Mathematical Biosciences and Engineering最新文献

{"title":"On the impossibility of increasing the MSY in a multisite Schaefer fishing model.","authors":"Pierre Auger, Tri Nguyen-Huu, Doanh Nguyen-Ngoc","doi":"10.3934/mbe.2025016","DOIUrl":"https://doi.org/10.3934/mbe.2025016","url":null,"abstract":"<p><p>Here, we consider a multisite Schaefer fishing model. The fishery resource grows logistically on each site and is exploited with different fishing efforts. We showed that the Maximum Sustainable Yield (MSY) of the multisite network, when the sites are connected, is always less than or equal to the sum of the MSY of the isolated sites. Equality occurred when the fish population is spatially distributed according to the ideal free distribution (IFD). In this case, the fish had the same access to the resource at each site. We generalized the known result for two sites and the same fishing effort to any number of sites and different fishing efforts. We also discussed how the creation of Marine Protected Areas impacts the fishing efforts. We showed that to minimize the fishing effort to reach the MSY, it is necessary to deploy the entire fishing fleet to the site where the fish is most abundant, the other sites being Marine Protected Areas.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"415-430"},"PeriodicalIF":2.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deterministic, stochastic and fractional mathematical approaches applied to AMR.","authors":"Sebastian Builes, Jhoana P Romero-Leiton, Leon A Valencia","doi":"10.3934/mbe.2025015","DOIUrl":"https://doi.org/10.3934/mbe.2025015","url":null,"abstract":"<p><p>In this work, we study the qualitative properties of a simple mathematical model that can be applied to the reversal of antimicrobial resistance. In particular, we analyze the model from three perspectives: ordinary differential equations (ODEs), stochastic differential equations (SDEs) driven by Brownian motion, and fractional differential equations (FDEs) with Caputo temporal derivatives. Finally, we address the case of Escherichia coli exposed to colistin using parameters from the literature in order to assess the validity of the qualitative properties of the model.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"389-414"},"PeriodicalIF":2.6,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic games of parental vaccination decision making and bounded rationality.","authors":"Andras Balogh, Tamer Oraby","doi":"10.3934/mbe.2025014","DOIUrl":"https://doi.org/10.3934/mbe.2025014","url":null,"abstract":"<p><p>Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of utility functions of the decisions over time, as well as in the disease transmission rates. This approach leads to a system of stochastic differential Eqs of a susceptible-infected-recovered (SIR) model coupled with a stochastic replicator Eq. We explore the dynamics of these Eqs and identify new behaviors emerging from stochastic influences. Interestingly, incorporating stochasticity into the utility functions for vaccination and nonvaccination leads to a decision-making model that reflects the bounded rationality of humans. Noise, like social norms, is a two-sided sword that depends on the degree of bounded rationality of each group. We also perform a stochastic optimal control as a discount to the cost of vaccination to counteract bounded rationality.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"355-388"},"PeriodicalIF":2.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models.","authors":"Mahmudul Bari Hridoy","doi":"10.3934/mbe.2025013","DOIUrl":"https://doi.org/10.3934/mbe.2025013","url":null,"abstract":"<p><p>Seasonal variations in the incidence of infectious diseases are a well-established phenomenon, driven by factors such as climate changes, social behaviors, and ecological interactions that influence host susceptibility and transmission rates. While seasonality plays a significant role in shaping epidemiological dynamics, it is often overlooked in both empirical and theoretical studies. Incorporating seasonal parameters into mathematical models of infectious diseases is crucial for accurately capturing disease dynamics, enhancing the predictive power of these models, and developing successful control strategies. In this paper, I highlight key modeling approaches for incorporating seasonality into disease transmission, including sinusoidal functions, periodic piecewise linear functions, Fourier series expansions, Gaussian functions, and data-driven methods. These approaches are evaluated in terms of their flexibility, complexity, and ability to capture distinct seasonal patterns observed in real-world epidemics. A comparative analysis showcases the relative strengths and limitations of each method, supported by real-world examples. Additionally, a stochastic Susceptible-Infected-Recovered (SIR) model with seasonal transmission is demonstrated through numerical simulations. Important outcome measures, such as the basic and instantaneous reproduction numbers and the probability of a disease outbreak derived from the branching process approximation of the Markov chain, are also presented to illustrate the impact of seasonality on disease dynamics.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"324-354"},"PeriodicalIF":2.6,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of Mpox in an HIV endemic community: A mathematical modelling approach.","authors":"Andrew Omame, Sarafa A Iyaniwura, Qing Han, Adeniyi Ebenezer, Nicola L Bragazzi, Xiaoying Wang, Woldegebriel A Woldegerima, Jude D Kong","doi":"10.3934/mbe.2025010","DOIUrl":"https://doi.org/10.3934/mbe.2025010","url":null,"abstract":"<p><p>During the 2022 monkeypox (Mpox) outbreak in non-endemic countries, sexual transmission was identified as the dominant mode of transmission, and particularly affected the community of men who have sex with men (MSM). This community experienced the highest incidence of Mpox cases, exacerbating the public health burden they already face due to the disproportionate impact of HIV. Given the simultaneous spread of HIV and Mpox within the MSM community, it is crucial to understand how these diseases interact. Specifically, since HIV is endemic within this population, understanding its influence on the spread and control of Mpox is essential. In this study, we analyze a mechanistic mathematical model of Mpox to explore the potential impact of HIV on the dynamics of Mpox within the MSM community. The model considered in this work incorporates the transmission dynamics of the two diseases, including antiretroviral therapy (ART) for HIV. We assumed that HIV was already endemic in the population at the onset of the Mpox outbreak. Through our analysis, we derived the Mpox invasion reproduction number within an HIV-endemic setting and established the existence and local asymptotic stability of the Mpox-free equilibrium under these conditions. Furthermore, we demonstrated the existence and local asymptotic stability of an Mpox-endemic equilibrium in an HIV-endemic regime. Notably, our findings revealed that the model exhibits a backward bifurcation, a phenomenon that may not have occurred in the absence of HIV within the population. The public health significance of our results is that the presence of HIV in the MSM community could hinder efforts to control Mpox, allowing the disease to become endemic even when its invasion reproduction number is below one. Additionally, we found that Mpox might be more challenging to control in scenarios where HIV increases susceptibility to Mpox. Finally, consistent with previous studies, our analysis confirms that reducing sexual contact can be effective for controlling the spread of Mpox within the MSM community.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"225-259"},"PeriodicalIF":2.6,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases.","authors":"Yi Jiang, Kristin M Kurianski, Jane HyoJin Lee, Yanping Ma, Daniel Cicala, Glenn Ledder","doi":"10.3934/mbe.2025011","DOIUrl":"https://doi.org/10.3934/mbe.2025011","url":null,"abstract":"<p><p>We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (Willing or Unwilling/Unable), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies the existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"260-289"},"PeriodicalIF":2.6,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Using asymptotics for efficient stability determination in epidemiological models.","authors":"Glenn Ledder","doi":"10.3934/mbe.2025012","DOIUrl":"https://doi.org/10.3934/mbe.2025012","url":null,"abstract":"<p><p>Local stability analysis is an important tool in the study of dynamical systems. When the goal is to determine the effect of parameter values on stability, it is necessary to perform the analysis without explicit parameter values. For systems with three components, the usual method of finding the characteristic polynomial as $ det(J-lambda I) $ and applying the Routh-Hurwitz conditions is reasonably efficient. For larger systems of four to six components, the method is impractical, as the calculations become too messy. In epidemiological models, there is often a very small parameter that appears as the ratio of a disease-based timescale to a demographic timescale; this allows efficient use of asymptotic approximation to simplify the calculations at little cost. Here, we describe the tools and a set of guidelines that are generally useful in applying the method, followed by two examples of efficient stability analysis.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 2","pages":"290-323"},"PeriodicalIF":2.6,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143626568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A within-host model on the interactions of sensitive and resistant <i>Helicobacter pylori</i> to antibiotic therapy considering immune response.","authors":"Edgar Alberto Vega Noguera, Simeón Casanova Trujillo, Eduardo Ibargüen-Mondragón","doi":"10.3934/mbe.2025009","DOIUrl":"https://doi.org/10.3934/mbe.2025009","url":null,"abstract":"<p><p>In this work, we formulated a mathematical model to describe growth, acquisition of bacterial resistance, and immune response for Helicobacter pylori (<i>H. pylori</i>). The qualitative analysis revealed the existence of five equilibrium solutions: (ⅰ) An infection-free state, in which the bacterial population and immune cells are suppressed, (ⅱ) an endemic state only with resistant bacteria without immune cells, (ⅲ) an endemic state only with resistant bacteria and immune cells, (ⅳ) an endemic state of bacterial coexistence without immune cells, and (ⅴ) an endemic coexistence state with immune response. The stability analysis showed that the equilibrium solutions (ⅰ) and (ⅳ) are locally asymptotically stable, whereas the equilibria (ⅱ) and (ⅲ) are unstable. We found four threshold conditions that establish the existence and stability of equilibria, which determine when the populations of sensitive <i>H. pylori</i> and resistant <i>H. pylori</i> are controlled or eliminated, or when the infection progresses only with resistant bacteria or with both bacterial populations. The numerical simulations corroborated the qualitative analysis, and provided information on the emergence of a limit cycle that breaks the stability of the coexistence equilibrium. The results revealed that the key to controlling bacterial progression is to keep bacterial growth thresholds below 1; this can be achieved by applying an appropriate combination of antibiotics and correct stimulation of the immune response. Otherwise, when bacterial growth thresholds exceed 1, the bacterial persistence scenarios mentioned above occur.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 1","pages":"185-224"},"PeriodicalIF":2.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143415508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fully automated U-net based ROIs localization and bone age assessment method.","authors":"Yuzhong Zhao, Yihao Wang, Haolei Yuan, Haolei Yuan, Qiaoqiao Ding, Xiaoqun Zhang","doi":"10.3934/mbe.2025007","DOIUrl":"https://doi.org/10.3934/mbe.2025007","url":null,"abstract":"<p><p>Bone age assessment (BAA) is a widely used clinical practice for the biological development of adolescents. The Tanner Whitehouse (TW) method is a traditionally mainstream method that manually extracts multiple regions of interest (ROIs) related to skeletal maturity to infer bone age. In this paper, we propose a deep learning-based method for fully automatic ROIs localization and BAA. The method consists of two parts: a U-net-based backbone, selected for its strong performance in semantic segmentation, which enables precise and efficient localization without the need for complex pre- or post-processing. This method achieves a localization precision of 99.1% on the public RSNA dataset. Second, an InceptionResNetV2 network is utilized for feature extraction from both the ROIs and the whole image, as it effectively captures both local and global features, making it well-suited for bone age prediction. The BAA neural network combines the advantages of both ROIs-based methods (TW3 method) and global feature-based methods (GP method), providing high interpretability and accuracy. Numerical experiments demonstrate that the method achieves a mean absolute error (MAE) of 0.38 years for males and 0.45 years for females on the public RSNA dataset, and 0.41 years for males and 0.44 years for females on an in-house dataset, validating the accuracy of both localization and prediction.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 1","pages":"138-151"},"PeriodicalIF":2.6,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143416045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traveling waves in a free boundary problem for the spread of ecosystem engineers.","authors":"Maryam Basiri, Frithjof Lutscher, Abbas Moameni","doi":"10.3934/mbe.2025008","DOIUrl":"https://doi.org/10.3934/mbe.2025008","url":null,"abstract":"<p><p>Reaction-diffusion equations are a trusted modeling framework for the dynamics of biological populations in space and time, and their traveling wave solutions are interpreted as the density of an invasive species that spreads at constant speed. Even though certain species can significantly alter their abiotic environment for their benefit, and even though some of these so-called \"ecosystem engineers\" are among the most destructive invasive species, most models neglect this feedback. Here, we extended earlier work that studied traveling waves of ecosystem engineers with a logistic growth function to study the existence of traveling waves in the presence of a strong Allee effect. Our model consisted of suitable and unsuitable habitat, each a semi-infinite interval, separated by a moving interface. The speed of this boundary depended on the engineering activity of the species. On each of the intervals, we had a reaction-diffusion equation for the population density, and at the interface, we had matching conditions for density and flux. We used phase-plane analysis to detect and classify several qualitatively different types of traveling waves, most of which have previously not been described. We gave conditions for their existence for different biological scenarios of how individuals alter their abiotic environment. As an intermediate step, we studied the existence of traveling waves in a so-called \"moving habitat model\", which can be interpreted as a model for the effects of climate change on the spatial dynamics of populations.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"22 1","pages":"152-184"},"PeriodicalIF":2.6,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143415885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}