We consider a special class of Lotka-Volterra systems where the associated interaction matrix is cyclic, but asymmetric, with a perturbation term on each row. After some discussion of the dynamics under a general sett...We consider a special class of Lotka-Volterra systems where the associated interaction matrix is cyclic, but asymmetric, with a perturbation term on each row. After some discussion of the dynamics under a general setting, we focus our attention on 3D systems for a more detailed study. We derive sufficient conditions for the existence and stability of the nontrivial interior equilibrium. We also show that Hopf bifurcation occurs when the size of the perturbation is large. Such analysis can be similarly extended to higher dimensional systems, and we mention some results in 4D case.展开更多
We propose a mathematical model to investigate the transmission dynamics of COVID-19.The model incorporates both human-to-human and environment-to-human transmission pathways,and employs different transmission rates t...We propose a mathematical model to investigate the transmission dynamics of COVID-19.The model incorporates both human-to-human and environment-to-human transmission pathways,and employs different transmission rates to represent the epidemiological characteristics at different time periods.Using this model and publicly reported data,we perform a case study for Hamilton County,the fourth-most populous county in the state of Tennessee and a region that could represent the typical situation of COVID-19 in the United States(US).Our data fitting and simulation results show that the environment may play an important role in the transmission and spread of the coronavirus.In addition,we numerically simulate a range of epidemic scenarios and make near-term forecasts on the development and trend of COVID-19 in Hamilton County.展开更多
We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host ...We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.展开更多
文摘We consider a special class of Lotka-Volterra systems where the associated interaction matrix is cyclic, but asymmetric, with a perturbation term on each row. After some discussion of the dynamics under a general setting, we focus our attention on 3D systems for a more detailed study. We derive sufficient conditions for the existence and stability of the nontrivial interior equilibrium. We also show that Hopf bifurcation occurs when the size of the perturbation is large. Such analysis can be similarly extended to higher dimensional systems, and we mention some results in 4D case.
文摘We propose a mathematical model to investigate the transmission dynamics of COVID-19.The model incorporates both human-to-human and environment-to-human transmission pathways,and employs different transmission rates to represent the epidemiological characteristics at different time periods.Using this model and publicly reported data,we perform a case study for Hamilton County,the fourth-most populous county in the state of Tennessee and a region that could represent the typical situation of COVID-19 in the United States(US).Our data fitting and simulation results show that the environment may play an important role in the transmission and spread of the coronavirus.In addition,we numerically simulate a range of epidemic scenarios and make near-term forecasts on the development and trend of COVID-19 in Hamilton County.
基金F. Bao was partially supported by the National Science Foundation under Grant No. 1720222. J. Wang was partially supported by the National Science Foundation under Grant Nos. 1412826 and 1557739. The authors are grateful to the two anonymous referees for their valuable comments that have improved this paper.
文摘We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.
