The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. I...The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. In this work we present a computational bifurcation analysis of the mathematical model of the repressilator. We show that the steady state undergoes a transition from stable to unstable giving rise to a stable limit-cycle in a Hopf bifurcation. The nonlinear analysis involves a center manifold reduction on the six-dimensional system, which yields closed form expressions for the frequency and amplitude of the oscillation born at the Hopf. A parameter study then shows how the dynamics of the system are influenced for different parameter values and their associated biological significance.展开更多
In November 2015,El Salvador reported their first case of Zika virus(ZIKV)infection,an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two months.National agencies began...In November 2015,El Salvador reported their first case of Zika virus(ZIKV)infection,an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two months.National agencies began implementing control measures that included vector control and recommending an increased use of repellents.Further,in response to the alarming and growing number of microcephaly cases in Brazil,the importance of avoiding pregnancies for two years was stressed.In this paper,we explore the role of mobility within communities characterized by extreme poverty,crime and violence.Specifically,the role of short term mobility between two idealized interconnected highly distinct communities is explored in the context of ZIKV outbreaks.We make use of a Lagrangian modeling approach within a two-patch setting in order to highlight the possible effects that short-term mobility,within highly distinct environments,may have on the dynamics of ZIKV outbreak when the overall goal is to reduce the number of cases not just in the most affluent areas but everywhere.Outcomes depend on existing mobility patterns,levels of disease risk,and the ability of federal or state public health services to invest in resource limited areas,particularly in those where violence is systemic.The results of simulations in highly polarized and simplified scenarios are used to assess the role of mobility.It quickly became evident that matching observed patterns of ZIKV outbreaks could not be captured without incorporating increasing levels of heterogeneity.The number of distinct patches and variations on patch connectivity structure required to match ZIKV patterns could not be met within the highly aggregated model that is used in the simulations.展开更多
文摘The repressilator is a genetic network that exhibits oscillations. The net-work is formed of three genes, each of which represses each other cyclically, creating a negative feedback loop with nonlinear interactions. In this work we present a computational bifurcation analysis of the mathematical model of the repressilator. We show that the steady state undergoes a transition from stable to unstable giving rise to a stable limit-cycle in a Hopf bifurcation. The nonlinear analysis involves a center manifold reduction on the six-dimensional system, which yields closed form expressions for the frequency and amplitude of the oscillation born at the Hopf. A parameter study then shows how the dynamics of the system are influenced for different parameter values and their associated biological significance.
基金This paper is dedicated to the inauguration of the Centro de Modelamiento Matematico Carlos Castillo-Chavez at Universidad Francisco Gavidia in San Salvador,El SalvadorThis project has been partially supported by grants from the National Science Foundation(DMS-1263374 and DUE-1101782),the National Security Agency(H98230-14-1-0157)the Office of the President of ASU,and the Office of the Provost of ASU.The views expressed are sole responsibility of the authors and not the funding agencies.
文摘In November 2015,El Salvador reported their first case of Zika virus(ZIKV)infection,an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two months.National agencies began implementing control measures that included vector control and recommending an increased use of repellents.Further,in response to the alarming and growing number of microcephaly cases in Brazil,the importance of avoiding pregnancies for two years was stressed.In this paper,we explore the role of mobility within communities characterized by extreme poverty,crime and violence.Specifically,the role of short term mobility between two idealized interconnected highly distinct communities is explored in the context of ZIKV outbreaks.We make use of a Lagrangian modeling approach within a two-patch setting in order to highlight the possible effects that short-term mobility,within highly distinct environments,may have on the dynamics of ZIKV outbreak when the overall goal is to reduce the number of cases not just in the most affluent areas but everywhere.Outcomes depend on existing mobility patterns,levels of disease risk,and the ability of federal or state public health services to invest in resource limited areas,particularly in those where violence is systemic.The results of simulations in highly polarized and simplified scenarios are used to assess the role of mobility.It quickly became evident that matching observed patterns of ZIKV outbreaks could not be captured without incorporating increasing levels of heterogeneity.The number of distinct patches and variations on patch connectivity structure required to match ZIKV patterns could not be met within the highly aggregated model that is used in the simulations.
