A four-dimensional mathematical model is formulated to explore the fear effect exerted by large carnivore in the grassland ecosystem.The model depicts the interactions among herbage,domestic herbivore,wild herbivore a...A four-dimensional mathematical model is formulated to explore the fear effect exerted by large carnivore in the grassland ecosystem.The model depicts the interactions among herbage,domestic herbivore,wild herbivore and large carnivore,which incorporates both direct predation and anti-predator mechanisms.The dynamic properties of the model are analytically investigated,including the dissipativity of solutions,and the existence and stability of different equilibria.Some numerical simulations are also presented to exhibit rich dynamical behaviors,such as various types of bistabilities,periodic oscillation and chaotic oscillation.The study reveals that the appropriate level of fear factors can stabilize the system and increase the density of herbage and domestic herbivore.The fear effect plays an important role in maintaining the balance of the grassland ecosystem and promoting the economy of human society.展开更多
In this paper,based on the classic Kermack-McKendrick SIR model,we propose an ordinary differential equation model to re-examine the COVID-19 epidemics in Wuhan where this disease initially broke out.The focus is on t...In this paper,based on the classic Kermack-McKendrick SIR model,we propose an ordinary differential equation model to re-examine the COVID-19 epidemics in Wuhan where this disease initially broke out.The focus is on the impact of all those major nonpharmaceutical interventions(NPIs)implemented by the local public healthy authorities and government during the epidemics.We use the data publicly available and the nonlinear least-squares solver lsqnonlin built in MATLAB to estimate the model parameters.Then we explore the impact of those NPIs,particularly the timings of these interventions,on the epidemics.The results can help people review the responses to the outbreak of the COVID-19 inWuhan,while the proposed model also offers a framework for studying epidemics of COVID-19 and/or other similar diseases in other places,and accordingly helping people better prepare for possible future outbreaks of similar diseases.展开更多
基金Pingping Cong is funded by the China Scholarship Council(No.202106620028)Meng Fan is funded by the National Natural Science Foundation of China(No.12071068)Xingfu Zou is funded by the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2022-04744).
文摘A four-dimensional mathematical model is formulated to explore the fear effect exerted by large carnivore in the grassland ecosystem.The model depicts the interactions among herbage,domestic herbivore,wild herbivore and large carnivore,which incorporates both direct predation and anti-predator mechanisms.The dynamic properties of the model are analytically investigated,including the dissipativity of solutions,and the existence and stability of different equilibria.Some numerical simulations are also presented to exhibit rich dynamical behaviors,such as various types of bistabilities,periodic oscillation and chaotic oscillation.The study reveals that the appropriate level of fear factors can stabilize the system and increase the density of herbage and domestic herbivore.The fear effect plays an important role in maintaining the balance of the grassland ecosystem and promoting the economy of human society.
基金Research partially supported by NSERC of Canada(No.RGPIN-2016-04665)CP was supported by the”Short-term Study Abroad Program for PhD Students”of Northeast Normal University(China).
文摘In this paper,based on the classic Kermack-McKendrick SIR model,we propose an ordinary differential equation model to re-examine the COVID-19 epidemics in Wuhan where this disease initially broke out.The focus is on the impact of all those major nonpharmaceutical interventions(NPIs)implemented by the local public healthy authorities and government during the epidemics.We use the data publicly available and the nonlinear least-squares solver lsqnonlin built in MATLAB to estimate the model parameters.Then we explore the impact of those NPIs,particularly the timings of these interventions,on the epidemics.The results can help people review the responses to the outbreak of the COVID-19 inWuhan,while the proposed model also offers a framework for studying epidemics of COVID-19 and/or other similar diseases in other places,and accordingly helping people better prepare for possible future outbreaks of similar diseases.
