Journal of Mathematical Biology最新文献

{"title":"wStri spread dynamics in Nilaparvata lugens via discrete mathematical models.","authors":"Bo Zheng, Huichao Yang, Saber Elaydi, Jianshe Yu","doi":"10.1007/s00285-025-02198-w","DOIUrl":"https://doi.org/10.1007/s00285-025-02198-w","url":null,"abstract":"<p><p>Wolbachia, an intracellular bacterium, is well-known for inducing cytoplasmic incompatibility, which has become a promising and environmentally sustainable strategy for controlling pest populations. The strain wStri, specifically identified in Nilaparvata lugens (brown planthopper), has shown potential for such biocontrol applications. In this study, we develop a comprehensive discrete mathematical model to analyze the dynamics of wStri spread in a mixed population of wStri-infected, wLug-infected, and uninfected Nilaparvata lugens under both constant and periodically varying environmental conditions. Under a constant environment, the model identifies the critical threshold necessary for the successful establishment of wStri within the population. Our analysis reveals that the model exhibits a strong Allee effect, where a population must exceed a certain critical density-the Allee threshold-for the wStri strain to persist and spread. Below this threshold, the wStri strain is likely to be eliminated, failing in pest control efforts. When the environment varies periodically, the model transforms into a non-autonomous periodic discrete model, introducing additional complexity. In this scenario, we derive sufficient conditions that ensure the composition of finitely many Allee maps continues to function as an Allee map. Furthermore, we prove that a unique periodic orbit exists within such a periodic environment. This orbit is characterized as unstable and acts as a threshold, determining whether wStri will establish itself in the population or die out over time. The findings from this model provide critical insights into the conditions under which wStri can be effectively used to control Nilaparvata lugens, particularly in environments that are not constant but fluctuate periodically. These insights have significant implications for the practical deployment of Wolbachia-based biocontrol methods in pest management strategies.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"38"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143568772","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":"On the stochastic global dynamics of the delayed Nicholson's blowflies model.","authors":"Islam M Elbaz, M A Sohaly, H El-Metwally","doi":"10.1007/s00285-025-02199-9","DOIUrl":"https://doi.org/10.1007/s00285-025-02199-9","url":null,"abstract":"<p><p>The well-known class of Nicholson's blowflies equations is considered under stochastic perturbations of the white noise type. We are concerned about the stability of the zero solution <math><msub><mi>x</mi> <mn>0</mn></msub> </math> which means the extinction of the species of Nicholson's blowflies, and the positive equilibrium <math><msup><mi>x</mi> <mo>∗</mo></msup> </math> which means their persistence. Using appropriate Lyapunov functionals, sufficient conditions of stochastic stability, uniform stability and stochastic global exponential mean-square stability are derived. Moreover, we develop a new way of constructing a delayed-deterministic system by Lyapunov functional that leads to the extinction in the sense of the mean-square. Areas of stability with some numerical simulations are given to illustrate our results.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"37"},"PeriodicalIF":2.2,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143537886","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":"Evaluating the long-term effects of combination antiretroviral therapy of HIV infection: a modeling study.","authors":"Jing Cai, Jun Zhang, Kai Wang, Zhixiang Dai, Zhiliang Hu, Yueping Dong, Zhihang Peng","doi":"10.1007/s00285-025-02196-y","DOIUrl":"10.1007/s00285-025-02196-y","url":null,"abstract":"<p><p>Current HIV/AIDS treatments effectively reduce viral loads to undetectable levels as measured by conventional clinical assays, but immune recovery remains highly variable among patients. To assess the long-term treatment efficacy, we propose a mathematical model that incorporates latently infected CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cells and the homeostatic proliferation of CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cells. We investigate the dynamics of this model both theoretically and numerically, demonstrating that homeostatic proliferation can induce bistability, which implies that steady-state CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell count is sensitively affected by initial conditions. The model exhibits rich dynamics, including saddle node bifurcations, Hopf bifurcations, and saddle node bifurcations related to periodic orbits. The interplay between homeostatic proliferation and latent HIV infection significantly influences the model's dynamic behavior. Additionally, we integrate combination antiretroviral therapy (cART) into the model and fit the revised model to clinical data on long-term CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell counts before and after treatment. Quantitative analysis estimates the effects of long-term cART, revealing an increasing sensitivity of steady-state CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell count to drug efficacy. Correlation analysis indicates that the heightened activation of latently infected cells helps enhance treatment efficacy. These findings underscore the critical roles of CD4 <math><mmultiscripts><mrow></mrow> <mrow></mrow> <mo>+</mo></mmultiscripts> </math> T cell homeostatic proliferation and latently infected cell production in HIV persistence despite treatment, providing valuable insights for understanding disease progression and developing more effective therapies, potentially towards eradication.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"36"},"PeriodicalIF":2.2,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11872777/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143537869","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":"The power of Allee effects: inducing multistability and oscillations in a stoichiometric producer-herbivore system.","authors":"Zhiwei Zhu, Tao Feng","doi":"10.1007/s00285-025-02197-x","DOIUrl":"https://doi.org/10.1007/s00285-025-02197-x","url":null,"abstract":"<p><p>Understanding producer-herbivore dynamics is fundamental for maintaining ecosystem stability and biodiversity. This study proposes a novel stoichiometric producer-herbivore model that incorporates positive density dependence induced by demographic factors. We conduct a rigorous mathematical analysis of the proposed model, covering well-posedness, nullcline analysis, and system stability. This analysis is expanded through numerical bifurcation analysis to explore the effects of critical biological parameters, including light intensity, on producer-herbivore interactions. Our findings reveal that variations in the severity of the Allee effect significantly influence these interactions, driving multistability and periodic oscillations. Severe Allee effects lead to complex dynamics, including four forms of bistability and three forms of tristability. Severe Allee effects can also lead to the extinction of both producer and herbivore populations due to positive density dependence. Intermediate levels of parameters such as light intensity, producer growth rate, herbivore loss rate, saturation levels of the Allee effect, total phosphorus, and sufficiently high production efficiency can lead to system instability and oscillations. Conversely, in scenarios with low-severity Allee effects, the system shows relatively simpler dynamics, with three types of bistability. Low producer growth rate and herbivore loss rate, moderate saturation levels of the Allee effect, light intensity, and sufficiently high herbivore production efficiency and total phosphorus levels can induce periodic oscillations. These findings emphasize the importance of managing Allee effect severity in conservation efforts to sustain biodiversity and prevent undesirable state transitions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"35"},"PeriodicalIF":2.2,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143517173","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":"Dynamics of an epidemic model arising in a spatial segregation control strategy.","authors":"Zhiguo Wang, Hua Nie, Sanyi Tang","doi":"10.1007/s00285-025-02195-z","DOIUrl":"https://doi.org/10.1007/s00285-025-02195-z","url":null,"abstract":"<p><p>In this paper, we propose a free boundary problem to model the spread of an epidemic by introducing a spatial segregation control strategy. The model consists of two coupled reaction-diffusion equations along with an ordinary differential equation, while the free boundary is described by an integro-differential equation. The results reveal a trichotomy in which the epidemic can shrink, reach equilibrium, or expand spatially. Moreover, we establish the final size of the cumulative number of infected populations and characterize the threshold phenomenon of epidemic outbreak using the principal eigenvalue of an elliptic operator. Additionally, we apply this model to simulate the spatial spread of the COVID-19 epidemic in Xi'an, China, during 2021-2022. This study provides valuable model references for dynamically designing spatial isolation control strategies for newly emerging major infectious diseases.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 4","pages":"34"},"PeriodicalIF":2.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143505777","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":"Convective stability of the critical waves of an FKPP-type model for self-organized growth.","authors":"Florian Kreten","doi":"10.1007/s00285-025-02189-x","DOIUrl":"10.1007/s00285-025-02189-x","url":null,"abstract":"<p><p>We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the wave. The considered reaction-diffusion system was introduced by Hannezo et al. (Cell 171(1):242-255, 2017) in the context of branching morphogenesis: active, branching particles accumulate inactive particles, which do not react. Thus, the system features a continuum of steady state solutions, complicating the analysis. We adopt a result by Faye and Holzer (J Differ Equ 269(9):6559-6601, 2020) for proving the stability of the critical traveling waves, and modify the semi-group estimates to spaces with unbounded weights. We use a Feynman-Kac formula to get an exponential a priori estimate for the tail of the PDE, a novel and simple approach.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"33"},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11832597/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143442624","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":"Basic concepts for the Kermack and McKendrick model with static heterogeneity.","authors":"Hisashi Inaba","doi":"10.1007/s00285-025-02187-z","DOIUrl":"10.1007/s00285-025-02187-z","url":null,"abstract":"<p><p>In this paper, we consider the infection-age-dependent Kermack-McKendrick model, where host individuals are distributed in a continuous state space. To provide a mathematical foundation for the heterogeneous model, we develop a <math><msup><mi>L</mi> <mn>1</mn></msup> </math> -framework to formulate basic epidemiological concepts. First, we show the mathematical well-posedness of the basic model under appropriate conditions allowing for unbounded structural variables in an unbounded domain. Next, we define the basic reproduction number and prove pandemic threshold results. We then present a systematic procedure to compute the effective reproduction number and the herd immunity threshold. Finally, we give some illustrative examples and concrete results by using the separable mixing assumption.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"32"},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143442621","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":"Description of chemical systems by means of response functions.","authors":"E Franco, B Kepka, J J L Velázquez","doi":"10.1007/s00285-025-02191-3","DOIUrl":"10.1007/s00285-025-02191-3","url":null,"abstract":"<p><p>In this paper we introduce a formalism that allows to describe the response of a part of a biochemical system in terms of renewal equations. In particular, we examine under which conditions the interactions between the different parts of a chemical system, described by means of linear ODEs, can be represented in terms of renewal equations. We show also how to apply the formalism developed in this paper to some particular types of linear and non-linear ODEs, modelling some biochemical systems of interest in biology (for instance, some time-dependent versions of the classical Hopfield model of kinetic proofreading). We also analyse some of the properties of the renewal equations that we are interested in, as the long-time behaviour of their solution. Furthermore, we prove that the kernels characterising the renewal equations derived by biochemical system with reactions that satisfy the detail balance condition belong to the class of completely monotone functions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"31"},"PeriodicalIF":2.2,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11830649/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143434299","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":"The effect of pathogens from environmental breeding and accumulative release by the infected individuals on spread dynamics of a SIRP epidemic model.","authors":"Ning Wang, Long Zhang, Zhidong Teng","doi":"10.1007/s00285-025-02194-0","DOIUrl":"10.1007/s00285-025-02194-0","url":null,"abstract":"<p><p>In this paper, a SIRP epidemic model is proposed, wherein the pathogens derive from two ways, i.e., environmental breeding, and accumulative excretion by the infected individuals. The former is characterized by Logistic growth, while the latter is in the form of infinite integral. First, the positivity and ultimate boundedness of solutions are obtained. Second, the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> is obtained, by which the model is analyzed if either the intrinsic growth rate of environmental pathogens is lower or higher than its clearance rate. For the first case, the disease-free equilibrium is globally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> , while the endemic equilibrium is globally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . Conversely, if the growth rate exceeds the removal rate, the disease-free equilibrium is always unstable, meanwhile, the uniform persistence of the model indicates that there could exist one or multi-endemic equilibria, and it is globally asymptotically stable if the endemic equilibrium is unique. Finally, the theoretical results are illustrated by numerical simulations. We find that the accumulative release of pathogens by the infected individuals in the form of infinite integral is more realistic and consistent with the disease spread than that of linear form by real data.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"30"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143411308","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 estimation of transmission networks for infectious diseases.","authors":"Jianing Xu, Huimin Hu, Gregory Ellison, Lili Yu, Christopher C Whalen, Liang Liu","doi":"10.1007/s00285-025-02193-1","DOIUrl":"10.1007/s00285-025-02193-1","url":null,"abstract":"<p><p>Reconstructing transmission networks is essential for identifying key factors like superspreaders and high-risk locations, which are critical for developing effective pandemic prevention strategies. This study presents a Bayesian transmission model that combines genomic and temporal data to reconstruct transmission networks for infectious diseases. The Bayesian transmission model incorporates the latent period and distinguishes between symptom onset and actual infection time, improving the accuracy of transmission dynamics and epidemiological models. It also assumes a homogeneous effective population size among hosts, ensuring that the coalescent process for within-host evolution remains unchanged, even with missing intermediate hosts. This allows the model to effectively handle incomplete samples. Simulation results demonstrate the model's ability to accurately estimate model parameters and transmission networks. Additionally, our proposed hypothesis test can reliably identify direct transmission events. The Bayesian transmission model was applied to a real dataset of Mycobacterium tuberculosis genomes from 69 tuberculosis cases. The estimated transmission network revealed two major groups, each with a superspreader who transmitted M. tuberculosis, either directly or indirectly, to 28 and 21 individuals, respectively. The hypothesis test identified 16 direct transmissions within the estimated network, demonstrating the Bayesian model's advantage over a fixed threshold by providing a more flexible criterion for identifying direct transmissions. This Bayesian approach highlights the critical role of genetic data in reconstructing transmission networks and enhancing our understanding of the origins and transmission dynamics of infectious diseases.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 3","pages":"29"},"PeriodicalIF":2.2,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143400543","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}