Bulletin of Mathematical Biology最新文献

{"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}

{"title":"Modeling the Impact of Seasonality on Mosquito Population Dynamics: Insights for Vector Control Strategies.","authors":"Joseph Baafi, Amy Hurford","doi":"10.1007/s11538-024-01409-7","DOIUrl":"10.1007/s11538-024-01409-7","url":null,"abstract":"<p><p>Mosquitoes are important vectors for the transmission of some major infectious diseases of humans, i.e., malaria, dengue, West Nile Virus and Zika virus. The burden of these diseases is different for different regions, being highest in tropical and subtropical areas, which have high annual rainfall, warm temperatures, and less pronounced seasonality. The life cycle of mosquitoes consists of four distinct stages: eggs, larvae, pupae, and adults. These life stages have different mortality rates and only adults can reproduce. Seasonal weather may affect the population dynamics of mosquitoes, and the relative abundance of different mosquito stages. We developed a stage-structured model that considers laboratory experiments describing how temperature and rainfall affects the reproduction, maturation and survival of different Anopheles mosquito stages, the species that transmits the parasite that causes malaria. We consider seasonal temperature and rainfall patterns and describe the stage-structured population dynamics of the Anopheles mosquito in Ain Mahbel, Algeria, Cape Town, South Africa, Nairobi, Kenya and Kumasi, Ghana. We find that neglecting seasonality leads to significant overestimation or underestimation of mosquito abundance. We find that depending on the region, mosquito abundance: peaks one, two or four times a year, periods of low abundance are predicted to occur for durations ranging from six months (Ain Mahbel) to not at all (Nairobi); and seasonal patterns of relative abundance of stages are substantially different. The region with warmer temperatures and higher rainfall across the year, Kumasi, Ghana, is predicted to have higher mosquito abundance, which is broadly consistent with reported malaria deaths relative to the other countries considered by our study. Our analysis reveals distinct patterns in mosquito abundance across different months and regions. Control strategies often target one specific life stage, for example, applying larvicides to kill mosquito larvae, or spraying insecticides to kill adult mosquitoes. Our findings suggest that differences in seasonal weather affect mosquito stage structure, and that the best approaches to vector control may differ between regions in timing, duration, and efficacy.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"33"},"PeriodicalIF":2.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143022280","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":"Mechanical Cell Interactions on Curved Interfaces.","authors":"Pascal R Buenzli, Shahak Kuba, Ryan J Murphy, Matthew J Simpson","doi":"10.1007/s11538-024-01406-w","DOIUrl":"10.1007/s11538-024-01406-w","url":null,"abstract":"<p><p>We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models of flat epithelia to investigate the influence of curvature for mechanical relaxation. We represent the mechanics of a cell body either by straight springs, or by curved springs that follow the curve's shape. To understand the collective dynamics of the cells, we devise an appropriate continuum limit in which the number of cells and the length of the substrate are constant but the number of springs tends to infinity. In this limit, cell density is governed by a diffusion equation in arc length coordinates, where diffusion may be linear or nonlinear depending on the choice of the spring restoring force law. Our results have important implications about modelling cells on curved geometries: (i) curved and straight springs can lead to different dynamics when there is a finite number of springs, but they both converge quadratically to the dynamics governed by the diffusion equation; (ii) in the continuum limit, the curvature of the tissue does not affect the mechanical relaxation of cells within the layer nor their tangential stress; (iii) a cell's normal stress depends on curvature due to surface tension induced by the tangential forces. Normal stress enables cells to sense substrate curvature at length scales much larger than their cell body, and could induce curvature dependences in experiments.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"29"},"PeriodicalIF":2.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11706888/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142944992","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 3D Computational Study on the Formation and Progression of Tumor Cells in Diffuse Gastric Cancer.","authors":"Valéria Lopes, Joana Figueiredo, Patrícia Carneiro, Marcos Gouveia, Rui D M Travasso, João Carvalho","doi":"10.1007/s11538-024-01405-x","DOIUrl":"10.1007/s11538-024-01405-x","url":null,"abstract":"<p><p>Hereditary diffuse gastric cancer is characterized by an increased risk of diffuse gastric cancer and lobular breast cancer, and is caused by pathogenic germline variants of E-cadherin and <math><mi>α</mi></math> -E-catenin, which are key regulators of cell-cell adhesion. However, how the loss of cell-cell adhesion promotes cell dissemination remains to be fully understood. Therefore, a three-dimensional computer model was developed to describe the initial steps of diffuse gastric cancer development. In this model, we have implemented a cellular Potts approach that contemplates cell adhesion to other cells and to the extracellular matrix, cell extrusion from the gastric epithelia, and subsequent proliferation. We demonstrate that early disease features are determined by decreased adhesion of mutant cells to their normal epithelial neighbors, with concomitant increased attachment to matrix components. Importantly, our simulation shows how mechanical pressure and uncontrolled proliferation of mutant cells lead to modifications in cell shape and in gastric gland morphology. In conclusion, this work underscores the potential of computational models to elucidate the role of cellular and noncellular components in gastric cancer that may be relevant targets in therapeutic interventions.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"28"},"PeriodicalIF":2.0,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142926550","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 Effect of Vaccination on the Competitive Advantage of Two Strains of an Infectious Disease.","authors":"Matthew D Johnston, Bruce Pell, Jared Pemberton, David A Rubel","doi":"10.1007/s11538-024-01378-x","DOIUrl":"10.1007/s11538-024-01378-x","url":null,"abstract":"<p><p>We investigate the impact of differential vaccine effectiveness, waning immunity, and natural cross-immunity on the capacity for vaccine-induced strain replacement in two-strain models of infectious disease spread. We focus specifically on the case where the first strain is more transmissible but the second strain is more immune-resistant. We consider two cases on vaccine-induced immunity: (1) a monovalent model where the second strain has immune escape with respect to vaccination; and (2) a bivalent model where the vaccine remains equally effective against both strains. Our analysis reaffirms the capacity for vaccine-induced strain replacement under a variety of circumstances; surprisingly, however, we find that which strain is preferred depends sensitively on the degree of differential vaccine effectiveness. In general, the monovalent model favors the more immune-resistant strain at high vaccination levels while the bivalent model favors the more transmissible strain at high vaccination levels. To further investigate this phenomenon, we parametrize the bifurcation space between the monovalent and bivalent model.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 2","pages":"19"},"PeriodicalIF":2.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920722","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}