In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke compari...In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).展开更多
Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencie...Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencies,and disease dynamic fluctuations.However,there is a notable methodological gap in existing studies examining the interplay between physical and virtual interactions and the impact of information dissemination and behavioural responses on disease propagation.We constructed a three-layer(information,cognition,and epidemic)network model to investigate the adoption of protective behaviours,such as wearing masks or practising social distancing,influenced by the diffusion and correction of misinformation.We examined five key events influencing the rate of information spread:(i)rumour transmission,(ii)information suppression,(iii)renewed interest in spreading misinformation,(iv)correction of misinformation,and(v)relapse to a stifler state after correction.We found that adopting information-based protection behaviours is more effective in mitigating disease spread than protection adoption induced by neighbourhood interactions.Specifically,our results show that warning and educating individuals to counter misinformation within the information network is a more effective strategy for curbing disease spread than suspending gossip spreaders from the network.Our study has practical implications for developing strategies to mitigate the impact of misinformation and enhance protective behavioural responses during disease outbreaks.展开更多
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reac...In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.展开更多
This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas,considering commuting patterns.It is a compartmental model with a vaccination rate for each city,acting ...This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas,considering commuting patterns.It is a compartmental model with a vaccination rate for each city,acting as a control function.The commuting patterns are incorporated through a weighted adjacency matrix and a parameter that selects day and night periods.The optimal control problem is formulated to minimize a functional cost that balances the number of hospitalizations and vaccines,including restrictions of a weekly availability cap and an application capacity of vaccines per unit of time.The key findings of this work are bounds for the basic reproduction number,particularly in the case of a metropolitan area,and the study of the optimal control problem.Theoretical analysis and numerical simulations provide insights into disease dynamics and the effectiveness of control measures.The research highlights the importance of prioritizing vaccination in the capital to better control the disease spread,as we depicted in our numerical simulations.This model serves as a tool to improve resource allocation in epidemic control across metropolitan regions.展开更多
This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is p...This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.展开更多
基金Supported by the Research Foundation of Education Department of Zhejiang Province( 2 0 0 380 4 9)
文摘In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).
基金supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq)-Brazil(Grant no.310984/2023-8)Fundação de AmparoàPesquisa do Estado de Minas Gerais(FAPEMIG)-Brazil(Grant no.APQ-01973-24)+1 种基金supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES)-Brazil-Finance Code 001Seyed M.Moghadas acknowledges the support from Natural Sciences and Engineering Research Council of Canada(NSERC),Discovery Grant and Alliance Grant.
文摘Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencies,and disease dynamic fluctuations.However,there is a notable methodological gap in existing studies examining the interplay between physical and virtual interactions and the impact of information dissemination and behavioural responses on disease propagation.We constructed a three-layer(information,cognition,and epidemic)network model to investigate the adoption of protective behaviours,such as wearing masks or practising social distancing,influenced by the diffusion and correction of misinformation.We examined five key events influencing the rate of information spread:(i)rumour transmission,(ii)information suppression,(iii)renewed interest in spreading misinformation,(iv)correction of misinformation,and(v)relapse to a stifler state after correction.We found that adopting information-based protection behaviours is more effective in mitigating disease spread than protection adoption induced by neighbourhood interactions.Specifically,our results show that warning and educating individuals to counter misinformation within the information network is a more effective strategy for curbing disease spread than suspending gossip spreaders from the network.Our study has practical implications for developing strategies to mitigate the impact of misinformation and enhance protective behavioural responses during disease outbreaks.
基金the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032)the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)
文摘In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
基金the financial support from the School of Applied Mathematics(FGV EMAp),and Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro(FAPERJ)for the funding through process E-26/203.223/2017the financial support of CNPq(Brazil)through process 310452/2019-8.
文摘This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas,considering commuting patterns.It is a compartmental model with a vaccination rate for each city,acting as a control function.The commuting patterns are incorporated through a weighted adjacency matrix and a parameter that selects day and night periods.The optimal control problem is formulated to minimize a functional cost that balances the number of hospitalizations and vaccines,including restrictions of a weekly availability cap and an application capacity of vaccines per unit of time.The key findings of this work are bounds for the basic reproduction number,particularly in the case of a metropolitan area,and the study of the optimal control problem.Theoretical analysis and numerical simulations provide insights into disease dynamics and the effectiveness of control measures.The research highlights the importance of prioritizing vaccination in the capital to better control the disease spread,as we depicted in our numerical simulations.This model serves as a tool to improve resource allocation in epidemic control across metropolitan regions.
文摘This paper aims to analyze the reduction of quasilinear differential equations,and the existence and uniqueness of its solution on its matrice coefficients. Anda mathematical charactorization of its impasse point is provided. One examplefrom practicc electrical network problem is used to test all these theory.
