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“PEOPLE” MEET “MARKOVIANS” — INDIVIDUAL-BASED MODELING WITH HYBRID STOCHASTIC SYSTEMS "人 "与 "马尔可夫人"--基于个体的混合随机系统建模
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-04-18 DOI: 10.1142/s0218339023400028
Molly Hawker, Ivo Siekmann
{"title":"“PEOPLE” MEET “MARKOVIANS” — INDIVIDUAL-BASED MODELING WITH HYBRID STOCHASTIC SYSTEMS","authors":"Molly Hawker, Ivo Siekmann","doi":"10.1142/s0218339023400028","DOIUrl":"https://doi.org/10.1142/s0218339023400028","url":null,"abstract":"Individual-based models (IBMs) enable modelers to avoid far-reaching abstractions and strong simplifications by allowing for a state-based representation of individuals. The fact that IBMs are not represented using a standardized mathematical framework such as differential equations makes it harder to reproduce IBMs and introduces difficulties in the analysis of IBMs. We propose a model architecture based on representing individuals via Markov models. Individuals are coupled to populations — for which individuals are not explicitly represented — that are modeled by differential equations. The resulting models consisting of continuous-time finite-state Markov models coupled to systems of differential equations are examples of piecewise-deterministic Markov processes (PDMPs). We will demonstrate that PDMPs, also known as hybrid stochastic systems, allow us to design detailed state-based representations of individuals which, at the same time, can be systematically analyzed by taking advantage of the theory of PDMPs. We will illustrate design and analysis of IBMs using PDMPs via the example of a predator that intermittently feeds on a logistically growing prey by stochastically switching between a resting and a feeding state. This simple model shows a surprisingly rich dynamics which, nevertheless, can be comprehensively analyzed using the theory of PDMPs.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140686482","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: 1
IMPULSIVE DIFFERENTIAL EQUATION MODEL IN HIV-1 INHIBITION: ADVANCES IN DUAL INHIBITORS OF HIV-1 RT AND IN FOR THE PREVENTION OF HIV-1 REPLICATION 抑制 HIV-1 的脉冲微分方程模型：HIV-1 RT 和 HIV-1 复制预防双重抑制剂的研究进展
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-27 DOI: 10.1142/s0218339024500141
SRIJITA MONDAL, JAMES F. PETERS, PRIYANKA GHOSH, ASHIS KUMAR SARKAR, SOURAV KUMAR SASMAL
{"title":"IMPULSIVE DIFFERENTIAL EQUATION MODEL IN HIV-1 INHIBITION: ADVANCES IN DUAL INHIBITORS OF HIV-1 RT AND IN FOR THE PREVENTION OF HIV-1 REPLICATION","authors":"SRIJITA MONDAL, JAMES F. PETERS, PRIYANKA GHOSH, ASHIS KUMAR SARKAR, SOURAV KUMAR SASMAL","doi":"10.1142/s0218339024500141","DOIUrl":"https://doi.org/10.1142/s0218339024500141","url":null,"abstract":"<p>Reverse transcriptase (RT) and integrase (IN) are two pivotal enzymes in HIV-1 replication. RT converts the single-stranded viral RNA genome into double-stranded DNA and IN catalyzes the integration of viral double-stranded DNA into host DNA. Currently, dual inhibitors of HIV-1 RT and IN have become a hotspot in new anti-HIV drug research and development. A dual inhibitor of HIV-1 RT/IN does the same thing as the two independent drugs would do. In this paper, we develop a mathematical model comprising a system of nonlinear differential equations describing HIV-1 RT/IN catalyzed biochemical reactions based on Michaelis–Menten enzyme kinetic reaction. In the formulated model we incorporate HIV-1 RT/IN dual inhibitor which simultaneously works as a non-nucleoside RT inhibitor and IN inhibitor. To examine the efficacy of HIV-1 RT/IN dual inhibitor in the treatment of HIV-1 infection, we have introduced a one-dimensional impulsive differential equation model and determined an effective dosing regimen for applying the inhibitor numerically. Furthermore, the exact closed form solution of the impulsive differential equation model is carried out by using the Lambert W function and the local stability of the periodic solution is also obtained analytically. The results obtained from analytical as well as numerical studies provide a basic idea to investigate the minimum dose with the highest efficacy for administering HIV-1 RT/IN dual inhibitors to prevent HIV-1 infection.</p>","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315533","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 AND BLOW-UP CONTROL OF A LESLIE–GOWER PREDATOR–PREY MODEL WITH GROUP DEFENCE IN PREY 带有猎物群防的leslie-gower捕食者-猎物模型的动力学和爆炸控制
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-27 DOI: 10.1142/s0218339024500165
RAJESH RANJAN PATRA, SARIT MAITRA, SOUMEN KUNDU
{"title":"DYNAMICS AND BLOW-UP CONTROL OF A LESLIE–GOWER PREDATOR–PREY MODEL WITH GROUP DEFENCE IN PREY","authors":"RAJESH RANJAN PATRA, SARIT MAITRA, SOUMEN KUNDU","doi":"10.1142/s0218339024500165","DOIUrl":"https://doi.org/10.1142/s0218339024500165","url":null,"abstract":"<p>In this paper, we designed a population model that shows how a prey species defends itself against a generalist predator by exhibiting group defence. A non-monotonic functional response is used to represent the group defence functionality. We have demonstrated the model’s local stability in the vicinity of the coexisting equilibrium solution employing a local Lyapunov function. Condition for existence of Hopf bifurcation is obtained along with its normal form. The suggested model has been validated by numerical simulations, which have also been used to verify the acquired analytical results. The parameters are subjected to sensitivity analysis by utilizing partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS). The <i>Z</i>-type dynamic method is used to prevent population blow-up.</p>","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316745","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 Delayed Autonomous Model with Carry-Over Effects, Including Prey Harvesting 包括猎物捕获在内的具有延续效应的延迟自主模型的动力学特性
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500268
Mahendra, Dwijendra N. Pandey
{"title":"Dynamics of Delayed Autonomous Model with Carry-Over Effects, Including Prey Harvesting","authors":"Mahendra, Dwijendra N. Pandey","doi":"10.1142/s0218339024500268","DOIUrl":"https://doi.org/10.1142/s0218339024500268","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242092","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
Exploring the Impact of PTH Therapy on Bone Remodeling: A Mathematical Investigation 探索 PTH 疗法对骨重塑的影响：数学研究
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s021833902450027x
Amrutha Sreekumar, Koyel Chakravarty
{"title":"Exploring the Impact of PTH Therapy on Bone Remodeling: A Mathematical Investigation","authors":"Amrutha Sreekumar, Koyel Chakravarty","doi":"10.1142/s021833902450027x","DOIUrl":"https://doi.org/10.1142/s021833902450027x","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242791","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
Effect of Delay in a Musca Domestica Houseflies Model: Stability and Global Hopf Bifurcation 家蝇模型中延迟的影响：稳定性和全局霍普夫分岔
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500281
Xin Zhang, Renxiang Shi
{"title":"Effect of Delay in a Musca Domestica Houseflies Model: Stability and Global Hopf Bifurcation","authors":"Xin Zhang, Renxiang Shi","doi":"10.1142/s0218339024500281","DOIUrl":"https://doi.org/10.1142/s0218339024500281","url":null,"abstract":". The houseflies model with discrete delay is studied in both theoretical and numerical ways. The solution of the delayed system is positive and bounded. Choosing the delay as the bifurcation parameter, stability analysis for the positive equilibrium of the delayed model, local and global Hopf bifurcation are given in theoretical aspect. Dynamical behaviors such as supercritical Hopf bifurcation is detected by computer simulations. The theoretical analysis and numerical observations in this work are interesting in biomathematics research area.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243238","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
Transmission Dynamics of COVID-19 with Diabetes in India: A Cost-Effective and Optimal Control Analysis COVID-19 糖尿病在印度的传播动态：成本效益和最佳控制分析
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500232
Jai Prakash Tripathi, Nitesh Kumawat, Komal Tanwar, Dhanumjaya Palla, M. Martcheva
{"title":"Transmission Dynamics of COVID-19 with Diabetes in India: A Cost-Effective and Optimal Control Analysis","authors":"Jai Prakash Tripathi, Nitesh Kumawat, Komal Tanwar, Dhanumjaya Palla, M. Martcheva","doi":"10.1142/s0218339024500232","DOIUrl":"https://doi.org/10.1142/s0218339024500232","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243815","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
Asymptotic stability for a free boundary model of an atherosclerotic plaque formation in the presence of reverse cholesterol transport with Holling type III functional response 具有霍林 III 型功能响应的胆固醇反向运输作用下动脉粥样硬化斑块形成的自由边界模型的渐近稳定性
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500244
Wenjun Liu, Li Zhang, Yanning An
{"title":"Asymptotic stability for a free boundary model of an atherosclerotic plaque formation in the presence of reverse cholesterol transport with Holling type III functional response","authors":"Wenjun Liu, Li Zhang, Yanning An","doi":"10.1142/s0218339024500244","DOIUrl":"https://doi.org/10.1142/s0218339024500244","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140241702","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 Leptospirosis in Human and Rodent Populations: A Multiscale Modelling Approach 人类和啮齿动物种群中的钩端螺旋体病动态：多尺度建模方法
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500220
M. O. Adewole, Farah A. Abdullah, Majid K. M. Ali
{"title":"Dynamics of Leptospirosis in Human and Rodent Populations: A Multiscale Modelling Approach","authors":"M. O. Adewole, Farah A. Abdullah, Majid K. M. Ali","doi":"10.1142/s0218339024500220","DOIUrl":"https://doi.org/10.1142/s0218339024500220","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243912","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
Exploring Fractional Dynamical Probes in the Context of Gender-Structured HIV-TB Coinfection: A Study of Control Strategies 在性别结构的艾滋病-结核病双重感染背景下探索分数动态探针：控制策略研究
IF 1.6 4区 数学
Journal of Biological Systems Pub Date : 2024-03-14 DOI: 10.1142/s0218339024500256
A. Saranya Devi, K. Pal, Pankaj Kumar Tiwari
{"title":"Exploring Fractional Dynamical Probes in the Context of Gender-Structured HIV-TB Coinfection: A Study of Control Strategies","authors":"A. Saranya Devi, K. Pal, Pankaj Kumar Tiwari","doi":"10.1142/s0218339024500256","DOIUrl":"https://doi.org/10.1142/s0218339024500256","url":null,"abstract":"","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242822","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
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