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Stability analysis in a mosquito population suppression model. 蚊子种群抑制模型的稳定性分析。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1792565
Genghong Lin, Yuanxian Hui
{"title":"Stability analysis in a mosquito population suppression model.","authors":"Genghong Lin,&nbsp;Yuanxian Hui","doi":"10.1080/17513758.2020.1792565","DOIUrl":"https://doi.org/10.1080/17513758.2020.1792565","url":null,"abstract":"<p><p>In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"578-589"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1792565","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38157878","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: 13
Onchocerciasis dynamics: modelling the effects of treatment, education and vector control. 盘尾丝虫病动态:模拟治疗、教育和病媒控制的效果。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1745306
Asha Hassan, Nyimvua Shaban
{"title":"Onchocerciasis dynamics: modelling the effects of treatment, education and vector control.","authors":"Asha Hassan,&nbsp;Nyimvua Shaban","doi":"10.1080/17513758.2020.1745306","DOIUrl":"https://doi.org/10.1080/17513758.2020.1745306","url":null,"abstract":"<p><p>A deterministic model of onchocerciasis disease dynamics is considered in a community partitioned into compartments based on the disease status. Public health education is offered in the community during the implementation of mass treatment using ivermectin drugs. Also, larviciding and trapping strategies are implemented in the vector population with the aim of controlling population growth of black flies. We fit the model to the data to check the suitability of the model. Expressions are derived for the influence on the reproduction numbers of these strategies. Numerical results show that the dynamics of onchocerciasis and the growth of black flies are best controlled when the four strategies are implemented simultaneously. Also, the results suggest that for the elimination of the disease in the society there is a need for finding another drug which will be implemented to ineligible human as well as killing the adult worms instead of ivermectin.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"245-268"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1745306","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37814049","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
Mathematical model for diffusion of the rhizosphere microbial degradation with impulsive feedback control. 脉冲反馈控制下根际微生物降解扩散的数学模型。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1786860
Zhong Zhao, Ying Chen, Qiuying Li, Xianbin Wu
{"title":"Mathematical model for diffusion of the rhizosphere microbial degradation with impulsive feedback control.","authors":"Zhong Zhao,&nbsp;Ying Chen,&nbsp;Qiuying Li,&nbsp;Xianbin Wu","doi":"10.1080/17513758.2020.1786860","DOIUrl":"https://doi.org/10.1080/17513758.2020.1786860","url":null,"abstract":"<p><p>Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizosphere. The sufficient conditions for existence of the order-1 periodic solution are obtained by using the geometrical theory of the impulsive semi-dynamical system. We show the impulsive control system tends to an order-1 periodic solution if the control measures are achieved. Furthermore, we investigate the stability of the order-1 periodic solution by means of a novel method introduced in the literature [Y. Ye, <i>The Theory of the Limit Cycle</i>, Shanghai Science and Technology Press, 1984.]. Finally, mathematical results are justified by some numerical simulations.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"566-577"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1786860","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38132329","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
Mathematical modelling on COVID-19 transmission impacts with preventive measures: a case study of Tanzania. 预防措施对COVID-19传播影响的数学建模:以坦桑尼亚为例
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1823494
Abdul-Rahman J Mumbu, Alfred K Hugo
{"title":"Mathematical modelling on COVID-19 transmission impacts with preventive measures: a case study of Tanzania.","authors":"Abdul-Rahman J Mumbu,&nbsp;Alfred K Hugo","doi":"10.1080/17513758.2020.1823494","DOIUrl":"https://doi.org/10.1080/17513758.2020.1823494","url":null,"abstract":"<p><p>The outbreak of COVID-19 was first experienced in Wuhan City, China, during December 2019 before it rapidly spread over globally. This paper has proposed a mathematical model for studying its transmission dynamics in the presence of face mask wearing and hospitalization services of human population in Tanzania. Disease-free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. The trace-determinant approach was used in the local stability of disease-free equilibrium point while Lyapunov function technique was used to determine the global stability of both disease-free and endemic equilibrium points. Basic reproduction number, <math><msub><mi>R</mi><mn>0</mn></msub></math> , was determined in which its numerical results revealed that, in the presence of face masks wearing and medication services or hospitalization as preventive measure for its transmission, <math><msub><mi>R</mi><mn>0</mn></msub><mo>=</mo><mn>0.698</mn></math> while in their absence <math><msub><mi>R</mi><mn>0</mn></msub><mo>=</mo><mn>3.8</mn></math> . This supports its analytical solution that the disease-free equilibrium point <math><msub><mi>E</mi><mn>0</mn></msub></math> is asymptotically stable whenever <math><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></math> , while endemic equilibrium point <math><msub><mi>E</mi><mo>∗</mo></msub></math> is globally asymptotically stable for <math><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></math> . Therefore, this paper proves the necessity of face masks wearing and hospitalization services to COVID-19 patients to contain the disease spread to the population.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"748-766"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1823494","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38434532","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: 25
Coinfection dynamics of heroin transmission and HIV infection in a single population. 单一人群中海洛因传播和HIV感染的共同感染动态。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1726516
Xi-Chao Duan, Xue-Zhi Li, Maia Martcheva
{"title":"Coinfection dynamics of heroin transmission and HIV infection in a single population.","authors":"Xi-Chao Duan,&nbsp;Xue-Zhi Li,&nbsp;Maia Martcheva","doi":"10.1080/17513758.2020.1726516","DOIUrl":"https://doi.org/10.1080/17513758.2020.1726516","url":null,"abstract":"<p><p>We propose a model of a joint spread of heroin use and HIV infection. The unique disease-free equilibrium always exists and it is stable if the basic reproduction numbers of heroin use and HIV infection are both less than 1. The semi-trivial equilibrium of HIV infection (heroin use) exists if the basic reproduction number of HIV infection (heroin use) is larger than 1 and it is locally stable if and only if the invasion number of heroin use (HIV infection) is less than 1. When both semi-trivial equilibria lose their stability, a coexistence equilibrium occurs, which may not be unique. We compare the model to US data on heroin use and HIV transmission. We conclude that the two diseases in the US are in a coexistence regime. Elasticities of the invasion numbers suggest two foci for control measures: targeting the drug abuse epidemic and reducing HIV risk in drug-users.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"116-142"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1726516","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37650055","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
Balance simplices of 3-species May-Leonard systems. 三种May-Leonard系统的平衡简式。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1736656
Stephen Baigent, Atheeta Ching
{"title":"Balance simplices of 3-species May-Leonard systems.","authors":"Stephen Baigent,&nbsp;Atheeta Ching","doi":"10.1080/17513758.2020.1736656","DOIUrl":"https://doi.org/10.1080/17513758.2020.1736656","url":null,"abstract":"<p><p>We investigate the existence of a two-dimensional invariant manifold that attracts all nonzero orbits in 3 species Lotka-Volterra systems with identical linear growth rates. This manifold, which we call the <i>balance simplex,</i> is the common boundary of the basin of repulsion of the origin and the basin of repulsion of infinity. The balance simplex is linked to ecological models where there is 'growth when rare' and competition for finite resources. By including alternative food sources for predators we cater for predator-prey type models. In the case that the model is competitive, the balance simplex coincides with the carrying simplex which is an unordered manifold (no two points may be ordered componentwise), but for non-competitive models the balance simplex need not be unordered. The balance simplex of our models contains all limit sets and is the graph of a piecewise analytic function over the unit probability simplex.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"187-199"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1736656","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37720288","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 role of asymptomatic class, quarantine and isolation in the transmission of COVID-19. 无症状分类、隔离隔离在COVID-19传播中的作用。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1773000
Mohsin Ali, Syed Touqeer H Shah, Mudassar Imran, Adnan Khan
{"title":"The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19.","authors":"Mohsin Ali,&nbsp;Syed Touqeer H Shah,&nbsp;Mudassar Imran,&nbsp;Adnan Khan","doi":"10.1080/17513758.2020.1773000","DOIUrl":"https://doi.org/10.1080/17513758.2020.1773000","url":null,"abstract":"<p><p>We formulate a deterministic epidemic model for the spread of Corona Virus Disease (COVID-19). We have included asymptomatic, quarantine and isolation compartments in the model, as studies have stressed upon the importance of these population groups on the transmission of the disease. We calculate the basic reproduction number [Formula: see text] and show that for [Formula: see text] the disease dies out and for [Formula: see text] the disease is endemic. Using sensitivity analysis we establish that [Formula: see text] is most sensitive to the rate of quarantine and isolation and that a high level of quarantine needs to be maintained as well as isolation to control the disease. Based on this we devise optimal quarantine and isolation strategies, noting that high levels need to be maintained during the early stages of the outbreak. Using data from the Wuhan outbreak, which has nearly run its course we estimate that [Formula: see text] which while in agreement with other estimates in the literature is on the lower side.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"389-408"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1773000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38014623","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: 67
Modeling the suppression dynamics of Aedes mosquitoes with mating inhomogeneity. 交配不均匀的伊蚊抑制动力学建模。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1799083
Mugen Huang, Linchao Hu
{"title":"Modeling the suppression dynamics of <i>Aedes</i> mosquitoes with mating inhomogeneity.","authors":"Mugen Huang,&nbsp;Linchao Hu","doi":"10.1080/17513758.2020.1799083","DOIUrl":"https://doi.org/10.1080/17513758.2020.1799083","url":null,"abstract":"<p><p>A novel strategy for controlling mosquito-borne diseases, such as dengue, malaria and Zika, involves releases of <i>Wolbachia</i>-infected mosquitoes as <i>Wolbachia</i> cause early embryo death when an infected male mates with an uninfected female. In this work, we introduce a delay differential equation model with mating inhomogeneity to discuss mosquito population suppression based on <i>Wolbachia</i>. Our analyses show that the wild mosquitoes could be eliminated if either the adult mortality rate exceeds the threshold [Formula: see text] or the release amount exceeds the threshold [Formula: see text] uniformly. We also present the nonlinear dependence of [Formula: see text] and [Formula: see text] on the parameters, respectively, as well as the effect of pesticide spraying on wild mosquitoes. Our simulations suggest that the releasing should be started at least 5 weeks before the peak dengue season, taking into account both the release amount and the suppression speed.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"656-678"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1799083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38233397","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
A generalized within-host model of dengue infection with a non-constant monocyte production rate. 一个具有非恒定单核细胞产生率的登革热感染的广义宿主模型。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1733678
Jeremy J Thibodeaux, Daniel Nuñez, Andres Rivera
{"title":"A generalized within-host model of dengue infection with a non-constant monocyte production rate.","authors":"Jeremy J Thibodeaux,&nbsp;Daniel Nuñez,&nbsp;Andres Rivera","doi":"10.1080/17513758.2020.1733678","DOIUrl":"https://doi.org/10.1080/17513758.2020.1733678","url":null,"abstract":"<p><p>In this paper, we generalize a previous model of within-host dengue infection with a nonconstant monocyte production rate. We establish the existence of three equilibria and give some local stability results. We then estimate three parameters in the model from clinical data for dengue virus serotype 2. It is then shown that the model can exhibit behaviours that are not possible under the assumption of constant monocyte production. Lastly, we perform a sensitivity analysis of the model in two contexts, antiviral treatment and immunostimulatory treatment. The results predict that antiviral treatments that reduce the viral replication rate in infected monocytes are the most effective, while immunostimulatory treatments that increase the rate at which infected monocytes are removed are best.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"143-161"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1733678","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37697625","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
Global stability analysis for a model with carriers and non-linear incidence rate. 带载波和非线性发生率模型的全局稳定性分析。
IF 2.8 4区 数学
Journal of Biological Dynamics Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1772998
Miller Cerón Gómez, Eduardo Ibarguen Mondragon, Patricia Lopez Molano
{"title":"Global stability analysis for a model with carriers and non-linear incidence rate.","authors":"Miller Cerón Gómez,&nbsp;Eduardo Ibarguen Mondragon,&nbsp;Patricia Lopez Molano","doi":"10.1080/17513758.2020.1772998","DOIUrl":"https://doi.org/10.1080/17513758.2020.1772998","url":null,"abstract":"<p><p>We analysed a epidemiological model with varying populations of susceptible, carriers, infectious and recovered (SCIR) and a general non-linear incidence rate of the form [Formula: see text]. We show that this model exhibits two positive equilibriums: the disease-free and disease equilibrium. We proved using the Lyapunov direct method that these two equilibriums are globally asymptotically stable under some sufficient conditions over the functions <i>f</i>, <i>g</i>, <i>h</i>.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"14 1","pages":"409-420"},"PeriodicalIF":2.8,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1772998","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38010275","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
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