Journal of Mathematical Biology最新文献

{"title":"Multitype SIR epidemics among a population partitioned into households with proportionate global mixing.","authors":"Frank Ball, Liam Critcher","doi":"10.1007/s00285-026-02359-5","DOIUrl":"10.1007/s00285-026-02359-5","url":null,"abstract":"<p><p>A stochastic model for an SIR epidemic among a population of households that contains J types of individuals is considered. Infectives make two kinds of contacts: local contacts with individuals in their own household and global contacts with individuals from the entire population. Global mixing is proportionate. The behaviour of the model as the population size tends to infinity is analysed. An approximating branching process for the early stages of an epidemic is used to determine several different reproduction numbers and the early exponential growth rate. The means of certain final outcome quantities of an epidemic which takes off are determined, together with an associated multivariate central limit theorem. The assumption of proportionate global mixing leads to considerable simplification in both the calculation and proof of asymptotic properties, since key underlying processes are one-dimensional rather than J-dimensional.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13111495/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147787696","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":"Theory and simulations of delayed stochastic and deterministic models of prion diseases.","authors":"Gangadhara Boregowda, Omar Sharif, Daniel Gutierrez Iii, Allegra Simmons, Laurent Pujo-Menjouet, Tamer Oraby, Michael R Lindstrom","doi":"10.1007/s00285-026-02390-6","DOIUrl":"10.1007/s00285-026-02390-6","url":null,"abstract":"<p><p>Neurodegenerative diseases (NDs), such as Alzheimer's, Parkinson's, and prion diseases, are characterized by the dynamical spread of toxic proteins through the brain. In prion diseases, cellular prion protein ( <math><msup><mtext>PrP</mtext> <mtext>C</mtext></msup> </math> ), produced by neurons, misfolds into a toxic form, known as scrapie prion protein ( <math><msup><mtext>PrP</mtext> <mtext>Sc</mtext></msup> </math> ). <math><msup><mtext>PrP</mtext> <mtext>Sc</mtext></msup> </math> induces neuronal stress which ultimately leads to cell death. In this paper, we develop mathematical models for the progression of prion diseases, incorporating a cellular defense mechanism that introduces a delay term affecting protein translation and a volatility term accounting for unaccounted biological factors influencing the system. We also extend the model to capture the spatial spread of toxic proteins over the brain connectome. Our first objective is to establish the existence and uniqueness of a global positive solution to the prion disease models. Afterwards, we analyze the asymptotic behavior of the models by identifying regimes of persistence and extinction of toxic proteins. For the deterministic delayed systems, we perform a stability analysis for the persistence and demonstrate that the system undergoes a Hopf bifurcation. We also study the intensity of fluctuations of the equilibrium state of the stochastic model. Additionally, we present numerical simulations to illustrate the model dynamics using biologically relevant parameters.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13106245/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147787699","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":"Propagation dynamics for neural field equations in time-space periodic media.","authors":"Ming-Zhen Xin, Wan-Tong Li, Bin-Guo Wang","doi":"10.1007/s00285-026-02403-4","DOIUrl":"10.1007/s00285-026-02403-4","url":null,"abstract":"<p><p>Neural field equations model population dynamics of large-scale networks of neurons. To investigate multiple effects of spatiotemporal heterogeneity on wave propagation, we propose a neural field equation with monostable nonlinearity in time-space periodic media. We first establish the existence of a positive, globally attractive, time-space periodic solution under appropriate conditions. For exponentially bounded kernels, we determine the spreading speed and demonstrate its equivalence to the minimal speed of time-space periodic traveling wave solutions. We also provide a variational characterization of this spreading speed via principal eigenvalues. Furthermore, employing the monotone iteration method and partial metric theory, we obtain an attractive traveling wave solution at noncritical speeds. In contrast, for exponentially unbounded kernels, we find the occurrence of accelerated spreading. Leveraging properties of subexponential kernels, we precisely determine the rate of acceleration. Our results comprehensively address the problem posed by Fang and Faye (Math. Models Methods Appl. Sci., 2016) in the absence of synaptic delay.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147787744","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":"First-order endotactic reaction networks.","authors":"Chuang Xu","doi":"10.1007/s00285-026-02378-2","DOIUrl":"10.1007/s00285-026-02378-2","url":null,"abstract":"<p><p>Reaction networks are a general framework widely used in modeling diverse phenomena in different science disciplines. The dynamical process of a reaction network endowed with mass-action kinetics is a mass-action system which is an ODE defined by a directed graph, the so-called \"reaction graph\". Endotacticity is a graph property used to study persistence and permanence of mass-action systems. In this paper, we provide a detailed characterization of first-order endotactic reaction graphs. Besides, we provide a sufficient condition for endotacticity of reaction networks which are not necessarily of first-order. Such a characterization of a first-order endotactic reaction graph yields the spectral property of the adjacency matrix of the reaction graph. As a consequence, we prove that every first-order endotactic mass-action system as a linear ODE has a weakly reversible deficiency zero realization, and has a unique equilibrium which is exponentially globally asymptotically stable (and is positive) in each (positive) stoichiometric compatibility class. Using a stability result for asymptotically autonomous differential equations, examples are constructed to illustrate that the global stability results can be extended to mass-action systems of higher-order reaction networks modeled by nonlinear ODEs, which are not necessarily endotactic. Different from the classical approaches for proving global asymptotic stability, the proof does not rely on the construction of a Lyapunov function. This paper may serve as a starting point of characterizing higher-order endotactic reaction graphs and studying global stability of mass-action systems in general.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147729955","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":"Spatiotemporal dynamics of HIV in the Brain: perspective of mathematical modeling for its control via antiretroviral therapy.","authors":"Naveen K Vaidya, Feng-Bin Wang","doi":"10.1007/s00285-026-02382-6","DOIUrl":"10.1007/s00285-026-02382-6","url":null,"abstract":"<p><p>The brain, as a reservoir of human immunodeficiency virus (HIV), has received tremendous attention due to the association with the brain's infection with HIV-associated neurocognitive disorders (HAND). Along with the blood-brain barrier (BBB), heterogeneity across the various regions inside the brain makes HIV infection particularly complex to identify the ideal treatment for controlling HIV in the brain. In this study, we developed a mathematical model to describe the spatiotemporal dynamics of HIV infection in three essential regions of the brain: the prefrontal cortex (PF), the choroid plexus (CP), and the primary visual cortex (V1). We use our model to study the impact of drug pharmacodynamics and the CPE score (a permeability index for drugs into the brain) on viral control in the brain. The infection invasion threshold, which we theoretically established as the determinant of infection avoidance or virus persistence, enables us to select drugs for treatment protocols with pharmacodynamic properties (dose-response curve slope, dose, half-life, dose interval, CPE score) that prevent and control HIV infection in the brain. Our novel model and related theoretical and numerical results provide further insights into the impact of antiretroviral therapy on the spatiotemporal dynamics of HIV infection in the brain.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718850","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":"Evolution of a trait distributed over a large fragmented population: propagation of chaos meets adaptive dynamics.","authors":"Amaury Lambert, Hélène Leman, Hélène Morlon, Josué Tchouanti","doi":"10.1007/s00285-026-02371-9","DOIUrl":"10.1007/s00285-026-02371-9","url":null,"abstract":"<p><p>We consider a metapopulation made up of K demes, each containing N individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait values. Mutation and migration rates are tuned so that each deme receives a migrant or a mutant in the same slow timescale and is thus essentially monomorphic at all times for the trait value (adaptive dynamics). In the timescale of mutation/migration, the metapopulation can then be seen as a giant spatial Moran model with size K that we characterize. As <math><mrow><mi>K</mi> <mo>→</mo> <mi>∞</mi></mrow> </math> and physical space becomes continuous, the empirical distribution of the trait value (over the physical and trait spaces) evolves deterministically according to an integro-differential evolution equation. In this limit, the trait value of every migrant is drawn from this global distribution, so that conditional on its initial state, trait values from finitely many demes evolve independently (propagation of chaos). Under mean-field dispersal, the value <math><msub><mi>X</mi> <mi>t</mi></msub> </math> of the trait at time t and at any given location has a law denoted <math><msub><mi>μ</mi> <mi>t</mi></msub> </math> and a jump kernel with two terms: a mutation-fixation term and a migration-fixation term involving <math><msub><mi>μ</mi> <mrow><mi>t</mi> <mo>-</mo></mrow> </msub> </math> (McKean-Vlasov equation). In the limit where mutations have small effects and migration is further slowed down accordingly, we obtain the convergence of X, in the new migration timescale, to the solution of a stochastic differential equation which can be referred to as a new, canonical jump-diffusion of adaptive dynamics. This equation includes an advection term representing selection, a diffusive term due to genetic drift, and a jump term, representing the effect of migration, to a state distributed according to its own law.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090215/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718890","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 predator-prey model with age-structured role reversal.","authors":"Luis Carlos Suarez, Maria K Cameron, William F Fagan, Doron Levy","doi":"10.1007/s00285-026-02402-5","DOIUrl":"10.1007/s00285-026-02402-5","url":null,"abstract":"<p><p>We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an \"ontogenetic niche shift,\" in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090279/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718839","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":"Spatio-temporal pattern formation under varying functional response parametrizations.","authors":"Indrajyoti Gaine, Malay Banerjee","doi":"10.1007/s00285-026-02393-3","DOIUrl":"10.1007/s00285-026-02393-3","url":null,"abstract":"<p><p>The limited availability of detailed ecological data introduces uncertainty in model predictions and constrains efforts to enhance the predictive power and robustness of nonlinear population dynamics models. While carefully chosen parameter values may yield a good fit to available datasets, alternative mathematical formulations of key component functions can sometimes provide an even better fit. The study of uncertainty in model predictions arising from such alternative formulations of component functions, such as those describing predation, is referred to as the study of structural sensitivity. In this work, we extend the concept of structural sensitivity to spatio-temporal ecological systems. We analytically derive parametric conditions that capture all possible cases for the number of homogeneous steady states, provide criteria for local bifurcations, and establish conditions for the existence or non-existence of spatially heterogeneous steady states, as well as for Turing instability, all expressed in terms of a generalized functional response. Numerical simulations using two ecologically well-established functional responses validate our analytical results and emphasize the importance of carefully selecting the mathematical formulation when modeling predator-prey interactions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718821","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":"Effects of host migration and travel loss on strain competition in a two-patch SIR model.","authors":"Bo-Sheng Chen, Chang-Hong Wu","doi":"10.1007/s00285-026-02397-z","DOIUrl":"10.1007/s00285-026-02397-z","url":null,"abstract":"<p><p>This paper investigates how host migration with travel loss affects competition between two pathogen strains in animal populations using a two-patch SIR model. We establish sufficient conditions involving migration rates and travel losses that ensure the global asymptotic stability of a single-strain endemic equilibrium or a coexistence equilibrium. Complemented by numerical simulations, our results provide insights into how competitive outcomes are shaped by the interplay among migration asymmetry, travel loss, and epidemiological traits.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090282/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718825","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":"Trajectory inference for a branching SDE model of cell differentiation via lineage tracing.","authors":"Elias Ventre, Aden Forrow, Nitya Gadhiwala, Parijat Chakraborty, Omer Angel, Geoffrey Schiebinger","doi":"10.1007/s00285-026-02375-5","DOIUrl":"10.1007/s00285-026-02375-5","url":null,"abstract":"<p><p>A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory inference methods cannot distinguish variability in net proliferation from cell differentiation dynamics, and hence require accurate prior knowledge of the proliferation rate. Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation. In particular, when there is neither death nor subsampling of cells, we show that we extend gWOT to the case with proliferation with similar theoretical guarantees and computational cost, without requiring any prior information. In the case of death and/or subsampling, our method introduces a bias, that we describe explicitly and argue to be inherent to these lineage tracing data. We demonstrate in both cases the ability of this method to reliably reconstruct the landscape of a branching SDE from time-courses of simulated datasets with lineage tracing, outperforming even a benchmark using the experimentally unavailable true branching rates.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13090286/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718819","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}