We focus on the stability analysis of two types of discrete dynamic models: a discrete dynamic equation and a discrete dynamics system consisting of two equations with mutualistic interaction given by xn+1=a+bxnλ−(xn−1+x
我们将重点分析两类离散动力学模型的稳定性：离散动力学方程和由两个互为作用方程组成的离散动力学系统，这两个方程的给定公式分别为 x n + 1 = a + b x n λ - ( x n - 1 + x n - k ) c + x n - 1 + x n - k {x}_{n+1}=a+frac{b{x}_{n}{lambda }^{-left({x}_{n-1}+{x}_{n-k})}}{c+{x}_{n-1}+{x}_{n-k}} 和 x n + 1 = a 1 + b 1 y n
{"title":"Behavior of solutions of a discrete population model with mutualistic interaction","authors":"Sibi C. Babu, D. S. Dilip, Smitha Mary Mathew","doi":"10.1515/cmb-2023-0121","DOIUrl":"https://doi.org/10.1515/cmb-2023-0121","url":null,"abstract":"\u0000 <jats:p>We focus on the stability analysis of two types of discrete dynamic models: a discrete dynamic equation and a discrete dynamics system consisting of two equations with mutualistic interaction given by <jats:disp-formula id=\"j_cmb-2023-0121_eq_001\">\u0000 <jats:alternatives>\u0000 <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmb-2023-0121_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>x</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>n</m:mi>\u0000 <m:mo>+</m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 </m:msub>\u0000 <m:mo>=</m:mo>\u0000 <m:mi>a</m:mi>\u0000 <m:mo>+</m:mo>\u0000 <m:mfrac>\u0000 <m:mrow>\u0000 <m:mi>b</m:mi>\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>x</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>n</m:mi>\u0000 </m:mrow>\u0000 </m:msub>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>λ</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mo>−</m:mo>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>x</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>n</m:mi>\u0000 <m:mo>−</m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 </m:msub>\u0000 <m:mo>+</m:mo>\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>x</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 ","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"31 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525867","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}
A. Manickam, A. Jaison, D. Lakshmi, Ram Singh, C. T. D. Pravina
In this research, we have introduced compartments for asymptomatic and symptomatic individuals, along with reduced susceptibility, as key factors defining our investigation. The study is carried out in diverse scenarios, considering them as crucial for the essential generation number of the model, set at 3.18( r 0 > 1 {r}_{0}gt 1 ). The persistent reproduction differential method was used to explore the impact of continuous adrenocorticotropic hormone (ACTH) administration on the global gene expression in primary cultures of both fetal and adult adrenal cells. The study also investigates ACTH’s genetic effects on both adult and fetal human adrenal cells. The conclusion of this study is demonstrated through relevant and correct medical applications.
{"title":"A mathematical study of the adrenocorticotropic hormone as a regulator of human gene expression in adrenal glands","authors":"A. Manickam, A. Jaison, D. Lakshmi, Ram Singh, C. T. D. Pravina","doi":"10.1515/cmb-2023-0122","DOIUrl":"https://doi.org/10.1515/cmb-2023-0122","url":null,"abstract":"\u0000 In this research, we have introduced compartments for asymptomatic and symptomatic individuals, along with reduced susceptibility, as key factors defining our investigation. The study is carried out in diverse scenarios, considering them as crucial for the essential generation number of the model, set at 3.18(\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 r\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 >\u0000 1\u0000 \u0000 {r}_{0}gt 1\u0000 \u0000 ). The persistent reproduction differential method was used to explore the impact of continuous adrenocorticotropic hormone (ACTH) administration on the global gene expression in primary cultures of both fetal and adult adrenal cells. The study also investigates ACTH’s genetic effects on both adult and fetal human adrenal cells. The conclusion of this study is demonstrated through relevant and correct medical applications.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"24 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140524391","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}
In this article, we present a susceptible, exposed, infected, hospitalized and recovered compartmental model for COVID-19 with vaccination strategies and mask efficiency. Initially, we established the positivity and boundedness of the solutions to ensure realistic predictions. To assess the epidemiological relevance of the system, an examination is conducted to ascertain the local stability of the endemic equilibrium and the global stability across two equilibrium points are carried out. The global stability of the system is demonstrated using Lyapunov’s direct method. The disease-free equilibrium is globally asymptotically stable when the basic reproduction number (BRN) is less than one, whereas the endemic equilibrium is globally asymptotically stable when BRN is greater than one. A sensitivity analysis is performed to identify the influential factors in the BRN. The impact of various time-dependent strategies for managing and regulating the dynamic transmission of COVID-19 is investigated. In this study, Pontryagin’s maximum principle for optimal control analysis is used to identify the most effective strategy for controlling the disease, including single, coupled, and threefold interventions. Single-control interventions reveal physical distancing as the most effective strategy, coupled measures reduce exposed populations, and implementing all controls reduces susceptibility and infections.
{"title":"Optimal control and bifurcation analysis of SEIHR model for COVID-19 with vaccination strategies and mask efficiency","authors":"Poosan Moopanar Muthu, Anagandula Praveen Kumar","doi":"10.1515/cmb-2023-0113","DOIUrl":"https://doi.org/10.1515/cmb-2023-0113","url":null,"abstract":"\u0000 In this article, we present a susceptible, exposed, infected, hospitalized and recovered compartmental model for COVID-19 with vaccination strategies and mask efficiency. Initially, we established the positivity and boundedness of the solutions to ensure realistic predictions. To assess the epidemiological relevance of the system, an examination is conducted to ascertain the local stability of the endemic equilibrium and the global stability across two equilibrium points are carried out. The global stability of the system is demonstrated using Lyapunov’s direct method. The disease-free equilibrium is globally asymptotically stable when the basic reproduction number (BRN) is less than one, whereas the endemic equilibrium is globally asymptotically stable when BRN is greater than one. A sensitivity analysis is performed to identify the influential factors in the BRN. The impact of various time-dependent strategies for managing and regulating the dynamic transmission of COVID-19 is investigated. In this study, Pontryagin’s maximum principle for optimal control analysis is used to identify the most effective strategy for controlling the disease, including single, coupled, and threefold interventions. Single-control interventions reveal physical distancing as the most effective strategy, coupled measures reduce exposed populations, and implementing all controls reduces susceptibility and infections.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"108 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140515754","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}
This article addresses the pressing issue of pest outbreaks in India, which poses significant challenges for farmers and ecologists. A novel system is proposed for effective control that leverages natural enemies. Here, the pests are classified into juveniles and mature individuals, further categorized as susceptible or infected. The study introduces harvesting, incorporating external efforts and natural phenomena, in a pest-epidemic prey–predator system featuring a prey-stage structure. The model reveals three equilibria: trivial, boundary (indicating the absence of natural enemies), and interior equilibria. Notably, the trivial equilibrium is consistently unstable. As demonstrated by stability analysis, the survival or extinction of natural enemies hinges on control variables, including the harvesting rate, disease transmission rate, and natural death rate. Local stability is assessed using the Routh–Hurwitz criterion, while global stability is explored through the Lyapunov method. Furthermore, optimal control theory and Pontryagin’s maximum principle are applied for model optimization, unveiling crucial optimality conditions and determining the optimal harvesting rate for susceptible mature prey. Numerical computations validate theoretical insights, offering valuable guidance for formulating policies that optimize the control of susceptible adult pests within a disease-induced pest-natural enemy system, ensuring sustained cost-effectiveness.
{"title":"Optimal control of susceptible mature pest concerning disease-induced pest-natural enemy system with cost-effectiveness","authors":"Kunwer Singh Mathur, Bhagwan Kumar","doi":"10.1515/cmb-2023-0120","DOIUrl":"https://doi.org/10.1515/cmb-2023-0120","url":null,"abstract":"\u0000 This article addresses the pressing issue of pest outbreaks in India, which poses significant challenges for farmers and ecologists. A novel system is proposed for effective control that leverages natural enemies. Here, the pests are classified into juveniles and mature individuals, further categorized as susceptible or infected. The study introduces harvesting, incorporating external efforts and natural phenomena, in a pest-epidemic prey–predator system featuring a prey-stage structure. The model reveals three equilibria: trivial, boundary (indicating the absence of natural enemies), and interior equilibria. Notably, the trivial equilibrium is consistently unstable. As demonstrated by stability analysis, the survival or extinction of natural enemies hinges on control variables, including the harvesting rate, disease transmission rate, and natural death rate. Local stability is assessed using the Routh–Hurwitz criterion, while global stability is explored through the Lyapunov method. Furthermore, optimal control theory and Pontryagin’s maximum principle are applied for model optimization, unveiling crucial optimality conditions and determining the optimal harvesting rate for susceptible mature prey. Numerical computations validate theoretical insights, offering valuable guidance for formulating policies that optimize the control of susceptible adult pests within a disease-induced pest-natural enemy system, ensuring sustained cost-effectiveness.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"24 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140521828","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}
This work builds machine learning models for the dataset generated using a numerical model developed on an idealized human artery. The model has been constructed accounting for varying blood characteristics as it flows through arteries with variable vascular properties, and it is applied to simulate blood flow in the femoral and its continued artery. For this purpose, we designed a pipeline model consisting of three components to include the major segments of the femoral artery: CFA, the common femoral artery and SFA, the superficial artery, and its continued one, the popliteal artery (PA). A notable point of this study is that the features and target variables of the former component pipe form the set of features of the latter, thus resulting in multicollinearity among the features in the third component pipe. Thus, we worked on understanding the effect of these correlated features on the target variables using regularized linear regression models, ensemble, and boosting algorithms. This study highlighted the blood velocity in CFA as the primary influential factor for wall shear stress in both CFA and SFA. Additionally, it established the blood rheology in PA as a significant factor for the same in it. Nevertheless, because the study relies on idealized conditions, these discoveries necessitate thorough clinical validation.
这项研究利用在理想化人体动脉上开发的数值模型，为生成的数据集建立机器学习模型。该模型的构建考虑到了血液在流经具有不同血管特性的动脉时的不同特性，并将其用于模拟股动脉及其连续动脉的血流。为此，我们设计了一个由三个部分组成的管道模型，包括股动脉的主要部分：股总动脉（CFA）、浅动脉（SFA）及其延续动脉腘动脉（PA）。本研究的一个显著特点是，前一个组成管道的特征和目标变量构成了后一个组成管道的特征集，从而导致第三个组成管道的特征之间存在多重共线性。因此，我们使用正则化线性回归模型、集合和提升算法来了解这些相关特征对目标变量的影响。这项研究强调了 CFA 中的血流速度是 CFA 和 SFA 中壁剪应力的主要影响因素。此外，它还确定了 PA 中的血液流变学是影响其相同情况的重要因素。然而，由于该研究依赖于理想化的条件，因此这些发现还需要全面的临床验证。
{"title":"On building machine learning models for medical dataset with correlated features","authors":"Debismita Nayak, Sai Lakshmi Radhika Tantravahi","doi":"10.1515/cmb-2023-0124","DOIUrl":"https://doi.org/10.1515/cmb-2023-0124","url":null,"abstract":"\u0000 This work builds machine learning models for the dataset generated using a numerical model developed on an idealized human artery. The model has been constructed accounting for varying blood characteristics as it flows through arteries with variable vascular properties, and it is applied to simulate blood flow in the femoral and its continued artery. For this purpose, we designed a pipeline model consisting of three components to include the major segments of the femoral artery: CFA, the common femoral artery and SFA, the superficial artery, and its continued one, the popliteal artery (PA). A notable point of this study is that the features and target variables of the former component pipe form the set of features of the latter, thus resulting in multicollinearity among the features in the third component pipe. Thus, we worked on understanding the effect of these correlated features on the target variables using regularized linear regression models, ensemble, and boosting algorithms. This study highlighted the blood velocity in CFA as the primary influential factor for wall shear stress in both CFA and SFA. Additionally, it established the blood rheology in PA as a significant factor for the same in it. Nevertheless, because the study relies on idealized conditions, these discoveries necessitate thorough clinical validation.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140521952","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}
As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.
{"title":"Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach","authors":"Manisha, Nidhi, Anuj Kumar","doi":"10.1515/cmb-2023-0123","DOIUrl":"https://doi.org/10.1515/cmb-2023-0123","url":null,"abstract":"\u0000 As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"26 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140519124","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}
Ambalarajan Venkatesh, M. A. Rao, Murugadoss Prakash Raj, Karuppusamy Arun Kumar, D. Vamsi
In this study, we formulate an eight-compartment mathematical model with vaccination as one of the compartments to analyze the dynamics of COVID-19 transmission. We examine the model’s qualitative properties, such as positivity and boundedness of solutions, and stability analysis of the illness-free equilibrium with respect to the basic reproduction number. We estimate ten significant parameters and also compute the magnitude of the basic reproduction number for India by fitting the proposed model to daily confirmed and cumulative confirmed COVID-19 cases in India. Sensitivity analysis with respect to basic reproduction number is conducted, and the main parameters that impact the widespread of disease are determined. We further extend this model to an optimal control problem by including four non-pharmaceutical and pharmaceutical intervention measures as control functions. Our numerical results show that the four control strategy has greater impact than the three control strategies, two control strategies, and single control strategies on reducing the dynamics of COVID-19 transmission.
{"title":"Mathematical modelling of COVID-19 dynamics using SVEAIQHR model","authors":"Ambalarajan Venkatesh, M. A. Rao, Murugadoss Prakash Raj, Karuppusamy Arun Kumar, D. Vamsi","doi":"10.1515/cmb-2023-0112","DOIUrl":"https://doi.org/10.1515/cmb-2023-0112","url":null,"abstract":"\u0000 In this study, we formulate an eight-compartment mathematical model with vaccination as one of the compartments to analyze the dynamics of COVID-19 transmission. We examine the model’s qualitative properties, such as positivity and boundedness of solutions, and stability analysis of the illness-free equilibrium with respect to the basic reproduction number. We estimate ten significant parameters and also compute the magnitude of the basic reproduction number for India by fitting the proposed model to daily confirmed and cumulative confirmed COVID-19 cases in India. Sensitivity analysis with respect to basic reproduction number is conducted, and the main parameters that impact the widespread of disease are determined. We further extend this model to an optimal control problem by including four non-pharmaceutical and pharmaceutical intervention measures as control functions. Our numerical results show that the four control strategy has greater impact than the three control strategies, two control strategies, and single control strategies on reducing the dynamics of COVID-19 transmission.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"30 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140526006","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}
Sandhya Rani Verma, V. Verma, Rachana Pathak, M. Agarwal, Ram Naresh
The outbreak of coronavirus disease 2019 (COVID-19) has been declared a pandemic by the world health organization on March 11, 2020,. Here, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease in a human habitat. In modeling the dynamics, the total population is divided into five subclasses: susceptible population, asymptomatic infective population, symptomatic infective population, recovered population, and vaccinated population. It is assumed that the disease is transmitted directly from infectives. It is further assumed that due to the effect of media, susceptible individuals become aware about the disease and avoid contact with the infectives. The analysis of the model is performed using the stability theory of differential equations. Furthermore, conditions that influence the persistence of the system are obtained. We have also conducted numerical simulations to validate the analytical results. The model analysis shows that with an increase in media awareness, the spread of coronavirus disease decreases with a decrease in the number of infective populations.
{"title":"Influence of media campaigns efforts to control spread of COVID-19 pandemic with vaccination: A modeling study","authors":"Sandhya Rani Verma, V. Verma, Rachana Pathak, M. Agarwal, Ram Naresh","doi":"10.1515/cmb-2023-0107","DOIUrl":"https://doi.org/10.1515/cmb-2023-0107","url":null,"abstract":"\u0000 The outbreak of coronavirus disease 2019 (COVID-19) has been declared a pandemic by the world health organization on March 11, 2020,. Here, a nonlinear mathematical model is proposed and analyzed to study the spread of coronavirus disease in a human habitat. In modeling the dynamics, the total population is divided into five subclasses: susceptible population, asymptomatic infective population, symptomatic infective population, recovered population, and vaccinated population. It is assumed that the disease is transmitted directly from infectives. It is further assumed that due to the effect of media, susceptible individuals become aware about the disease and avoid contact with the infectives. The analysis of the model is performed using the stability theory of differential equations. Furthermore, conditions that influence the persistence of the system are obtained. We have also conducted numerical simulations to validate the analytical results. The model analysis shows that with an increase in media awareness, the spread of coronavirus disease decreases with a decrease in the number of infective populations.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525962","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}
In this study, we present a variational multiscale stabilized finite element method for steady-state incompressible fluid flow under magnetic forces. In particular, an algebraic approach of approximating the subscales has been considered, and then, the stabilization parameters are derived using Fourier analysis. The proposed scheme is used to trace the blood flow dynamics in complex arterial vessels under multiple pathological conditions. We examine the pressure and stress distribution in addition to the flow pattern to assess the criticality of the diseased condition.
{"title":"Variational multiscale stabilized FEM for cardiovascular flows in complex arterial vessels under magnetic forces","authors":"D. Sahoo, Anil Rathi, B. V. R. Kumar","doi":"10.1515/cmb-2023-0118","DOIUrl":"https://doi.org/10.1515/cmb-2023-0118","url":null,"abstract":"\u0000 In this study, we present a variational multiscale stabilized finite element method for steady-state incompressible fluid flow under magnetic forces. In particular, an algebraic approach of approximating the subscales has been considered, and then, the stabilization parameters are derived using Fourier analysis. The proposed scheme is used to trace the blood flow dynamics in complex arterial vessels under multiple pathological conditions. We examine the pressure and stress distribution in addition to the flow pattern to assess the criticality of the diseased condition.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"24 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140526554","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}
Abstract This study discusses an SIR epidemic model with modified saturated incidence rates and Holling functional type-II therapy. In this study, we take the new alert compartment (A) in the SIR compartment model. Consider the modified non-linear incidence rate from the susceptible to the infected class and the second non-linear incidence rate from the alert to the infected class. Further, we investigate the elementary reproduction number, the equilibrium points of the model, and their stability. We apply manifold theory to discuss bifurcations of the disease-free equilibrium point. This study shows that the infected population decreases with the Holling functional type II treatment rate. It also shows that the number of infected people decreases when the psychological rate increases and the contact rate decreases.
{"title":"Stability analysis of an SIR model with alert class modified saturated incidence rate and Holling functional type-II treatment","authors":"Shivram Sharma, P. Sharma","doi":"10.1515/cmb-2022-0145","DOIUrl":"https://doi.org/10.1515/cmb-2022-0145","url":null,"abstract":"Abstract This study discusses an SIR epidemic model with modified saturated incidence rates and Holling functional type-II therapy. In this study, we take the new alert compartment (A) in the SIR compartment model. Consider the modified non-linear incidence rate from the susceptible to the infected class and the second non-linear incidence rate from the alert to the infected class. Further, we investigate the elementary reproduction number, the equilibrium points of the model, and their stability. We apply manifold theory to discuss bifurcations of the disease-free equilibrium point. This study shows that the infected population decreases with the Holling functional type II treatment rate. It also shows that the number of infected people decreases when the psychological rate increases and the contact rate decreases.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47588824","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}
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