Bulletin of Mathematical Biology最新文献

{"title":"Mathematical Model of CAR T-Cell Therapy for a B-Cell Lymphoma Lymph Node.","authors":"Soukaina Sabir, Odelaisy León-Triana, Sergio Serrano, Roberto Barrio, Victor M Pérez-García","doi":"10.1007/s11538-025-01417-1","DOIUrl":"10.1007/s11538-025-01417-1","url":null,"abstract":"<p><p>CAR T-cell therapies have demonstrated significant success in treating B-cell leukemia in children and young adults. However, their effectiveness in treating B-cell lymphomas has been limited in comparison to leukemia. In this paper we present a mathematical model that elucidates the dynamics of diffuse large B-cell lymphoma and CAR T-cells in a lymph node. The mathematical model aids in understanding the complex interplay between the cell populations involved and proposes ways to identify potential underlying dynamical causes of treatment failure. We also study the phenomenon of immunosuppression induced by tumor cells and theoretically demonstrate its impact on cell dynamics. Through the examination of various response scenarios, we underscore the significance of product characteristics in treatment outcomes.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 3","pages":"40"},"PeriodicalIF":2.0,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11805830/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143363717","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":"Employing Observability Rank Conditions for Taking into Account Experimental Information a priori.","authors":"Alejandro F Villaverde","doi":"10.1007/s11538-025-01415-3","DOIUrl":"10.1007/s11538-025-01415-3","url":null,"abstract":"<p><p>The concept of identifiability describes the possibility of inferring the parameters of a dynamic model by observing its output. It is common and useful to distinguish between structural and practical identifiability. The former property is fully determined by the model equations, while the latter is also influenced by the characteristics of the available experimental data. Structural identifiability can be determined by means of symbolic computations, which may be performed before collecting experimental data, and are hence sometimes called a priori analyses. Practical identifiability is typically assessed numerically, with methods that require simulations-and often also optimization-and are applied a posteriori. An approach to study structural local identifiability is to consider it as a particular case of observability, which is the possibility of inferring the internal state of a system from its output. Thus, both properties can be analysed jointly, by building a generalized observability matrix and computing its rank. The aim of this paper is to investigate to which extent such observability-based methods can also inform about practical aspects related with the experimental setup, which are usually not approached in this way. To this end, we explore a number of possible extensions of the rank tests, and discuss the purposes for which they can be informative as well as others for which they cannot.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 3","pages":"39"},"PeriodicalIF":2.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11802610/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143254620","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":"Differentiating Contact with Symptomatic and Asymptomatic Infectious Individuals in a SEIR Epidemic Model.","authors":"Victoria Chebotaeva, Anish Srinivasan, Paula A Vasquez","doi":"10.1007/s11538-025-01416-2","DOIUrl":"10.1007/s11538-025-01416-2","url":null,"abstract":"<p><p>This manuscript introduces a new Erlang-distributed SEIR model. The model incorporates asymptomatic spread through a subdivided exposed class, distinguishing between asymptomatic ( <math><msub><mtext>E</mtext> <mi>a</mi></msub> </math> ) and symptomatic ( <math><msub><mtext>E</mtext> <mi>s</mi></msub> </math> ) cases. The model identifies two key parameters: relative infectiousness, <math><msub><mi>β</mi> <mrow><mi>SA</mi></mrow> </msub> </math> , and the percentage of people who become asymptomatic after being infected by a symptomatic individual, <math><mi>κ</mi></math> . Lower values of these parameters reduce the peak magnitude and duration of the infectious period, highlighting the importance of isolation measures. Additionally, the model underscores the need for strategies addressing both symptomatic and asymptomatic transmissions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 3","pages":"38"},"PeriodicalIF":2.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11794362/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143188115","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":"Evolution of Human Pair Bonds as a Consequence of Male-Biased Mating Sex Ratios?","authors":"Matthew C Nitschke, Viney Kumar, Katrina E Milliner, Kristen Hawkes, Peter S Kim","doi":"10.1007/s11538-025-01414-4","DOIUrl":"10.1007/s11538-025-01414-4","url":null,"abstract":"<p><p>Compared to our closest primate relatives, human life history involves greater longevity, which includes a distinctive postmenopausal life stage. Given mammalian reproductive physiology in which females build a finite stock of cells that can become oocytes early in life, which then continuously deplete mostly through cell death while males produce new sperm throughout adulthood, the postmenopausal stage makes the sex ratio in the fertile pool, called the adult sex ratio (ASR), male biased. Additionally, this affects a more fine-grained ratio, the operational sex ratio (OSR), defined as the ratio of males to females currently able to conceive. Here, we construct an ODE model in which males compete for paternities using either a multiple-mating or mate-guarding strategy. Our focus is on investigating the differences of strategy choice between populations with varying life histories, which include a distinct post-fertile stage for adult females. By simulating the system, we determine the dominant strategy and its dependence on various parameter combinations. Our results show that an increase in OSR and ASR correlates well with a change in the dominant strategy from multiple mating to guarding.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 3","pages":"37"},"PeriodicalIF":2.0,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11782467/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143064006","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":"Adaptive Immunity Determines the Cancer Treatment Outcome of Oncolytic Virus and Anti-PD-1.","authors":"Kang-Ling Liao, Kenton D Watt","doi":"10.1007/s11538-025-01413-5","DOIUrl":"10.1007/s11538-025-01413-5","url":null,"abstract":"<p><p>The immune checkpoint inhibitor, anti-programmed death protein-1 (anti-PD-1), enhances adaptive immunity to kill tumor cells, and the oncolytic virus (OV) triggers innate immunity to clear the infected tumor cells. We create a mathematical model to investigate how the interaction between adaptive and innate immunities under OV and anti-PD-1 affects tumor reduction. For different immunity strength, we create the corresponding virtual baseline patients and cohort patients to decipher the major factors determining the treatment outcome. Global sensitivity analysis indicates that adaptive immunity has more control on the treatment outcome than innate immunity, and whether anti-PD-1 cancels out the OV treatment efficacy depends on the OV dosage and the balance between clearance of infected tumor cells and OV by T cells. The optimal OV infection rate and dosage suggest that OV treatment is more sensitive to adaptive immunity than innate immunity. Our model prediction also indicates that tumor reduction is more sensitive to anti-PD-1 efficacy as adaptive immunity becomes stronger, and anti-PD-1 trends to cancel out the OV treatment efficacy as innate immunity becomes stronger. Based on these results, the recommended treatment protocol for patients with different immunity strength can be determined.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 3","pages":"36"},"PeriodicalIF":2.0,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143058219","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":"Key Structural Features of Microvascular Networks Leading to the Formation of Multiple Equilibria.","authors":"George Atkinson, Yaron Ben-Ami, Philip Maini, Joe Pitt-Francis, Helen Byrne","doi":"10.1007/s11538-024-01404-y","DOIUrl":"10.1007/s11538-024-01404-y","url":null,"abstract":"<p><p>We analyse mathematical models of blood flow in two simple vascular networks in order to identify structural features that lead to the formation of multiple equilibria. Our models are based on existing rules for blood rheology and haematocrit splitting. By performing bifurcation analysis on these simple network flow models, we identify a link between the changing flow direction in key vessels and the existence of multiple equilibria. We refer to these key vessels as redundant vessels, and relate the maximum number of equilibria with the number of redundant vessels. We vary geometric parameters of the two networks, such as vessel length ratios and vessel diameters, to demonstrate that equilibria are uniquely defined by the flow in the redundant vessels. Equilibria typically emerge in sets of three, each having a different flow characteristic in one of the network's redundant vessels. For one of the three equilibria, the flow within the relevant redundant vessel will be smaller in magnitude than the other two and the redundant vessel will contain few Red Blood Cells (RBCs), if any. For the other two equilibria, the redundant vessel contains RBCs and significant flow in the two available directions. These structural features of networks provide a useful geometric property when studying the equilibria of blood flow in microvascular networks.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"30"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11757897/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022274","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":"Non-spatial Dynamics and Spatiotemporal Patterns Formation in a Predator-Prey Model with Double Allee and Dome-shaped Response Function.","authors":"Debjit Pal, Ritwika Mondal, Dipak Kesh, Debasis Mukherjee","doi":"10.1007/s11538-025-01411-7","DOIUrl":"10.1007/s11538-025-01411-7","url":null,"abstract":"<p><p>The extinction of species is a major threat to the biodiversity. Allee effects are strongly linked to population extinction vulnerability. Emerging ecological evidence from numerous ecosystems reveals that the Allee effect, which is brought on by two or more processes, can work on a single species concurrently. The cooperative behavior which raises Allee effect in low population density, can create group defence in species to protect themselves from predation. This article focuses on the dynamics of a predator-prey system with double Allee effect in prey growth and simplified Monod-Haldane form of dome-shaped response function to incorporate group defence ability of prey as time and space vary. The study obtains that, to some extent, group defence of prey plays a positive role for the stability of both the species, but on negative side, if defensive ability exceeds a threshold value then both the population can not survive simultaneously and predator population dies out. The Allee effect produces bi-stability (weak Allee) even tri-stability (strong Allee) in phase space reflecting that the system dynamics is very sensitive subject to initial population of the species. The combined impact of double Allee and group defence of prey leads in populations enduring stable periods punctuated by oscillations. The species' mobility based on only its own population is insufficient to this model for Turing instability. The presence of double Allee effect increases the instability regions that enhances the likelihood of various patterns. Whereas increasing group defence of prey decreases the instability region in spatial system. The species distribution stabilizes in forms of spots, stripes and mixture of both in heterogeneous environment. But for prey, gathering decreases with increasing growth rate and gathering increases with increasing Allee effect due to cross-diffusion which results paradox to temporal system. In contrast, populations in the Hopf and Hopf-Turing regions fluctuate (oscillatory) or their distribution becomes unpredictable (chaotic).</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"35"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022296","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 Data-Informed Mathematical Model of Microglial Cell Dynamics During Ischemic Stroke in the Middle Cerebral Artery.","authors":"Sara Amato, Andrea Arnold","doi":"10.1007/s11538-025-01412-6","DOIUrl":"10.1007/s11538-025-01412-6","url":null,"abstract":"<p><p>Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this study, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"31"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022270","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":"Bayesian Inference of Phylogenetic Distances: Revisiting the Eigenvalue Approach.","authors":"Matthew J Penn, Neil Scheidwasser, Christl A Donnelly, David A Duchêne, Samir Bhatt","doi":"10.1007/s11538-024-01403-z","DOIUrl":"10.1007/s11538-024-01403-z","url":null,"abstract":"<p><p>Using genetic data to infer evolutionary distances between molecular sequence pairs based on a Markov substitution model is a common procedure in phylogenetics, in particular for selecting a good starting tree to improve upon. Many evolutionary patterns can be accurately modelled using substitution models that are available in closed form, including the popular general time reversible model (GTR) for DNA data. For more complex biological phenomena, such as variations in lineage-specific evolutionary rates over time (heterotachy), other approaches such as the GTR with rate variation (GTR <math><mrow><mo>+</mo> <mi>Γ</mi></mrow> </math> ) are required, but do not admit analytical solutions and do not automatically allow for likelihood calculations crucial for Bayesian analysis. In this paper, we derive a hybrid approach between these two methods, incorporating <math><mrow><mi>Γ</mi> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>α</mi> <mo>)</mo></mrow> </math> -distributed rate variation and heterotachy into a hierarchical Bayesian GTR-style framework. Our approach is differentiable and amenable to both stochastic gradient descent for optimisation and Hamiltonian Markov chain Monte Carlo for Bayesian inference. We show the utility of our approach by studying hypotheses regarding the origins of the eukaryotic cell within the context of a universal tree of life and find evidence for a two-domain theory.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"32"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11759294/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022272","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":"Modeling Innate Immunity Causing Chronic Inflammation and Tissue Damage.","authors":"Kosei Matsuo, Yoh Iwasa","doi":"10.1007/s11538-024-01410-0","DOIUrl":"10.1007/s11538-024-01410-0","url":null,"abstract":"<p><p>Mathematical models of immune responses have traditionally focused on adaptive immunity and pathogen-immune dynamics. However, recent advances in immunology have highlighted the critical role of innate immunity. In response to physical damage or pathogen attacks, innate immune cells circulating throughout the body rapidly migrate from blood vessels and accumulate at the site of injury, triggering inflammation. These cells engulf, break down, and eliminate pathogens. This innate immune response occurs much faster than adaptive immune responses, which require time for cell activation and proliferation. While inflammation helps eliminate pathogens, it can sometimes lead to chronic inflammation by triggering excessive immune responses, ultimately causing tissue damage. In this study, we examine a simple dynamical model of innate immunity. The analysis indicates that when an infection occurs, it triggers inflammation, which activates the innate immune system and initiates the activation cycle. Consequently, pathogens may be eradicated, leaving behind persistent chronic inflammation. Alternatively, the pathogens may not be eradicated, with their abundance either stabilizing at a positive level or oscillating indefinitely. The dynamics exhibit both transcritical and Hopf bifurcations. When innate immunity is activated in the absence of inflammation, pathogens are eradicated more easily, and the likelihood of oscillations in inflammation, immune responses, and pathogen abundance is reduced.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"34"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11760608/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022276","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}