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Dynamical analysis of a modified Leslie-Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input. 具有种间竞争和脉冲毒物输入的污染环境中改进的Leslie-Gower holling型II型捕食者-猎物随机模型的动力学分析
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 DOI: 10.1080/17513758.2022.2155717
Yongxin Gao, Shuyuan Yao
{"title":"Dynamical analysis of a modified Leslie-Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input.","authors":"Yongxin Gao,&nbsp;Shuyuan Yao","doi":"10.1080/17513758.2022.2155717","DOIUrl":"https://doi.org/10.1080/17513758.2022.2155717","url":null,"abstract":"<p><p>In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying <math><mi>It</mi><msup><mrow><mrow><mover><mi>o</mi><mo>^</mo></mover></mrow></mrow><mo>'</mo></msup><mi>s</mi></math> formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10838564","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
Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay. 具有Holling II感染率和免疫延迟的HIV-1模型的稳定性和Hopf分岔
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 Epub Date: 2021-03-08 DOI: 10.1080/17513758.2021.1895334
Maoxin Liao, Yanjin Liu, Shinan Liu, Ali M Meyad
{"title":"Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay.","authors":"Maoxin Liao,&nbsp;Yanjin Liu,&nbsp;Shinan Liu,&nbsp;Ali M Meyad","doi":"10.1080/17513758.2021.1895334","DOIUrl":"https://doi.org/10.1080/17513758.2021.1895334","url":null,"abstract":"<p><p>This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov-LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2021.1895334","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25447433","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: 3
Dynamics of a glucose-insulin model. 葡萄糖-胰岛素模型的动力学。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 DOI: 10.1080/17513758.2022.2146769
Mingju Ma, Jun Li
{"title":"Dynamics of a glucose-insulin model.","authors":"Mingju Ma,&nbsp;Jun Li","doi":"10.1080/17513758.2022.2146769","DOIUrl":"https://doi.org/10.1080/17513758.2022.2146769","url":null,"abstract":"<p><p>Diabetes mellitus is a noncommunicable disease, which is a serious threat to human health around the world. In this paper, we propose a simple glucose-insulin model with Michaelis-Menten function as insulin degradation rate to mimic the pathogenic mechanism of diabetes. By theoretical analysis, a unique positive equilibrium of model exists and it is globally asymptotically stable. The four strategies are designed for diabetes patients based on the sensitivity of parameters, including insulin injection and medicine treatments. Numerical simulations are given to support the theoretical results.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40469574","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 multi-strain malaria model with diffusion in a periodic environment. 周期环境下具有扩散的多株疟疾模型动力学。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 DOI: 10.1080/17513758.2022.2144648
Yangyang Shi, Hongyong Zhao, Xuebing Zhang
{"title":"Dynamics of a multi-strain malaria model with diffusion in a periodic environment.","authors":"Yangyang Shi,&nbsp;Hongyong Zhao,&nbsp;Xuebing Zhang","doi":"10.1080/17513758.2022.2144648","DOIUrl":"https://doi.org/10.1080/17513758.2022.2144648","url":null,"abstract":"<p><p>This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers <math><msub><mi>R</mi><mrow><mi>i</mi></mrow></msub></math> and <math><msub><mrow><mover><mi>R</mi><mo>^</mo></mover></mrow><mrow><mi>i</mi></mrow></msub></math> (<i>i</i> = 1, 2). Quantitative analysis indicates that the disease-free <i>ω</i>-periodic solution is globally attractive when <math><msub><mi>R</mi><mrow><mi>i</mi></mrow></msub><mo><</mo><mn>1</mn></math>, while if <math><msub><mi>R</mi><mrow><mi>i</mi></mrow></msub><mo>></mo><mn>1</mn><mo>></mo><msub><mi>R</mi><mrow><mi>j</mi></mrow></msub></math> (<math><mi>i</mi><mo>≠</mo><mi>j</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math>), then strain <i>i</i> persists and strain <i>j</i> dies out. More interestingly, when <math><msub><mi>R</mi><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mi>R</mi><mrow><mn>2</mn></mrow></msub></math> are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are <math><msub><mrow><mover><mi>R</mi><mo>^</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>></mo><mn>1</mn></math> and <math><msub><mrow><mover><mi>R</mi><mo>^</mo></mover></mrow><mrow><mn>2</mn></mrow></msub><mo>></mo><mn>1</mn></math>. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40701777","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
The blood-stage dynamics of malaria infection with immune response. 疟疾感染与免疫反应的血期动力学。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 Epub Date: 2021-12-22 DOI: 10.1080/17513758.2021.2017033
Jian Liu, Zhiming Guo, Hongpeng Guo
{"title":"The blood-stage dynamics of malaria infection with immune response.","authors":"Jian Liu,&nbsp;Zhiming Guo,&nbsp;Hongpeng Guo","doi":"10.1080/17513758.2021.2017033","DOIUrl":"https://doi.org/10.1080/17513758.2021.2017033","url":null,"abstract":"<p><p>This article is concerned with the dynamics of malaria infection model with diffusion and delay. The disease free threshold <math><msub><mi>ℜ</mi><mn>0</mn></msub></math> and the immune response threshold value <math><msub><mi>ℜ</mi><mn>1</mn></msub></math> of the malaria infection are obtained, which characterize the stability of the disease free equilibrium and infection equilibrium (with or without immune response). In addition, fluctuations occur when the model undergoes Hopf bifurcation as the delay passes through a certain critical value <math><msub><mi>τ</mi><mn>0</mn></msub></math>. In this case, periodic oscillation appears near the positive steady state, which implies the recurrent attacks of disease. Finally, numerical simulations are provided to illustrate the theoretical results.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39748526","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 an SIRWS model with waning of immunity and varying immune boosting period. 免疫减弱和免疫增强期变化的SIRWS模型动力学。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 DOI: 10.1080/17513758.2022.2109766
Richmond Opoku-Sarkodie, Ferenc A Bartha, Mónika Polner, Gergely Röst
{"title":"Dynamics of an SIRWS model with waning of immunity and varying immune boosting period.","authors":"Richmond Opoku-Sarkodie,&nbsp;Ferenc A Bartha,&nbsp;Mónika Polner,&nbsp;Gergely Röst","doi":"10.1080/17513758.2022.2109766","DOIUrl":"https://doi.org/10.1080/17513758.2022.2109766","url":null,"abstract":"<p><p>SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a <i>W</i> compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from <i>R</i> to <i>W</i> and from <i>W</i> to <i>S</i>. This implicitly assumes equal length for the period of full immunity and of waned immunity. We relax this restriction, and allow an asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of bistability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40692633","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: 8
Dynamic analysis and optimal control of a class of SISP respiratory diseases. 一类SISP呼吸系统疾病的动态分析与最优控制。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-12-01 DOI: 10.1080/17513758.2022.2027529
Lei Shi, Longxing Qi
{"title":"Dynamic analysis and optimal control of a class of SISP respiratory diseases.","authors":"Lei Shi,&nbsp;Longxing Qi","doi":"10.1080/17513758.2022.2027529","DOIUrl":"https://doi.org/10.1080/17513758.2022.2027529","url":null,"abstract":"<p><p>In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> is taken into account. The concentration response function of PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission <math><msub><mi>P</mi><mrow><mn>0</mn></mrow></msub></math> of PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> and PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> pathogenic threshold <i>K</i>. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate <i>β</i> and the inhalation rate <i>η</i> has the largest positive correlation. The cure rate <i>γ</i> of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> by reducing the PM<math><msub><mi></mi><mrow><mn>2.5</mn></mrow></msub></math> emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39896570","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: 4
Dynamics analysis of stage-structured wild and sterile mosquito interaction impulsive model 阶段结构野生与不育蚊子相互作用脉冲模型动力学分析
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-06-02 DOI: 10.1080/17513758.2022.2079739
Yiyou Pang, Shuai Wang, Siyu Liu
{"title":"Dynamics analysis of stage-structured wild and sterile mosquito interaction impulsive model","authors":"Yiyou Pang, Shuai Wang, Siyu Liu","doi":"10.1080/17513758.2022.2079739","DOIUrl":"https://doi.org/10.1080/17513758.2022.2079739","url":null,"abstract":"In this paper, we study a stage-structured wild and sterile mosquito interaction impulsive model. The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically. The existence of trivial periodic solutions is obtained, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem, respectively. And we prove the existence conditions of non-trivial periodic solutions and their local stability. We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions. All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range and even make them extinct. Finally, numerical simulation verifies our theoretical results.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46992426","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: 4
Mathematical modelling of echinococcosis in human, dogs and sheep with intervention 人、狗和羊棘球蚴病干预的数学模型
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-05-30 DOI: 10.1080/17513758.2022.2081368
Birhan Getachew Bitew, J. Munganga, Adamu Shitu Hassan
{"title":"Mathematical modelling of echinococcosis in human, dogs and sheep with intervention","authors":"Birhan Getachew Bitew, J. Munganga, Adamu Shitu Hassan","doi":"10.1080/17513758.2022.2081368","DOIUrl":"https://doi.org/10.1080/17513758.2022.2081368","url":null,"abstract":"In this study, a model for the spread of cyst echinococcosis with interventions is formulated. The disease-free and endemic equilibrium points of the model are calculated. The control reproduction number for the model is derived, and the global dynamics are established by the values of . The disease-free equilibrium is globally asymptotically stable if and only if . For , using Volterra–Lyapunov stable matrices, it is proven that the endemic equilibrium is globally asymptotically stable. Sensitivity analysis to identify the most influential parameters in the dynamics of CE is carried out. To establish the long-term behaviour of the disease, numerical simulations are performed. The impact of control strategies is investigated. It is shown that, whenever vaccination of sheep is carried out solely or in combination with cleaning or disinfecting of the environment, cyst echinococcosis can be wiped out.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47234122","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
Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic 疫情早期严重急性呼吸系统综合征冠状病毒2型模型的参数可识别性和最优控制
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2022-05-30 DOI: 10.1080/17513758.2022.2078899
N. Tuncer, A. Timsina, M. Nuño, G. Chowell, M. Martcheva
{"title":"Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic","authors":"N. Tuncer, A. Timsina, M. Nuño, G. Chowell, M. Martcheva","doi":"10.1080/17513758.2022.2078899","DOIUrl":"https://doi.org/10.1080/17513758.2022.2078899","url":null,"abstract":"We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48722633","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: 16
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