Mathematical medicine and biology : a journal of the IMA最新文献_第3页

Asymptotic properties of the Lotka-Volterra competition and mutualism model under stochastic perturbations. 随机扰动下 Lotka-Volterra 竞争与互惠模型的渐近特性

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-03-15 DOI: 10.1093/imammb/dqae001

Leonid Shaikhet, Andrei Korobeinikov

{"title":"Asymptotic properties of the Lotka-Volterra competition and mutualism model under stochastic perturbations.","authors":"Leonid Shaikhet, Andrei Korobeinikov","doi":"10.1093/imammb/dqae001","DOIUrl":"10.1093/imammb/dqae001","url":null,"abstract":"Stochastically perturbed models, where the white noise type stochastic perturbations are proportional to the current system state, the most realistically describe real-life biosystems. However, such models essentially have no equilibrium states apart from one at the origin. This feature makes analysis of such models extremely difficult. Probably, the best result that can be found for such models is finding of accurate estimations of a region in the model phase space that serves as an attractor for model trajectories. In this paper, we consider a classical stochastically perturbed Lotka-Volterra model of competing or symbiotic populations, where the white noise type perturbations are proportional to the current system state. Using the direct Lyapunov method in a combination with a recently developed technique, we establish global asymptotic properties of this model. In order to do this, we, firstly, construct a Lyapunov function that is applicable to the both competing (and globally stable) and symbiotic deterministic Lotka-Volterra models. Then, applying this Lyapunov function to the stochastically perturbed model, we show that solutions with positive initial conditions converge to a certain compact region in the model phase space and oscillate around this region thereafter. The direct Lyapunov method allows to find estimates for this region. We also show that if the magnitude of the noise exceeds a certain critical level, then some or all species extinct via process of the stochastic stabilization ('stabilization by noise'). The approach applied in this paper allows to obtain necessary conditions for the extinction. Sufficient conditions for the extinction (that for this model occurs via the process that is known as the 'stochastic stabilization', or the 'stabilization by noise') are found applying the Khasminskii-type Lyapunov functions.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"19-34"},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139643727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dosage optimization for reducing tumor burden using a phenotype-structured population model with a drug-resistance continuum. 利用具有耐药性连续体的表型结构群体模型优化剂量，减轻肿瘤负担。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-03-15 DOI: 10.1093/imammb/dqae003

Lifeng Han, Osman N Yogurtcu, Marisabel Rodriguez Messan, Wencel Valega-Mackenzie, Ujwani Nukala, Hong Yang

{"title":"Dosage optimization for reducing tumor burden using a phenotype-structured population model with a drug-resistance continuum.","authors":"Lifeng Han, Osman N Yogurtcu, Marisabel Rodriguez Messan, Wencel Valega-Mackenzie, Ujwani Nukala, Hong Yang","doi":"10.1093/imammb/dqae003","DOIUrl":"10.1093/imammb/dqae003","url":null,"abstract":"Drug resistance is a significant obstacle to effective cancer treatment. To gain insights into how drug resistance develops, we adopted a concept called fitness landscape and employed a phenotype-structured population model by fitting to a set of experimental data on a drug used for ovarian cancer, olaparib. Our modeling approach allowed us to understand how a drug affects the fitness landscape and track the evolution of a population of cancer cells structured with a spectrum of drug resistance. We also incorporated pharmacokinetic (PK) modeling to identify the optimal dosages of the drug that could lead to long-term tumor reduction. We derived a formula that indicates that maximizing variation in plasma drug concentration over a dosing interval could be important in reducing drug resistance. Our findings suggest that it may be possible to achieve better treatment outcomes with a drug dose lower than the levels recommended by the drug label. Acknowledging the current limitations of our work, we believe that our approach, which combines modeling of both PK and drug resistance evolution, could contribute to a new direction for better designing drug treatment regimens to improve cancer treatment.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"35-52"},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Impact of climate change on vegetation patterns in Altay Prefecture, China. 气候变化对中国阿勒泰地区植被格局的影响。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2024-03-15 DOI: 10.1093/imammb/dqae002

Li Li, Yi-Zhi Pang, Gui-Quan Sun, Shigui Ruan

{"title":"Impact of climate change on vegetation patterns in Altay Prefecture, China.","authors":"Li Li, Yi-Zhi Pang, Gui-Quan Sun, Shigui Ruan","doi":"10.1093/imammb/dqae002","DOIUrl":"10.1093/imammb/dqae002","url":null,"abstract":"Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction-diffusion model of the climate-vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"53-80"},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139992245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effects of vaccination on the two-strain transmission dynamics of COVID-19: Dougherty County, Georgia, USA, as a case study. 疫苗接种对COVID-19两株传播动态的影响:以美国乔治亚州多尔蒂县为例

Mathematical medicine and biology : a journal of the IMA Pub Date : 2023-12-15 DOI: 10.1093/imammb/dqad007

Buddhi Pantha, Jemal Mohammed-Awel, Naveen K Vaidya

{"title":"Effects of vaccination on the two-strain transmission dynamics of COVID-19: Dougherty County, Georgia, USA, as a case study.","authors":"Buddhi Pantha, Jemal Mohammed-Awel, Naveen K Vaidya","doi":"10.1093/imammb/dqad007","DOIUrl":"10.1093/imammb/dqad007","url":null,"abstract":"The emergence of multiple strains of SARS-COV-2 has made it complicated to predict and control the COVID-19 pandemic. Although some vaccines have been effective in reducing the severity of the disease, these vaccines are designed for a specific strain of the virus and are usually less effective for other strains. In addition, the waning of vaccine-induced immunity, reinfection of recovered people, and incomplete vaccination are challenging to the vaccination program. In this study, we developed a detailed model to describe the multi-strain transmission dynamics of COVID-19 under vaccination. We implemented our model to examine the impact of inter-strain transmission competition under vaccination on the critical outbreak indicators: hospitalized cases, undiagnosed cases, basic reproduction numbers, and the overtake-time by a new strain to the existing strain. In particular, our results on the dependence of the overtake-time on vaccination rates, progression-to-infectious rate, and relative transmission rates provide helpful information for managing a pandemic with circulating two strains. Furthermore, our results suggest that a reduction in the relative transmission rates and a decrease in vaccination dropout rates or an increase in vaccination rates help keep the reproduction number of both strains below unity and keep the number of hospitalized cases and undiagnosed cases at their lowest levels. Moreover, our analysis shows that the second and booster-dose vaccinations are useful for further reducing the reproduction number.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"308-326"},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"107593169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Which airways should we treat? Structure-function relationships and estimation of the singular input modes from the forward model alone. 我们应该治疗哪种呼吸道？结构-函数关系以及仅从正向模型对奇异输入模式的估计。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2023-12-15 DOI: 10.1093/imammb/dqad006

Graham M Donovan

引用次数: 0

Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth. 肿瘤生长多相移动边界模型的模式形成和行波。

Mathematical medicine and biology : a journal of the IMA Pub Date : 2023-12-15 DOI: 10.1093/imammb/dqad008

Jacob M Jepson, Reuben D O'Dea, John Billingham, Nabil T Fadai

{"title":"Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth.","authors":"Jacob M Jepson, Reuben D O'Dea, John Billingham, Nabil T Fadai","doi":"10.1093/imammb/dqad008","DOIUrl":"10.1093/imammb/dqad008","url":null,"abstract":"We employ the multiphase, moving boundary model of Byrne et al. (2003, Appl. Math. Lett., 16, 567-573) that describes the evolution of a motile, viscous tumour cell phase and an inviscid extracellular liquid phase. This model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tumour edge, and here we characterize and analyse its travelling-wave and pattern-forming behaviour. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tumour growth or extinction, respectively. A travelling-wave analysis allows us to find the corresponding wave speed, as well as criteria for the growth or extinction of the tumour. Furthermore, a stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. Finally, we discuss how the initial cell distribution, as well as parameters related to cellular motion and cell-liquid drag, control the qualitative features of patterned solutions.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":" ","pages":"327-347"},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138300845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations 双心室、健康和衰竭心外循环的集总参数模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2021-09-01 DOI: 10.1093/imammb/dqab012

Matthew G Doyle;Marina Chugunova;S Lucy Roche;James P Keener

引用次数: 1

Synchronization in epidemic growth and the impossibility of selective containment 流行病增长的同步性和选择性遏制的不可能性

Mathematical medicine and biology : a journal of the IMA Pub Date : 2021-09-01 DOI: 10.1093/imammb/dqab013

Jan C Budich;Emil J Bergholtz

{"title":"Synchronization in epidemic growth and the impossibility of selective containment","authors":"Jan C Budich;Emil J Bergholtz","doi":"10.1093/imammb/dqab013","DOIUrl":"10.1093/imammb/dqab013","url":null,"abstract":"Containment, aiming to prevent the epidemic stage of community-spreading altogether, and mitigation, aiming to merely ‘flatten the curve’ of a wide-ranged outbreak, constitute two qualitatively different approaches to combating an epidemic through non-pharmaceutical interventions. Here, we study a simple model of epidemic dynamics separating the population into two groups, namely a low-risk group and a high-risk group, for which different strategies are pursued. Due to synchronization effects, we find that maintaining a slower epidemic growth behaviour for the high-risk group is unstable against any finite coupling between the two groups. More precisely, the density of infected individuals in the two groups qualitatively evolves very similarly, apart from a small time delay and an overall scaling factor quantifying the coupling between the groups. Hence, selective containment of the epidemic in a targeted (high-risk) group is practically impossible whenever the surrounding society implements a mitigated community-spreading. We relate our general findings to the ongoing COVID-19 pandemic.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 4","pages":"467-473"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9686632","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39555501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Accurate numerical simulation of electrodiffusion and water movement in brain tissue 脑组织中电扩散和水运动的精确数值模拟

Mathematical medicine and biology : a journal of the IMA Pub Date : 2021-09-01 DOI: 10.1093/imammb/dqab016

Ada J Ellingsrud;Nicolas Boullé;Patrick E Farrell;Marie E Rognes

{"title":"Accurate numerical simulation of electrodiffusion and water movement in brain tissue","authors":"Ada J Ellingsrud;Nicolas Boullé;Patrick E Farrell;Marie E Rognes","doi":"10.1093/imammb/dqab016","DOIUrl":"10.1093/imammb/dqab016","url":null,"abstract":"Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide a new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"38 4","pages":"516-551"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/9686629/09686655.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39743841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Diffusion of dermatological irritant in drying laundered cloth 皮肤刺激物在干洗布中的扩散

Mathematical medicine and biology : a journal of the IMA Pub Date : 2021-09-01 DOI: 10.1093/imammb/dqab014

P Broadbridge;B S Tilley

引用次数: 0