International Journal of Biomathematics最新文献

{"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":"53 1","pages":""},"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":"94 1","pages":""},"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":"121 1","pages":""},"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":"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":"74 1","pages":""},"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 analysis and pattern formation of a delayed diffusive toxic-phytoplankton–zooplankton model","authors":"Ming Wu, Hongxing Yao","doi":"10.1142/s1793524523501152","DOIUrl":"https://doi.org/10.1142/s1793524523501152","url":null,"abstract":"<p>This study considers a model which incorporates delays, diffusion and toxicity in a phytoplankton–zooplankton system. Initially, we analyze the global existence, asymptotic behavior and persistence of the solution. We then analyze the equilibria’s local stability and investigate the non-delayed system’s bifurcation phenomena, including Turing and Hopf bifurcations and their combination. Subsequently, we explore the effects of delays on bifurcation and the global stability of the system using Lyapunov functional, focusing on Hopf and Turing–Hopf bifurcations. Finally, we present numerical simulations to validate the theoretical results and verify the emergence of various spatial patterns in the system.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"2020 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075191","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":"Dynamical behavior of a stochastic COVID-19 model with two Ornstein–Uhlenbeck processes and saturated incidence rates","authors":"Xiaoyu Li, Zhiming Li","doi":"10.1142/s1793524523501085","DOIUrl":"https://doi.org/10.1142/s1793524523501085","url":null,"abstract":"<p>According to the transmission characteristics of COVID-19, this paper proposes a stochastic SAIRS epidemic model with two mean reversion Ornstein–Uhlenbeck processes and saturated incidence rates. We first prove the existence and uniqueness of the global solution in the stochastic model. Using several suitable Lyapunov methods, we then derive the extinction and persistence of COVID-19 under certain conditions. Further, stationary distribution and ergodic properties are obtained. Moreover, we obtain the probability density function of the stochastic model around the equilibrium. Numerical simulations illustrate our theoretical results and the effect of essential parameters. Finally, we apply the model to investigate the latest outbreak of the COVID-19 epidemic in Guangzhou city, China.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075135","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":"Assessment of vaccination and underreporting on COVID-19 infections in Turkey based on effective reproduction number","authors":"Tuğba Akman, Emek Köse, Necibe Tuncer","doi":"10.1142/s1793524523501024","DOIUrl":"https://doi.org/10.1142/s1793524523501024","url":null,"abstract":"<p>In this paper, we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care (ICUs) and ventilation units. The model is calibrated with the symptomatic COVID-19 cases, deaths, and the number of patients in ICUs and ventilation units as reported by Republic of Turkey, Ministry of Health for the period 11 March 2020 through 30 May 2020 when the nationwide lockdown is in order. COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately. We tested the effect of underreporting and we found that the peaks of the disease differ significantly depending on the rate of underreporting, however, the timing of the peaks remains constant. The lockdown is lifted on 1 June, and the model is modified to include a time-dependent transmission rate which is linked to the effective reproduction number <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> through basic reproduction number <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>. The modified model captures the changing dynamics and peaks of the outbreak successfully. With the onset of vaccination on 13 January 2021, we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy. We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"64 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075192","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":"Global analysis of a network-based SIR epidemic model with a saturated treatment function","authors":"Xiaodan Wei","doi":"10.1142/s1793524523501127","DOIUrl":"https://doi.org/10.1142/s1793524523501127","url":null,"abstract":"<p>In this paper, we study a network-based SIR epidemic model with a saturated treatment function in which a parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> is introduced to measure the extent of the effect of the infected being delayed for treatment. Our aim is to present a global analysis and to investigate how the parameter <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> affects the spreading of diseases. Our main results are as follows: (1) In the case of the threshold value <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></math></span><span></span>, there exist two values of <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span>: <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span><span></span> and <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>, such that the disease-free equilibrium is globally asymptotically stable when <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi><mo>≤</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span><span></span> and multiple endemic equilibria exist when <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi><mo>≥</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>. This means that the parameter <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> has an essential influence on the spreading of the disease. (2) In the case of the threshold value <span><math altimg=\"eq-00010.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>, if the model has only one endemic equilibrium, then the unique endemic equilibrium is globally attractive. In this case, it is also proved that if <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi><mo>≤</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span><span></span>, then the endemic equilibrium has only one, so is globally attractive. In addition, numerical simulation is performed to illustrate our theoretical results.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"26 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097348","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":"Threshold dynamics of a nonlocal dispersal SIS epidemic model with free boundaries","authors":"Yachun Tong, Inkyung Ahn, Zhigui Lin","doi":"10.1142/s179352452350095x","DOIUrl":"https://doi.org/10.1142/s179352452350095x","url":null,"abstract":"<p>To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptible (SIS) reaction–diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.</p>","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075355","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":"Threshold dynamics of a reaction-advection-diffusion waterborne disease model with seasonality and human behavior change","authors":"Wei Wang, Xiaotong Wang, Xiaoting Fan","doi":"10.1142/s1793524523501061","DOIUrl":"https://doi.org/10.1142/s1793524523501061","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"887 ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139178239","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}