Pub Date : 2023-10-27DOI: 10.1142/s1793524523500894
Xuebing Zhang, Jia Liu, Guanglan Wang
{"title":"Impacts of nonlocal fear effect and delay on a reaction-diffusion predator-prey model","authors":"Xuebing Zhang, Jia Liu, Guanglan Wang","doi":"10.1142/s1793524523500894","DOIUrl":"https://doi.org/10.1142/s1793524523500894","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"10 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312477","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}
Pub Date : 2023-10-19DOI: 10.1142/s179352452350081x
Tan Yang, Yang Lin
In this paper, we propose an epidemic model with the impact of information intervention and general incidence rate in deterministic and stochastic environment, respectively. The information intervention prompts susceptible individuals to change their behavior to protect themselves from infection. First, the asymptotic dynamics of the disease-free equilibrium and the unique endemic equilibrium are analyzed and the results indicate that the basic reproduction number is a pointy disease threshold about the stability under some conditions. Then, we formulate the corresponding stochastic model by perturbing the disease transmission rate and information response rate parameters by white noise terms and provide verifiable sufficient conditions for extinction and persistence in mean. Two sufficient conditions for extinction show that if the noise intensity of the disease transmission rate is large enough or small enough, the infected population of the stochastic system will tend to go extinct. For the persistence, we get the sufficient conditions which guarantee the infected population to be persistent in the mean. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic and the stochastic system.
{"title":"The analysis of deterministic and stochastic model with general information intervention","authors":"Tan Yang, Yang Lin","doi":"10.1142/s179352452350081x","DOIUrl":"https://doi.org/10.1142/s179352452350081x","url":null,"abstract":"In this paper, we propose an epidemic model with the impact of information intervention and general incidence rate in deterministic and stochastic environment, respectively. The information intervention prompts susceptible individuals to change their behavior to protect themselves from infection. First, the asymptotic dynamics of the disease-free equilibrium and the unique endemic equilibrium are analyzed and the results indicate that the basic reproduction number is a pointy disease threshold about the stability under some conditions. Then, we formulate the corresponding stochastic model by perturbing the disease transmission rate and information response rate parameters by white noise terms and provide verifiable sufficient conditions for extinction and persistence in mean. Two sufficient conditions for extinction show that if the noise intensity of the disease transmission rate is large enough or small enough, the infected population of the stochastic system will tend to go extinct. For the persistence, we get the sufficient conditions which guarantee the infected population to be persistent in the mean. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic and the stochastic system.","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135667692","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}
Pub Date : 2023-10-17DOI: 10.1142/s1793524523500833
Qura tul Ain, Jinrong Wang
The paper focuses on the study of an epidemic model for the evolution of diseases, using stochastic models. We demonstrated the encoding of this intricate model into formalisms suitable for analysis with advanced stochastic model checkers. A co-infection model’s dynamics were modeled as an Ito–Levy stochastic differential equations system, representing a compartmental system shaped by disease complexity. Initially, we established a deterministic system based on presumptions and disease-related traits. Through non-traditional analytical methods, two key asymptotic properties: eradication and continuation in the mean were demonstrated. Section 2 provides a detailed construction of the model. Section 3 results confirm that the outcome is biologically well-behaved. Utilizing simulations, we tested and confirmed the stability of all equilibrium points. The ergodic stationary distribution and extinction conditions of the system are thoroughly analyzed. Investigations were made into the stochastic system’s probability density function, and digital simulations were employed to illustrate the probability density function and systems’ extinction. Although infectious disease control and eradication are major public health goals, global eradication proves challenging. Local disease extinction is possible, but it may reoccur. Extinction is more feasible with a lower [Formula: see text]. Notably, our simulations showed that reducing the [Formula: see text] value significantly increases the likelihood of disease extinction and reduces the probability of future recurrence. Additionally, our study provides insights into the conditions under which a disease can persist or become extinct, contributing to more effective disease control strategies in public health.
{"title":"A stochastic analysis of co-infection model in a finite carrying capacity population","authors":"Qura tul Ain, Jinrong Wang","doi":"10.1142/s1793524523500833","DOIUrl":"https://doi.org/10.1142/s1793524523500833","url":null,"abstract":"The paper focuses on the study of an epidemic model for the evolution of diseases, using stochastic models. We demonstrated the encoding of this intricate model into formalisms suitable for analysis with advanced stochastic model checkers. A co-infection model’s dynamics were modeled as an Ito–Levy stochastic differential equations system, representing a compartmental system shaped by disease complexity. Initially, we established a deterministic system based on presumptions and disease-related traits. Through non-traditional analytical methods, two key asymptotic properties: eradication and continuation in the mean were demonstrated. Section 2 provides a detailed construction of the model. Section 3 results confirm that the outcome is biologically well-behaved. Utilizing simulations, we tested and confirmed the stability of all equilibrium points. The ergodic stationary distribution and extinction conditions of the system are thoroughly analyzed. Investigations were made into the stochastic system’s probability density function, and digital simulations were employed to illustrate the probability density function and systems’ extinction. Although infectious disease control and eradication are major public health goals, global eradication proves challenging. Local disease extinction is possible, but it may reoccur. Extinction is more feasible with a lower [Formula: see text]. Notably, our simulations showed that reducing the [Formula: see text] value significantly increases the likelihood of disease extinction and reduces the probability of future recurrence. Additionally, our study provides insights into the conditions under which a disease can persist or become extinct, contributing to more effective disease control strategies in public health.","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944435","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}
Pub Date : 2023-10-14DOI: 10.1142/s1793524523500821
Yahong Peng, Ke Yu, Yujing Li
In this paper, we introduce spatial memory into a predator–prey model with herd behavior. Taking memory-based diffusion coefficient and average memory period of predators as control parameters, we obtain the stable conditions of the positive equilibrium of system and prove the existence of Hopf bifurcation. In addition, a double Hopf bifurcation occurs at the intersection of the nonhomogeneous Hopf bifurcation curves, and a spatially nonhomogeneous quasi-periodic pattern can be observed near the double Hopf bifurcation point by numerical simulation.
{"title":"Effect of spatial memory on a predator-prey model with herd behaviour","authors":"Yahong Peng, Ke Yu, Yujing Li","doi":"10.1142/s1793524523500821","DOIUrl":"https://doi.org/10.1142/s1793524523500821","url":null,"abstract":"In this paper, we introduce spatial memory into a predator–prey model with herd behavior. Taking memory-based diffusion coefficient and average memory period of predators as control parameters, we obtain the stable conditions of the positive equilibrium of system and prove the existence of Hopf bifurcation. In addition, a double Hopf bifurcation occurs at the intersection of the nonhomogeneous Hopf bifurcation curves, and a spatially nonhomogeneous quasi-periodic pattern can be observed near the double Hopf bifurcation point by numerical simulation.","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767369","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}
Pub Date : 2023-10-06DOI: 10.1142/s1793524523500845
C. Kabiwa Kadje, A. Nana Yakam, S. Bowong, G. Mophou
{"title":"Impact of water stress on plants production: A study case of banana-plantain","authors":"C. Kabiwa Kadje, A. Nana Yakam, S. Bowong, G. Mophou","doi":"10.1142/s1793524523500845","DOIUrl":"https://doi.org/10.1142/s1793524523500845","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135303757","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}
Pub Date : 2023-10-06DOI: 10.1142/s1793524523500857
Ihtisham Ul Haq, Nigar Ali, Hijaz Ahmad, Ramadan Sabra, M. Daher Albalwi, Imtiaz Ahmad
{"title":"Mathematical analysis of a Corona virus model with Caputo, Caputo-Fabrizio-Caputo fractional and Atangana-Baleanu-Caputo differential operators","authors":"Ihtisham Ul Haq, Nigar Ali, Hijaz Ahmad, Ramadan Sabra, M. Daher Albalwi, Imtiaz Ahmad","doi":"10.1142/s1793524523500857","DOIUrl":"https://doi.org/10.1142/s1793524523500857","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135303331","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":"Instability and bifurcation analysis of a diffusive predator-prey model with fear effect and delay","authors":"Hongyan Sun, Jianzhi Cao, Pengmiao Hao, Lijie Zhang","doi":"10.1142/s1793524523500808","DOIUrl":"https://doi.org/10.1142/s1793524523500808","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91025994","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}
Pub Date : 2023-09-01DOI: 10.1142/s1793524523500754
Bang-Sheng Han, Shao-yue Mi, Miao-Miao Wen, Lin Zhao
{"title":"Dynamics of a Predator-Prey model with mutation and nonlocal effect","authors":"Bang-Sheng Han, Shao-yue Mi, Miao-Miao Wen, Lin Zhao","doi":"10.1142/s1793524523500754","DOIUrl":"https://doi.org/10.1142/s1793524523500754","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"43 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74744619","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}
Pub Date : 2023-09-01DOI: 10.1142/s179352452350078x
Shuyang Xue, Feng Yang, Yong-Li Song
{"title":"Stability and spatially inhomogeneous patterns induced by nonlocal prey competition in a generalist predator-prey system","authors":"Shuyang Xue, Feng Yang, Yong-Li Song","doi":"10.1142/s179352452350078x","DOIUrl":"https://doi.org/10.1142/s179352452350078x","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"70 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83856332","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}
Pub Date : 2023-09-01DOI: 10.1142/s1793524523500766
Chuanjia Wan, Pan Zheng, Wenhai Shan
{"title":"Global stability of a quasilinear predator-prey model with indirect pursuit-evasion interaction","authors":"Chuanjia Wan, Pan Zheng, Wenhai Shan","doi":"10.1142/s1793524523500766","DOIUrl":"https://doi.org/10.1142/s1793524523500766","url":null,"abstract":"","PeriodicalId":49273,"journal":{"name":"International Journal of Biomathematics","volume":"44 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89861136","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}
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