Edgardo Villar-Sepúlveda, Alan R Champneys, Andrew L Krause
{"title":"Designing reaction-cross-diffusion systems with Turing and wave instabilities.","authors":"Edgardo Villar-Sepúlveda, Alan R Champneys, Andrew L Krause","doi":"10.1007/s00285-025-02274-1","DOIUrl":"10.1007/s00285-025-02274-1","url":null,"abstract":"<p><p>General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general n-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"37"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12426155/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145042128","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":"Transition behavior of the waiting time distribution in a stochastic model with the internal state.","authors":"Zhe Xue, Yuan Zhang, Zhennan Zhou, Min Tang","doi":"10.1007/s00285-025-02275-0","DOIUrl":"https://doi.org/10.1007/s00285-025-02275-0","url":null,"abstract":"<p><p>It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power-law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to normal diffusion can be observed at the population level. However, the mechanism behind the transition of waiting time distribution is rarely studied. In this paper, we provide one possible mechanism to explain the origin of such a transition. A stochastic model terminated by a state-dependent Poisson clock is studied by a formal asymptotic analysis for the time evolutionary equation of its probability density function (PDF). The waiting time behavior under a more relaxed setting can be rigorously characterized by probability tools. Both approaches show the transition phenomenon of the waiting time T, which is complemented by particle simulations to shed light on the transition time scale. Our results indicate that small drift relative to noise in the state equation and a stiff response in the Poisson rate are crucial to the transitional phenomena.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"35"},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145034560","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}
Oskar Henriksson, Carlos Améndola, Jose Israel Rodriguez, Polly Y Yu
{"title":"Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks.","authors":"Oskar Henriksson, Carlos Améndola, Jose Israel Rodriguez, Polly Y Yu","doi":"10.1007/s00285-025-02262-5","DOIUrl":"10.1007/s00285-025-02262-5","url":null,"abstract":"<p><p>A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"34"},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12423244/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145031021","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":"Population size in stochastic discrete-time ecological dynamics.","authors":"Alexandru Hening, Siddharth Sabharwal","doi":"10.1007/s00285-025-02277-y","DOIUrl":"https://doi.org/10.1007/s00285-025-02277-y","url":null,"abstract":"<p><p>We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is coexistence, it is usually impossible to say anything about the invariant probability measure which describes the coexisting species. We are able to circumvent this problem for some important ecological models by noticing that the per-capita growth rates at stationarity are zero, something which can sometimes yield information about the invariant probability measure. For more complicated models we use a recent result by Cuello to explore how small noise influences the population size. We are able to show that environmental fluctuations can decrease, increase, or leave unchanged the expected population size. The results change according to the dynamical model and, within a fixed model, also according to which parameters (growth rate, carrying capacity, etc) are affected by environmental fluctuations. Moreover, we show that not only do things change if we introduce noise differently in a model, but it also matters what one takes as the deterministic 'no-noise' baseline for comparison.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 4","pages":"36"},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145034531","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":"Effect of host movement on the prevalence of vector-borne diseases.","authors":"Daozhou Gao, Yuan Lou","doi":"10.1007/s00285-025-02254-5","DOIUrl":"10.1007/s00285-025-02254-5","url":null,"abstract":"<p><p>Human movement plays a key role in spreading vector-borne diseases globally. Various spatial models of vector-borne diseases have been proposed and analyzed, mainly focusing on disease dynamics. In this paper, based on a multi-patch Ross-Macdonald model, we study the impact of host migration on the local and global host disease prevalences. Specifically, we find that the local disease prevalence of any patch is bounded by the minimum and maximum disease prevalences of all disconnected patches and establish a weak order-preserving property. For global disease prevalence, we derive its formula at both zero and infinite dispersal rates and compare them under certain conditions, and calculate the right derivative at no dispersal. In the case of two patches, we give two complete classifications of the model parameter space: one is to compare the host disease prevalences with and without host dispersal, and the other is to determine the monotonicity of host disease prevalence with respect to host dispersal rate. Numerical simulations confirm inconsistence between disease persistence and host disease prevalence, as well as between host prevalence and vector prevalence in response to host movement. In general, a more uneven distribution of hosts and vectors in a homogeneous environment leads to lower host prevalence but higher vector prevalence and stronger disease persistence.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"33"},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12413432/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145001859","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":"Spaces of ranked tree-child networks.","authors":"Vincent Moulton, Andreas Spillner","doi":"10.1007/s00285-025-02265-2","DOIUrl":"10.1007/s00285-025-02265-2","url":null,"abstract":"<p><p>Ranked tree-child networks are a recently introduced class of rooted phylogenetic networks in which the evolutionary events represented by the network are ordered so as to respect the flow of time. This class includes the well-studied ranked phylogenetic trees (also known as ranked genealogies). An important problem in phylogenetic analysis is to define distances between phylogenetic trees and networks in order to systematically compare them. Various distances have been defined on ranked binary phylogenetic trees, but very little is known about comparing ranked tree-child networks. In this paper, we introduce an approach to compare binary ranked tree-child networks on the same leaf set that is based on a new encoding of such networks that is given in terms of a certain partially ordered set. This allows us to define two new spaces of ranked binary tree-child networks. The first space can be considered as a generalization of the recently introduced space of ranked binary phylogenetic trees whose distance is defined in terms of ranked nearest neighbor interchange moves. The second space is a continuous space that captures all equidistant tree-child networks and generalizes the space of ultrametric trees. In particular, we show that this continuous space is a so-called CAT(0)-orthant space which, for example, implies that the distance between two equidistant tree-child networks can be efficiently computed.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"32"},"PeriodicalIF":2.3,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12405416/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144977100","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}
Nonthakorn Olaranont, Chaozhen Wei, John Lowengrub, Min Wu
{"title":"Chemomechanical regulation of growing tissues from a thermodynamically-consistent framework and its application to tumor spheroid growth.","authors":"Nonthakorn Olaranont, Chaozhen Wei, John Lowengrub, Min Wu","doi":"10.1007/s00285-025-02257-2","DOIUrl":"10.1007/s00285-025-02257-2","url":null,"abstract":"<p><p>It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression such as cancer. However, how exactly cells and tissues regulate growth in response to chemical and mechanical cues is still not clear. Here, we propose a framework for the chemomechanical regulation of growth based on thermodynamics of continua and growth-elasticity to predict growth patterns. Combining the elastic and chemical energies, we use an energy variational approach to derive a novel formulation that isolates the mass-conserving tissue rearrangement from the mass-accretion volumetric growth, and incorporates independent energy-dissipating stress relaxation and biochemomechanical regulation of the volumetric growth rate respectively. We validate the model using experimental data from growth of tumor spheroids in confined environments. We also investigate the influence of model parameters, including tissue rearrangement rate, tissue compressibility, strength of mechanical feedback and external mechanical stimuli, on the growth patterns of tumor spheroids.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"31"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12404680/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144977064","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}
Francesca Scarabel, Mónika Polner, Daniel Wylde, Maria Vittoria Barbarossa, Gergely Röst
{"title":"Bistability and complex bifurcation diagrams generated by waning and boosting of immunity.","authors":"Francesca Scarabel, Mónika Polner, Daniel Wylde, Maria Vittoria Barbarossa, Gergely Röst","doi":"10.1007/s00285-025-02264-3","DOIUrl":"10.1007/s00285-025-02264-3","url":null,"abstract":"","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"30"},"PeriodicalIF":2.3,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12373696/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144977136","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":"Decoding how higher-order network interactions shape contagion dynamics.","authors":"István Z Kiss, Christian Bick, Péter L Simon","doi":"10.1007/s00285-025-02247-4","DOIUrl":"10.1007/s00285-025-02247-4","url":null,"abstract":"<p><p>Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models often exhibit a similar form, resulting in qualitatively comparable global bifurcation patterns. Motivated by this observation, we investigate a generalised mean-field-type model that provides a unified framework for analysing a range of different models. In particular, we derive analytical conditions for the emergence of different bifurcation regimes exhibited by three models of increasing complexity-ranging from three- and four-body interactions to two connected populations which simultaneously includes both pairwise and three-body interactions. For the first two cases, we give a complete characterisation of all possible outcomes, along with the corresponding conditions on network and epidemic parameters. In the third case, we demonstrate that multistability is possible despite only three-body interactions. Our results reveal that single population models with three-body interactions can only exhibit simple transcritical transitions or bistability, whereas with four-body interactions multistability with two distinct endemic steady states is possible. Surprisingly, the two-population model exhibits multistability via symmetry breaking despite three-body interactions only. Our work sheds light on the relationship between equation structure and model behaviour and makes the first step towards elucidating mechanisms by which different system behaviours arise, and how network and dynamic properties facilitate or hinder outcomes.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"29"},"PeriodicalIF":2.3,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12364762/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144876539","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":"Learned behavioral avoidance can alter outbreak dynamics in a model for waterborne infectious diseases.","authors":"Anna J Poulton, Stephen P Ellner","doi":"10.1007/s00285-025-02252-7","DOIUrl":"10.1007/s00285-025-02252-7","url":null,"abstract":"<p><p>Many animals show avoidance behavior in response to disease. For instance, in some species of frogs, individuals that survive infection of the fungal disease chytridiomycosis may learn to avoid areas where the pathogen is present. As chytridiomycosis has caused substantial declines in many amphibian populations worldwide, it is a highly relevant example for studying these behavioral dynamics. Here we develop compartmental ODE models to study the epidemiological consequences of avoidance behavior of animals in response to waterborne infectious diseases. Individuals with avoidance behavior are less likely to become infected, but avoidance may also entail increased risk of mortality. We compare the outbreak dynamics with avoidance behavior that is innate (present from birth) or learned (gained after surviving infection). We also consider how management to induce learned avoidance might affect the resulting dynamics. Using methods from dynamical systems theory, we calculate the basic reproduction number [Formula: see text] for each model, analyze equilibrium stability of the systems, and perform a detailed bifurcation analysis. We show that disease persistence when [Formula: see text] is possible with learned avoidance, but not with innate avoidance. Our results imply that management to induce behavioral avoidance can actually cause such a scenario, but it is also less likely to occur for high-mortality diseases (e.g., chytridiomycosis). Furthermore, the learned avoidance model demonstrates a variety of codimension-1 and -2 bifurcations not found in the innate avoidance model. Simulations with parameters based on chytridiomycosis are used to demonstrate these features and compare the outcomes with innate, learned, and no avoidance behavior.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"28"},"PeriodicalIF":2.3,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12360992/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144876540","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}