Mathematical Modelling of Natural Phenomena最新文献_第9页

Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics 非马尔科维奇模型强调年龄结构对新冠肺炎流行病学动态的重要性

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-03-02 DOI: 10.1051/mmnp/2022008

B. Reyné, Q. Richard, C. Selinger, Mircea T. Sofonea, R. Djidjou-Demasse, S. Alizon

{"title":"Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics","authors":"B. Reyné, Q. Richard, C. Selinger, Mircea T. Sofonea, R. Djidjou-Demasse, S. Alizon","doi":"10.1051/mmnp/2022008","DOIUrl":"https://doi.org/10.1051/mmnp/2022008","url":null,"abstract":"The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. A global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43286414","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: 9

Higher-order semi-rational solutions for the coupled complex modified Korteweg-de Vries equation 耦合复修正Korteweg-de Vries方程的高阶半有理解

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-02-02 DOI: 10.1051/mmnp/2022006

Yu Lou, Yi Zhang, Rusuo Ye

引用次数: 0

Mathematical Modeling of Inflammatory Processes of Atherosclerosis 动脉粥样硬化炎症过程的数学模型

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-01-31 DOI: 10.1051/mmnp/2022004

G. Abi Younes, N. El Khatib

{"title":"Mathematical Modeling of Inflammatory Processes of Atherosclerosis","authors":"G. Abi Younes, N. El Khatib","doi":"10.1051/mmnp/2022004","DOIUrl":"https://doi.org/10.1051/mmnp/2022004","url":null,"abstract":"In this paper we study the early stages of atherosclerosis via a mathematical model of partial differential equations of reaction-diffusion type. The model includes several key species and identifies endothelial hyperpermeability, believed to be a precursor on the onset of atherosclerosis. We reduce the system to a monotone system and provide a biological interpretation for the stability analysis according to endothelial functionality. We investigate as well the existence of solutions of traveling waves type along with numerical simulations. The obtained results are in good agreement with current biological knowledge. Likewise, they confirm and generalize results of mathematical models previously performed in literature. Then, we study the non monotone reduced model and prove the existence of perturbed solutions and perturbed waves, particularly in the bistable case. Finally, we consider the complete model proposed initially, perform numerical simulations and provide more specific results. We study the consistency between the reduced and complete models for a certain range of parameters. We elaborate bifurcation diagrams showing the evolution of inflammation upon endothelial permeability and LDL accumulation. We show that the regulation of atherosclerosis progression is mediated by anti-inflammatory responses that, up to certain extent, lead to plaque regression.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41706537","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: 9

A fractional diffusion model of CD8+T cells response to parasitic infection in the brain CD8+T细胞对脑内寄生虫感染反应的分数扩散模型

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-01-24 DOI: 10.1051/mmnp/2022003

A. Farhadi, E. Hanert

{"title":"A fractional diffusion model of CD8+T cells response to parasitic infection in the brain","authors":"A. Farhadi, E. Hanert","doi":"10.1051/mmnp/2022003","DOIUrl":"https://doi.org/10.1051/mmnp/2022003","url":null,"abstract":"Toxoplasma gondii (T. gondii) is a parasitic pathogen that causes serious brain diseases in fetuses and patients with immunodeficiency, particularly AIDS patients. In the field of immunology, a large number of studies have shown that effector CD8 + T cells respond to T. gondii infection in the brain tissue through controlling the proliferation of intracellular parasites and killing infected brain cells. These protective mechanisms do not occur without T cell movement and searching for infected cells, as a fundamental feature of the immune system. Following infection with a pathogen in a tissue, in their search for infected cells, CD8 + T cells can perform different stochastic searches, including Levy and Brownian random walks. Statistical analysis of CD8 + T cells in response to infected brain cells could be described by a Levy random walk., In this work, by considering a Levy distribution for the displacements, we propose a space fractional-order diffusion equation for the T cell density in the infected brain tissue. Furthermore, we derive a mathematical model representing CD8 + T cell response to infected brain cells. By solving the model equations numerically, we perform a comparison between Levy and Brownian search strategies.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47795529","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 of a stochastic population model with Allee effect and jumps 具有Allee效应和跳跃的随机种群模型动力学

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-01-13 DOI: 10.1051/mmnp/2022002

Rong Liu, Guirong Liu

引用次数: 0

Quantifying the effects of non-pharmaceutical and pharmaceutical interventions against COVID-19 epidemic in the Republic of Korea: Mathematical model-based approach considering age groups and the Delta variant 量化大韩民国非药物和药物干预措施对COVID-19流行病的影响:考虑年龄组和Delta变体的基于数学模型的方法

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2021-11-01 DOI: 10.1101/2021.11.01.21265729

Y. Ko, V. M. Mendoza, Y. Seo, J. Lee, Y. Kim, D. Kwon, E. Jung

{"title":"Quantifying the effects of non-pharmaceutical and pharmaceutical interventions against COVID-19 epidemic in the Republic of Korea: Mathematical model-based approach considering age groups and the Delta variant","authors":"Y. Ko, V. M. Mendoza, Y. Seo, J. Lee, Y. Kim, D. Kwon, E. Jung","doi":"10.1101/2021.11.01.21265729","DOIUrl":"https://doi.org/10.1101/2021.11.01.21265729","url":null,"abstract":"Background: Early vaccination efforts and non-pharmaceutical interventions were insufficient to prevent a surge of coronavirus disease 2019 (COVID-19) cases triggered by the Delta variant. This study aims to understand how vaccination and variants contribute to the spread of COVID-19 so that appropriate measures are implemented. Methods: A compartment model that includes age, vaccination, and infection with the Delta or non-Delta variants was developed. We estimated the transmission rates using maximum likelihood estimation and phase-dependent reduction effect of non-pharmaceutical interventions (NPIs) according to government policies from 26 February to 8 October 2021. We extended our model simulation until 31 December considering the initiation of eased NPIs. Furthermore, we also performed simulations to examine the effect of NPIs, arrival timing of Delta variant, and speed of vaccine administration. Results: The estimated transmission rate matrices show distinct pattern, with the transmission rates of younger age groups (0~39 years) much larger than non-Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.64 to 0.69 and 0.70 to 0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below the capacity of Korean healthcare system. Simulation results also showed that a surge prompted by the spread of the Delta variant can be prevented if the number of people vaccinated daily was larger. Conclusions: Simulations showed that the timing of easing and intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62335697","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: 5

Exact insurance premiums for cyber risk of small and medium-sized enterprises 准确的中小企业网络风险保费

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2021-10-17 DOI: 10.1051/mmnp/2022041

Stefano Chiaradonna, N. Lanchier

{"title":"Exact insurance premiums for cyber risk of small and medium-sized enterprises","authors":"Stefano Chiaradonna, N. Lanchier","doi":"10.1051/mmnp/2022041","DOIUrl":"https://doi.org/10.1051/mmnp/2022041","url":null,"abstract":"As cyber attacks have become more frequent, cyber insurance premiums have increased, resulting in the need for better modeling of cyber risk. Jevtic and Lanchier[20] proposed a dynamic structural model of aggregate loss distribution for cyber risk of small-and-medium-sized enterprises under the assumption of a tree-based local-area-network topology that consists of the combination of a Poisson process, homogeneous random trees, bond percolation processes, and cost topology. Their model assumes that the contagion spreads through the edges of the network with the same fixed probability in both directions, thus overlooking a dynamic cyber security environment implemented in most networks, and their results give an exact expression for the mean of the aggregate loss but only a rough upper bound for the variance. In this paper, we consider a bidirectional version of their percolation model in which the contagion spreads through the edges of the network with a certain probability moving toward the lower level assets of the network but with another probability moving toward the higher level assets of the network. Also, our different mathematical approach leads to exact expressions for both the mean and the variance of the aggregate loss, and therefore an exact expression for the insurance premiums.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44046379","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: 2

A mathematical justification for metronomic chemotherapy in oncology 肿瘤节律化疗的数学依据

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2021-10-14 DOI: 10.21203/rs.3.rs-1113138/v1

L. Fern'andez, C. Pola, Judith Sáinz-Pardo:

引用次数: 1

Mathematical analysis of an age structured epidemic model with a quarantine class 具有隔离类的年龄结构流行病模型的数学分析

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2021-10-07 DOI: 10.1051/mmnp/2021049

B. Ainseba, T. Touaoula, Z. Sari

{"title":"Mathematical analysis of an age structured epidemic model with a quarantine class","authors":"B. Ainseba, T. Touaoula, Z. Sari","doi":"10.1051/mmnp/2021049","DOIUrl":"https://doi.org/10.1051/mmnp/2021049","url":null,"abstract":"In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave their class of quarantine before being completely recovered and thus will participate again to the transmission of the disease. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give the explicit expression of the epidemic reproduction number $R_{0}.$ This number is a combination of the classical epidemic reproduction number for the SIQR model and a new epidemic reproduction number corresponding to the individuals infected by a relapsed person from the R-class. It is shown that, if $R_{0}leq 1$, the disease free equilibrium is globally asymptotically stable and becomes unstable for $R_{0}>1$. Secondly, while $R_{0}>1$, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset $Omega_{0}.$","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49326548","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

Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source logistic源双曲型非菲克扩散平流模型小振幅周期波的谱不稳定性

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2021-10-07 DOI: 10.1051/mmnp/2022020

E. Alvarez, Ricardo Murillo, R. Plaza

引用次数: 3