International Journal of Biomathematics最新文献

{"title":"Control Dengue with Wolbachia: Insights from a Two-Strain Vector-Host Model with Larval Competition","authors":"Shuanghui Fang, Kaihui Liu, Jun Wang","doi":"10.1142/s1793524524500189","DOIUrl":"https://doi.org/10.1142/s1793524524500189","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140718744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Supercritical Hopf bifurcations in the stage-structured model of housefly populations","authors":"Xiangming Zhang, Mengmeng Hou, Hai-Feng Huo","doi":"10.1142/s1793524523501164","DOIUrl":"https://doi.org/10.1142/s1793524523501164","url":null,"abstract":"<p>Insect populations, which are diverse and widespread, provide a principal area of utilization of the stage-structured modeling approach. In this paper, housefly populations incorporating a stage-structured model are investigated theoretically and graphically. First, stability charts and rightmost characteristic roots of the positive equilibrium are elucidated analytically and numerically. Furthermore, the Hopf bifurcation at the positive equilibrium is derived employing geometric stability switch criterion. Second, the properties of Hopf bifurcation are determined using the center manifold theorem and by reducing the equation to the Poincaré normal form. Finally, the correctness of the theoretical derivation is confirmed using a numerical simulation based on specific parameter values. Our results show that with an increase in delay <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi></math></span><span></span>, the unique positive equilibrium may undergo two stability switches: from stable to unstable, and from unstable to stable. Interestingly, the characteristic equation has pure imaginary roots at the second pair and subsequent critical values. However, Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts, except the pure imaginary roots. We also simulate the unstable periodic solutions at the second pair of critical values through a bifurcation diagram. Therefore, a pair of supercritical Hopf bifurcations appear around the positive equilibrium of the housefly population stage-structured model.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability analysis of a pine wood nematode prevention and control model with delay","authors":"Jia Li, Yuting Ding","doi":"10.1142/s1793524524500128","DOIUrl":"https://doi.org/10.1142/s1793524524500128","url":null,"abstract":"<p>Pine wilt disease is a destructive forest disease with strong infectivity, a wide spread range and high difficulty in prevention and control. Since controlling <i>Monochamus alternatus</i>, the vector of pine wood nematode (<i>Bursaphelenchus xylophilus</i>) can reduce the occurrence of pine wilt disease efficiently, the parasitic natural enemy of <i>M. alternatus</i>, <i>Dastarcus helophoroides</i>, is introduced in this paper. Considering the influence of parasitic time of <i>D. helophoroides</i> on the control effect, based on the mutualistic symbiosis and parasitic relationship among pine wood nematode, <i>M. alternatus</i> and <i>D. heloporoides</i>, this paper establishes a pine wood nematode prevention and control model with delay. Then, the stability of positive equilibrium and the existence of Hopf bifurcation are discussed. Besides, we obtain the normal form of Hopf bifurcation by applying the multiple time scales method. Finally, numerical simulations with two sets of meaningful parameters selected by means of statistical analysis are carried out to support the theoretical findings. Through the comparative analysis of numerical simulations, the factors affecting the control effect of pine wilt disease are obtained, and some suggestions are put forward for practical control in the forest.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic analysis of an SSvEIQR model with nonlinear contact rate, isolation rate and vaccination rate dependent on media coverage","authors":"Yantao Luo, Pengfei Liu, Tingting Zheng, Zhidong Teng","doi":"10.1142/s1793524524500116","DOIUrl":"https://doi.org/10.1142/s1793524524500116","url":null,"abstract":"<p>In this paper, we study an SS_<i>v</i>EIQR model with nonlinear contact rate, isolation rate and vaccination rate driven by media coverage. First, the basic reproduction number <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span> is derived. Then, the threshold dynamics of the disease are obtained in terms of <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>: when <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span><span></span>, the global stability of the disease-free equilibrium is obtained by constructing an appropriate Lyapunov function; when <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span><span></span>, the sufficient conditions to prove the globally stability of endemic equilibrium are obtained by applying the geometric method into the four-dimensional system, which needs to estimate the Lozinski<span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>ǐ</mi></math></span><span></span> measure of a <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mn>6</mn><mo stretchy=\"false\">×</mo><mn>6</mn></math></span><span></span> matrix. Further, we conduct some numerical simulations to validate our theoretical results, and analyze the impact of media coverage on disease transmission, the results show that media coverage could effectively suppress the spread of the disease and reduce the number of infected individuals. Finally, through the sensitivity analysis of <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>, we obtain some measures to control the spread of the disease, such as reducing contact, strengthening isolation and vaccination.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Boundary Control for a Competitive Population System with Size Structure and Time Delay in a Polluted Environment","authors":"Fenghui Qin, Zhanping Wang","doi":"10.1142/s1793524524500141","DOIUrl":"https://doi.org/10.1142/s1793524524500141","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Noise propagation and amplification in microbial communities with different resistance mechanisms","authors":"Zhao Yang, Fang Yan, Haihong Liu","doi":"10.1142/s1793524524500153","DOIUrl":"https://doi.org/10.1142/s1793524524500153","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and analysis of a periodic delays spatial diffusion HIV model with three-stage infection process","authors":"Peng Wu, Zerong He","doi":"10.1142/s179352452450013x","DOIUrl":"https://doi.org/10.1142/s179352452450013x","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139963165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and stability of steady state bifurcations in a prey-predator system with a nonmonotonic functional response","authors":"M. Farshid, Y. Jalilian","doi":"10.1142/s1793524524500165","DOIUrl":"https://doi.org/10.1142/s1793524524500165","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139963181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comprehensive analysis of disease dynamics using nonlinear fractional order SEIRS model with Crowley–Martin functional response and saturated treatment","authors":"Bouissa Ayoub, Tsouli Najib","doi":"10.1142/s1793524523501140","DOIUrl":"https://doi.org/10.1142/s1793524523501140","url":null,"abstract":"<p>This paper presents a comprehensive study of disease spreading dynamics through the application of a nonlinear fractional order epidemic SEIRS model. By incorporating the Crowley–Martin type functional response and a saturated treatment function, the model effectively captures the intricacies of real-world epidemics. Our research establishes the existence, uniqueness, non-negativity and boundedness of the solution, while also investigating the model’s fundamental reproduction number. Additionally, we conduct a thorough analysis of the specific conditions governing the local and global stability of the model’s equilibriums. A notable observation is the variation of the reproduction number with the fractional-order <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span>, which represents a memory effect on individuals’ dynamic behavior and reveals the influence of interactions between compartments. To validate these theoretical findings, we employ numerical simulations using Matlab, demonstrating that inhibition measures for susceptibles and the saturated treatment parameters play a pivotal role in determining the disease state. Specifically, we observe that as these parameter values increase, the transition from endemic equilibrium to disease-free equilibrium occurs.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation and Dynamic Analysis of Prey-predator Model with Combined Nonlinear Harvesting","authors":"Kshirod Sarkar, Biswajit Mondal","doi":"10.1142/s1793524524500104","DOIUrl":"https://doi.org/10.1142/s1793524524500104","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139811058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}