Journal of Mathematical Biology最新文献

{"title":"Model analysis and data validation of structured prevention and control interruptions of emerging infectious diseases","authors":"Hao Zhou, He Sha, Robert A. Cheke, Sanyi Tang","doi":"10.1007/s00285-024-02083-y","DOIUrl":"https://doi.org/10.1007/s00285-024-02083-y","url":null,"abstract":"<p>The design of optimized non-pharmaceutical interventions (NPIs) is critical to the effective control of emergent outbreaks of infectious diseases such as SARS, A/H1N1 and COVID-19 and to ensure that numbers of hospitalized cases do not exceed the carrying capacity of medical resources. To address this issue, we formulated a classic SIR model to include a close contact tracing strategy and structured prevention and control interruptions (SPCIs). The impact of the timing of SPCIs on the maximum number of non-isolated infected individuals and on the duration of an infectious disease outside quarantined areas (i.e. implementing a dynamic zero-case policy) were analyzed numerically and theoretically. These analyses revealed that to minimize the maximum number of non-isolated infected individuals, the optimal time to initiate SPCIs is when they can control the peak value of a second rebound of the epidemic to be equal to the first peak value. More individuals may be infected at the peak of the second wave with a stronger intervention during SPCIs. The longer the duration of the intervention and the stronger the contact tracing intensity during SPCIs, the more effective they are in shortening the duration of an infectious disease outside quarantined areas. The dynamic evolution of the number of isolated and non-isolated individuals, including two peaks and long tail patterns, have been confirmed by various real data sets of multiple-wave COVID-19 epidemics in China. Our results provide important theoretical support for the adjustment of NPI strategies in relation to a given carrying capacity of medical resources.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"300 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601228","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 two-phase thin-film model for cell-induced gel contraction incorporating osmotic effects","authors":"J. R. Reoch, Y. M. Stokes, J. E. F. Green","doi":"10.1007/s00285-024-02072-1","DOIUrl":"https://doi.org/10.1007/s00285-024-02072-1","url":null,"abstract":"<p>We present a mathematical model of an experiment in which cells are cultured within a gel, which in turn floats freely within a liquid nutrient medium. Traction forces exerted by the cells on the gel cause it to contract over time, giving a measure of the strength of these forces. Building upon our previous work (Reoch et al. in J Math Biol 84(5):31, 2022), we exploit the fact that the gels used frequently have a thin geometry to obtain a reduced model for the behaviour of a thin, two-dimensional cell-seeded gel. We find that steady-state solutions of the reduced model require the cell density and volume fraction of polymer in the gel to be spatially uniform, while the gel height may vary spatially. If we further assume that all three of these variables are initially spatially uniform, this continues for all time and the thin film model can be further reduced to solving a single, non-linear ODE for gel height as a function of time. The thin film model is further investigated for both spatially-uniform and varying initial conditions, using a combination of analytical techniques and numerical simulations. We show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e., the chemical potentials) and the strength of the cell traction forces. However, unlike in the earlier one-dimensional model, we do not observe cases where the gel oscillates between swelling and contraction. For the case of initially uniform cell and gel density, our model predicts that the relative change in the gels’ height and length are equal, which justifies an assumption previously used in the work of Stevenson et al. (Biophys J 99(1):19–28, 2010). Conversely, however, even for non-uniform initial conditions, we do not observe cases where the length of the gel changes whilst its height remains constant, which have been reported in another model of osmotic swelling by Trinschek et al. (AIMS Mater Sci 3(3):1138–1159, 2016; Phys Rev Lett 119:078003, 2017).</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601262","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":"Infection-induced increases to population size during cycles in a discrete-time epidemic model","authors":"Laura F. Strube, Shoshana Elgart, Lauren M. Childs","doi":"10.1007/s00285-024-02074-z","DOIUrl":"https://doi.org/10.1007/s00285-024-02074-z","url":null,"abstract":"<p>One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the ‘hydra effect,’ i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called ‘infection-induced hydra effect.’ Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"123 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600789","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 role of memory-based movements in the formation of animal home ranges","authors":"Nathan Ranc, John W. Cain, Francesca Cagnacci, Paul R. Moorcroft","doi":"10.1007/s00285-024-02055-2","DOIUrl":"https://doi.org/10.1007/s00285-024-02055-2","url":null,"abstract":"<p>Most animals live in spatially-constrained home ranges. The prevalence of this space-use pattern in nature suggests that general biological mechanisms are likely to be responsible for their occurrence. Individual-based models of animal movement in both theoretical and empirical settings have demonstrated that the revisitation of familiar areas through memory can lead to the formation of stable home ranges. Here, we formulate a deterministic, mechanistic home range model that includes the interplay between a bi-component memory and resource preference, and evaluate resulting patterns of space-use. We show that a bi-component memory process can lead to the formation of stable home ranges and control its size, with greater spatial memory capabilities being associated with larger home range size. The interplay between memory and resource preferences gives rise to a continuum of space-use patterns–from spatially-restricted movements into a home range that is influenced by local resource heterogeneity, to diffusive-like movements dependent on larger-scale resource distributions, such as in nomadism. Future work could take advantage of this model formulation to evaluate the role of memory in shaping individual performance in response to varying spatio-temporal resource patterns.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"21 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600843","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":"Phylogenetic network classes through the lens of expanding covers","authors":"Andrew Francis, Daniele Marchei, Mike Steel","doi":"10.1007/s00285-024-02075-y","DOIUrl":"https://doi.org/10.1007/s00285-024-02075-y","url":null,"abstract":"<p>It was recently shown that a large class of phylogenetic networks, the ‘labellable’ networks, is in bijection with the set of ‘expanding’ covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call ‘spinal’ phylogenetic networks.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"36 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600844","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":"Memory effects in disease modelling through kernel estimates with oscillatory time history","authors":"Adam Mielke, Mads Peter Sørensen, John Wyller","doi":"10.1007/s00285-024-02080-1","DOIUrl":"https://doi.org/10.1007/s00285-024-02080-1","url":null,"abstract":"<p>We design a linear chain trick algorithm for dynamical systems for which we have oscillatory time histories in the distributed time delay. We make use of this algorithmic framework to analyse memory effects in disease evolution in a population. The modelling is based on a susceptible-infected-recovered SIR—model and on a susceptible-exposed-infected-recovered SEIR—model through a kernel that dampens the activity based on the recent history of infectious individuals. This corresponds to adaptive behavior in the population or through governmental non-pharmaceutical interventions. We use the linear chain trick to show that such a model may be written in a Markovian way, and we analyze the stability of the system. We find that the adaptive behavior gives rise to either a stable equilibrium point or a stable limit cycle for a close to constant number of susceptibles, i.e. locally in time. We also show that the attack rate for this model is lower than it would be without the dampening, although the adaptive behavior disappears as time goes to infinity and the number of infected goes to zero.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"52 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600999","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":"Hopf bifurcation in an age-structured predator–prey system with Beddington–DeAngelis functional response and constant harvesting","authors":"San-Xing Wu, Zhi-Cheng Wang, Shigui Ruan","doi":"10.1007/s00285-024-02070-3","DOIUrl":"https://doi.org/10.1007/s00285-024-02070-3","url":null,"abstract":"<p>In this paper, an age-structured predator–prey system with Beddington–DeAngelis (B–D) type functional response, prey refuge and harvesting is investigated, where the predator fertility function <i>f</i>(<i>a</i>) and the maturation function <span>(beta (a))</span> are assumed to be piecewise functions related to their maturation period <span>(tau )</span>. Firstly, we rewrite the original system as a non-densely defined abstract Cauchy problem and show the existence of solutions. In particular, we discuss the existence and uniqueness of a positive equilibrium of the system. Secondly, we consider the maturation period <span>(tau )</span> as a bifurcation parameter and show the existence of Hopf bifurcation at the positive equilibrium by applying the integrated semigroup theory and Hopf bifurcation theorem. Moreover, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied by applying the center manifold theorem and normal form theory. Finally, some numerical simulations are given to illustrate of the theoretical results and a brief discussion is presented.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"33 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600998","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":"Modelling non-local cell-cell adhesion: a multiscale approach","authors":"Anna Zhigun, Mabel Lizzy Rajendran","doi":"10.1007/s00285-024-02079-8","DOIUrl":"https://doi.org/10.1007/s00285-024-02079-8","url":null,"abstract":"<p>Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in Armstrong et al. (J Theoret Biol 243(1): 98–113, 2006). Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"16 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600760","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":"Back to the fundamentals: a reply to Basener and Sanford 2018","authors":"Zachary B. Hancock, Daniel Stern Cardinale","doi":"10.1007/s00285-024-02077-w","DOIUrl":"https://doi.org/10.1007/s00285-024-02077-w","url":null,"abstract":"<p>Fisher’s fundamental theorem of natural selection has haunted theoretical population genetic literature since it was proposed in 1930, leading to numerous interpretations. Most of the confusion stemmed from Fisher’s own obscure presentation. By the 1970s, a clearer view of Fisher’s theorem had been achieved and it was found that, regardless of its utility or significance, it represents a general theorem of evolutionary biology. Basener and Sanford (J Math Biol 76:1589–1622, 2018) writing in <i>JOMB</i>, however, paint a different picture of the fundamental theorem as one hindered by its assumptions and incomplete due to its failure to explicitly incorporate mutational effects. They argue that Fisher saw his theorem as a “mathematical proof of Darwinian evolution”. In this reply, we show that, contrary to Basener and Sanford, Fisher’s theorem is a general theorem that applies to any evolving population, and that, far from their assertion that it needed to be expanded, the theorem already implicitly incorporates ancestor–descendant variation. We also show that their numerical simulations produce unrealistic results. Lastly, we argue that Basener and Sanford’s motivations were in undermining not merely Fisher’s theorem, but the concept of universal common descent itself.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"21 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600588","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":"Global analysis of an age-structured tuberculosis model with an application to Jiangsu, China.","authors":"Shuanglin Jing, Ling Xue, Hao Wang, Zhihang Peng","doi":"10.1007/s00285-024-02066-z","DOIUrl":"10.1007/s00285-024-02066-z","url":null,"abstract":"<p><p>Diagnostic delay for TB infected individuals and the lack of TB vaccines for adults are the main challenges to achieve the goals of WHO by 2050. In order to evaluate the impacts of diagnostic delay and vaccination for adults on prevalence of TB, we propose an age-structured model with latent age and infection age, and we incorporate Mycobacterium TB in the environment and vaccination into the model. Diagnostic delay is indicated by the age of infection before receiving treatment. The threshold dynamics are established in terms of the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . When <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; When <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . We estimate that the basic reproduction number <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>=</mo> <mn>0.5320</mn></mrow> </math> (95% CI (0.3060, 0.7556)) in Jiangsu Province, which means that TB epidemic will die out. However, we find that the annual number of new TB cases by 2050 is 1,151 (95%CI: (138, 8,014)), which means that it is challenging to achieve the goal of WHO by 2050. To this end, we evaluate the possibility of achieving the goals of WHO if we start vaccinating adults and reduce diagnostic delay in 2025. Our results demonstrate that when the diagnostic delay is reduced from longer than four months to four months, or 20% adults are vaccinated, the goal of WHO in 2050 can be achieved, and 73,137 (95%CI: (23,906, 234,086)) and 54,828 (95%CI: (15,811, 206,468)) individuals will be prevented from being infected from 2025 to 2050, respectively. The modeling approaches and simulation results used in this work can help policymakers design control measures to reduce the prevalence of TB.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"88 5","pages":"52"},"PeriodicalIF":2.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140337477","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}