addressing individual patient needs. The insights gained from our analysis offer valuable guidance for future research and clinical practice, paving the way for more effective and personalised cancer therapies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109404"},"PeriodicalIF":1.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508981","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":"How environmental stochasticity can destroy the persistence of macroalgae in a coral reefs ecosystem","authors":"Chaoqun Xu,&nbsp;Qiucun Chen","doi":"10.1016/j.mbs.2025.109402","DOIUrl":"10.1016/j.mbs.2025.109402","url":null,"abstract":"<div><div>In this study, we mainly investigate how environmental stochasticity can destroy the persistence of macroalgae in a coral reefs ecosystem by analyzing the noise-induced tipping behavior. Firstly, detailed mathematical analysis for all feasible system parameters shows that the deterministic system has rich dynamics, including two types of bifurcations and two types of bistabilities. This also reveals that the dynamic behavior of coral reefs ecosystem could be highly sensitive to the system parameters and initial values. For the stochastic system, two kinds of noise-induced tipping behaviors are numerically found: Transition from coral-free state to macroalgae-free state; transition from coexistence state to macroalgae-free state. We then mainly analyze the impacts of noise intensity on the probability and time that coral reef ecosystem tips between different states, evaluate the extinction risk of macroalgae for different initial values, and eventually assign extinction warning levels to these values. Our analysis reveals that as a fragile marine ecosystem, the evolution trend of the coral reefs depends not only on the system parameters and initial values, but also on the intensity of the stochasticity experienced by the system.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109402"},"PeriodicalIF":1.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464002","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":"Stability of periodic solution for a free boundary problem modeling small plaques","authors":"Jingyi Liu,&nbsp;Bei Hu","doi":"10.1016/j.mbs.2025.109397","DOIUrl":"10.1016/j.mbs.2025.109397","url":null,"abstract":"<div><div>Mathematical models describing the growth of plaque in the arteries (e.g., Friedman and Hao (2015), Friedman et al. (2015), Hao and Friedman (2014), McKay et al. (2005) and Mukherjee et al. (2019)) were introduced. All of these models include the interaction of the “bad” cholesterols, low-density lipoprotein (LDL), and the “good” cholesterols, high-density lipoprotein (HDL), in triggering whether plaque will grow or shrink.</div><div>Because the blood vessels tend to be circular, 2D cross-section model is a good approximation, and the 2D models are studied in Friedman et al. (2015), Zhang et al. (2023) and Zhao and Hu (2022). A bifurcation into a 3D plaque was recently studied in Huang and Hu (2022). All of these models assume a constant supply of LDL and HDL from the blood vessel.</div><div>In reality, nutrient concentration changes with the intake of food, which happens very often in a periodic manner. When the LDL and HDL supplies from the blood vessel are periodic and are not too far away from the prevalent values, a periodic solution was obtained in Huang and Hu (2023). In this paper, we carry out the linear stability analysis of this periodic solution and provide simulation results to confirm our analysis.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109397"},"PeriodicalIF":1.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420931","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":"Hybrid analysis with phylogeny and population modeling to estimate the recent founding date of a population: A case study in the origins of COVID-19 illustrates how a branching process approximation can simplify a hybrid analysis","authors":"John L. Spouge","doi":"10.1016/j.mbs.2025.109401","DOIUrl":"10.1016/j.mbs.2025.109401","url":null,"abstract":"<div><div>The exact date of the primary infection in COVID-19 remains unknown. One influential article (Pekar et al. (2021)) estimated the date with a hybrid analysis combining epidemiological and phylogenetic methods. The phylogenetic methods analyzed 583 SARS-COV-2 complete genomes to estimate the sample tMRCA (time of the most recent common ancestor). Before igniting as an epidemic, however, COVID-19 may have had several population bottlenecks with only a single infected person, so the MRCA merely represents the last such bottleneck. Pekar et al. (2021) therefore used epidemiological methods to estimate the time from the primary infection to the sample MRCA. The hybrid method involved several arbitrary decisions, however, reflecting the fact that the epidemiological and phylogenetic analyses overlap at the sample MRCA and are generally probabilistically dependent. Towards removing the dependence, note that the start of an epidemic has a branching process approximation. Let the branching process have a single ancestor. If the branching process does not go extinct, define skeleton particles (individuals) to be particles whose lineages do not go extinct, and define the long-time MRCA as the earliest skeleton particle with at least two skeleton offspring. A linear phylogeny of skeleton particles therefore separates the ancestor from the long-time MRCA. Probabilistically, the linear phylogeny is a defective renewal process of skeleton particles, making the generation count geometrically distributed. Moreover, the terminology “long-time MRCA” is apt, because as time becomes arbitrarily large, the MRCA of the corresponding extant population approaches the long-time MRCA. Effectively, the focus on the long-time MRCA makes the forward epidemiological and backward phylogenetic analyses probabilistically independent. The present article can therefore confirm most of the epidemiological conclusions of the hybrid analysis of Pekar et al. (2021). Its use of branching process approximations also points the way to noticeable simplifications in the hybrid method.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109401"},"PeriodicalIF":1.9,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143416645","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":"A conceptual framework for modeling a latching mechanism for cell cycle regulation","authors":"Punit Gandhi ,&nbsp;Yangyang Wang","doi":"10.1016/j.mbs.2025.109396","DOIUrl":"10.1016/j.mbs.2025.109396","url":null,"abstract":"<div><div>Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109396"},"PeriodicalIF":1.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143411670","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}