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A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-08 DOI: 10.1007/s00285-025-02190-4
M C Bortolan, P Kalita, J A Langa, R O Moura
{"title":"A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems.","authors":"M C Bortolan, P Kalita, J A Langa, R O Moura","doi":"10.1007/s00285-025-02190-4","DOIUrl":"10.1007/s00285-025-02190-4","url":null,"abstract":"<p><p>In general, global attractors are composed of isolated invariant sets and the connections between them. This structure can possibly be highly complex, encompassing attraction basins, repeller sets and invariant sets that, collectively, form a dynamical landscape. Lotka-Volterra systems have long been pivotal as preliminary models for dynamics in complex networks exhibiting pairwise interactions. In scenarios involving Volterra-Lyapunov (VL) stable matrices, the dynamics is simplified in such a way that the positive solutions converge to a single, globally asymptotically stable stationary point as time tends to infinity, thereby excluding the existence of periodic solutions. In this work, we conduct a systematic study on the emergence of heteroclinic cycles within Lotka-Volterra systems characterized by Volterra-Lyapunov stable matrices. Although VL stability of the matrix implies that <math><mi>ω</mi></math> -limit sets of solutions are always stationary points, our analysis of <math><mi>α</mi></math> -limit sets reveals finite sets of stationary points interconnected by global trajectories, forming structures referred to as heteroclinic cycles. Our findings indicate that even within the framework of VL stable matrices, such structures are more prevalent than previously thought in literature, driven by the interplay between the symmetric and antisymmetric components of the model matrix. This understanding also reinforces our comprehension of the classical three-dimensional May-Leonard model, which is known to be the unique case exhibiting heteroclinic cycle within the VL framework in dimension three, while also pointing to a surprising richness in the dynamics of these structures in higher dimensions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"28"},"PeriodicalIF":2.2,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11805806/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143371431","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}
引用次数: 0
Feedback-delay dependence of the stability of cluster periodic orbits in populations of degrade-and-fire oscillators with common activator.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-06 DOI: 10.1007/s00285-024-02169-7
Bastien Fernandez, Matteo Tanzi
{"title":"Feedback-delay dependence of the stability of cluster periodic orbits in populations of degrade-and-fire oscillators with common activator.","authors":"Bastien Fernandez, Matteo Tanzi","doi":"10.1007/s00285-024-02169-7","DOIUrl":"10.1007/s00285-024-02169-7","url":null,"abstract":"<p><p>Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire oscillators coupled via a common activator protein, full mathematical certifications remained to be provided. Here, we prove from a rigorous mathematical viewpoint that, for the very same model, the synchronized degrade-and-fire oscillations are 1/ unstable with respect to out-of-sync perturbations in absence of delay, and 2/ are otherwise asymptotically stable in presence of delay, no matter how small is its amplitude. To that goal, we proceed to an extensive study of the population dynamics in this system, which in particular identifies the mechanisms of, and related criteria for, the delay-dependent stability of periodic orbits with respect to out-of-sync perturbations. As an additional outcome, the analysis also reveals that, depending on the parameters, multiple stable partially synchronized periodic orbits can coexist with the fully synchronized one.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"27"},"PeriodicalIF":2.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11802712/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143257085","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}
引用次数: 0
Evolutionary rescue of bacterial populations by heterozygosity on multicopy plasmids.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-06 DOI: 10.1007/s00285-025-02182-4
Ian Dewan, Hildegard Uecker
{"title":"Evolutionary rescue of bacterial populations by heterozygosity on multicopy plasmids.","authors":"Ian Dewan, Hildegard Uecker","doi":"10.1007/s00285-025-02182-4","DOIUrl":"10.1007/s00285-025-02182-4","url":null,"abstract":"<p><p>Bacterial plasmids and other extrachromosomal DNA elements frequently carry genes with important fitness effects for their hosts. Multicopy plasmids can additionally carry distinct alleles of host-fitness-relevant genes on different plasmid copies, allowing for heterozygosity not possible for loci on haploid chromosomes. Plasmid-mediated heterozygosity may increase the fitness of bacterial cells in circumstances where there is an advantage to having multiple distinct alleles (heterozyogote advantage); however, plasmid-mediated heterozygosity is also subject to constant loss due to random segregation of plasmid copies on cell division. We analyze a multitype branching process model to study the evolution and maintenance of plasmid-mediated heterozygosity under a heterozygote advantage. We focus on an evolutionary rescue scenario in which a novel mutant allele on a plasmid must be maintained together with the wild-type allele to allow population persistance (although our results apply more generally to the maintenance of heterozygosity due to heterozygote advantage). We determine the probability of rescue and derive an analytical expression for the threshold on the fitness of heterozygotes required to overcome segregation and make rescue possible; this threshold decreases with increasing plasmids copy number. We further show that the formation of cointegrates from the fusion of plasmid copies increases the probability of rescue. Overall, our results provide a rigorous quantitative assessment of the conditions under which bacterial populations can adapt to multiple stressors through plasmid-mediated heterozygosity. Many of the results are furthermore applicable to the related problem of the maintenance of incompatible plasmids in the same cell under selection for both.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"26"},"PeriodicalIF":2.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11799102/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143256898","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}
引用次数: 0
Multi-objective control to schedule therapies for acute viral infections.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-04 DOI: 10.1007/s00285-025-02188-y
Mara Perez, Marcelo Actis, Ignacio Sanchez, Esteban A Hernandez-Vargas, Alejandro H González
{"title":"Multi-objective control to schedule therapies for acute viral infections.","authors":"Mara Perez, Marcelo Actis, Ignacio Sanchez, Esteban A Hernandez-Vargas, Alejandro H González","doi":"10.1007/s00285-025-02188-y","DOIUrl":"10.1007/s00285-025-02188-y","url":null,"abstract":"<p><p>Antiviral therapies can yield different outcomes depending on their scheduling: a highly effective drug may produce treatment results ranging from successful to inconsequential, depending on therapeutic timing, dosing intervals, and dosage. The effectiveness of antiviral therapies can be assessed using mathematical models that describe viral spread within a host. In this work, we conduct a study based on the dynamic characterization of a target-cell model to address a multi-objective control problem aimed at designing highly effective and host-customizable antiviral therapies. These therapies involve finite-time antiviral treatments that minimize the viral load peak and the infection final size until infection clearance, while simultaneously reducing the total amount of drug intake as much as possible. Two optimization-based control strategies are proposed: a fixed-dose and a variable-dose approach. The variable-dose strategy achieves superior performance by explicitly considering the system dynamics in the design of the control. Simulation results, based on an identified model for COVID-19 patients treated with Paxlovid, illustrate the potential benefits of the proposed strategies.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"25"},"PeriodicalIF":2.2,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143191355","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}
引用次数: 0
Asymptotic behavior of the basic reproduction number for periodic nonlocal dispersal operators and applications.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-03 DOI: 10.1007/s00285-025-02192-2
Yan-Xia Feng, Wan-Tong Li, Yuan Lou, Fei-Ying Yang
{"title":"Asymptotic behavior of the basic reproduction number for periodic nonlocal dispersal operators and applications.","authors":"Yan-Xia Feng, Wan-Tong Li, Yuan Lou, Fei-Ying Yang","doi":"10.1007/s00285-025-02192-2","DOIUrl":"10.1007/s00285-025-02192-2","url":null,"abstract":"<p><p>This paper is concerned with asymptotic behavior of the basic reproduction number defined by next generation nonlocal (convolution) dispersal operators in a time-periodic environment and applications. First we investigate the influence of the frequency and dispersal rate on the basic reproduction number, and we obtain that the basic reproduction number is monotone on the frequency. In the nonautonomous situation, the basic reproduction number is not a monotone function of dispersal rate in general. We derive the monotonicity for large frequency or dispersal rate. Then we apply the obtained results to a time-periodic SIS epidemic model and establish the existence and asymptotic profiles of the endemic periodic solution. Since solution maps of nonlocal system lack compactness, the standard uniform persistence theory and topological degree theory are unapplicable to obtain the existence of the endemic periodic solution. To overcome this difficulty, we apply the asymptotic fixed point theorem with the help of the Kuratowski measure of noncompactness.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"24"},"PeriodicalIF":2.2,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124056","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}
引用次数: 0
Dynamics analysis of a reaction-diffusion-advection benthic-drift model with logistic growth.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-03 DOI: 10.1007/s00285-025-02183-3
Hua Nie, Qian Qin, Lei Zhang
{"title":"Dynamics analysis of a reaction-diffusion-advection benthic-drift model with logistic growth.","authors":"Hua Nie, Qian Qin, Lei Zhang","doi":"10.1007/s00285-025-02183-3","DOIUrl":"10.1007/s00285-025-02183-3","url":null,"abstract":"<p><p>This paper aims to investigate the benthic-drift population model in both open and closed advective environments, focusing on the logistic growth of benthic populations. We obtain the threshold dynamics using the monotone iteration method, and show that the zero solution is globally attractive straightforward when linearly stable. When unstable, limits from monotonic iteration of upper and lower solutions are upper and lower semi-continuous, respectively. By employing a part metric, we prove these limits are equal and continuous, leading to a positive steady state. In the critical case, we establish that the limit function from the upper solution iteration must be the zero solution by analyzing an algebraic equation. Furthermore, we conduct a quantitative analysis of the principal eigenvalue for a non-self-adjoint eigenvalue problem to examine how the diffusion rate, advection rate, and population release rates influence the dynamics. The results suggest that the diffusion rate and advection rate have distinct effects on population dynamics in open and closed advective environments, depending on the population release rates.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"23"},"PeriodicalIF":2.2,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143081905","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}
引用次数: 0
A network aggregation model for amyloid- β dynamics and treatment of Alzheimer's diseases at the brain scale.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-02-01 DOI: 10.1007/s00285-024-02179-5
Georgia S Brennan, Alain Goriely
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">A network aggregation model for amyloid- <ns0:math><ns0:mi>β</ns0:mi></ns0:math> dynamics and treatment of Alzheimer's diseases at the brain scale.","authors":"Georgia S Brennan, Alain Goriely","doi":"10.1007/s00285-024-02179-5","DOIUrl":"10.1007/s00285-024-02179-5","url":null,"abstract":"<p><p>Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an autocatalytic protein progression. The growth and transport of these assemblies depend on various mechanisms that can be targeted therapeutically. Here, we use spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain to study the effect of different drugs on whole-brain Alzheimer's disease progression.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"22"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11787187/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143076211","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}
引用次数: 0
A branching model for intergenerational telomere length dynamics.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-01-26 DOI: 10.1007/s00285-025-02185-1
Athanasios Benetos, Olivier Coudray, Anne Gégout-Petit, Lionel Lenôtre, Simon Toupance, Denis Villemonais
{"title":"A branching model for intergenerational telomere length dynamics.","authors":"Athanasios Benetos, Olivier Coudray, Anne Gégout-Petit, Lionel Lenôtre, Simon Toupance, Denis Villemonais","doi":"10.1007/s00285-025-02185-1","DOIUrl":"10.1007/s00285-025-02185-1","url":null,"abstract":"<p><p>We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean telomere length and its age. We study its Malthusian's behaviour and provide numerical simulations to understand the influence of biologically relevant parameters.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"21"},"PeriodicalIF":2.2,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143043216","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}
引用次数: 0
Total population for a resource-limited single consumer model.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-01-25 DOI: 10.1007/s00285-025-02186-0
Xiaoqing He, Wei-Ming Ni, Zihan Ye, Bo Zhang
{"title":"Total population for a resource-limited single consumer model.","authors":"Xiaoqing He, Wei-Ming Ni, Zihan Ye, Bo Zhang","doi":"10.1007/s00285-025-02186-0","DOIUrl":"10.1007/s00285-025-02186-0","url":null,"abstract":"<p><p>In the past several decades, much attention has been focused on the effects of dispersal on total populations of species. In Zhang (EL 20:1118-1128, 2017), a rigorous biological experiment was performed to confirm the mathematical conclusion: Dispersal tends to enhance populations under a suitable hypothesis. In addition, mathematical models keeping track of resource dynamics in population growth were also proposed in Zhang (EL 20:1118-1128, 2017) to understand this remarkable phenomenon. In these models, the self-regulated quantity \"loss rate\" of the population seems, in general, difficult to measure experimentally. Our main goal in this paper is to study the effects of relations between the loss rate and the resources, the role of dispersal, and the impact of their interactions on total populations. We compare the total population for small and large diffusion under various correlations between loss rate and the resources. Biological evidence seems to support some specific correlations between the loss rate and the resources.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"20"},"PeriodicalIF":2.2,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143043222","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}
引用次数: 0
Persistent prey species in the Lotka-Volterra apparent competition system with a single shared predator.
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2025-01-23 DOI: 10.1007/s00285-025-02184-2
Hiromi Seno
{"title":"Persistent prey species in the Lotka-Volterra apparent competition system with a single shared predator.","authors":"Hiromi Seno","doi":"10.1007/s00285-025-02184-2","DOIUrl":"10.1007/s00285-025-02184-2","url":null,"abstract":"<p><p>We analyze the Lotka-Volterra n prey-1 predator system with no direct interspecific interaction between prey species, in which every prey species undergoes the effect of apparent competition via a single shared predator with all other prey species. We prove that the considered system necessarily has a globally asymptotically stable equilibrium, and we find the necessary and sufficient condition to determine which of feasible equilibria becomes asymptotically stable. Such an asymptotically stable equilibrium shows which prey species goes extinct or persists, and we investigate the composition of persistent prey species at the equilibrium apparent competition system. Making use of the results, we discuss the transition of apparent competition system with a persistent single shared predator through the extermination and invasion of prey species. Our results imply that the long-lasting apparent competition system with a persistent single shared predator would tend toward an implicit functional homogenization in coexisting prey species, or would transfer to a 1 prey-1 predator system in which the predator must be observed as a specialist (monophagy).</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 2","pages":"19"},"PeriodicalIF":2.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11758177/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143025605","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}
引用次数: 0
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