This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic re...This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R0 is derived as a function of the two contact rates?β1?and β2?. There is a disease free equilibrium point (DFE) of our model. When R0 R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.展开更多
The growth of COVID-19 pandemic throughout more than 213 countries around the world have put a lot of pressures on governments and health services to try to stop the rapid expansion of the pandemic.During 2009,H1N1 In...The growth of COVID-19 pandemic throughout more than 213 countries around the world have put a lot of pressures on governments and health services to try to stop the rapid expansion of the pandemic.During 2009,H1N1 Influenza pandemic,statistical and mathematical methods were used to track how the virus spreads around countries.Most of these models that were developed at the beginning of the XXI century are based on the classical susceptible-infected-recovered(SIR)model developed almost a hundred years ago.The evolution of this model allows us to forecast and compute basic and effective reproduction numbers(R_(t) and R_(0)),measures that quantify the epidemic potential of a pathogen and estimates different scenarios.In this study,we present a traditional estimation technique for R_(0) with statistical distributions by best fitting and a Bayesian approach based on continuous feed of prior distributions to obtain posterior distributions and computing real time R_(t).We use data from COVID-19 officially reported cases in Ecuador since the first confirmed case on February 29th.Because of the lack of data,in the case of R_(0) we compare two methods for the estimation of these parameters below exponential growth and maximum likelihood estimation.We do not make any assumption about the evolution of cases due to limited information and we use previous methods to compare scenarios about R_(0) and in the case of R_(t) we used Bayesian inference to model uncertainty in contagious proposing a new modification to the well-known model of Bettencourt and Ribeiro based on a time window of m days to improve estimations.Ecuadorian R_(0) with exponential growth criteria was 3.45 and with the maximum likelihood estimation method was 2.93.The results show that Guayas,Pichincha and Manabíwere the provinces with the highest number of cases due to COVID-19.Some reasons explain the increased transmissibility in these localities:massive events,population density,cities dispersion patterns,and the delayed time of public health actions to contain pandemic.In conclusion,this is a novel approach that allow us to measure infection dynamics and outbreak distribution when not enough detailed data is available.The use of this model can be used to predict pandemic distribution and to implement data-based effective measures.展开更多
Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more ...Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.展开更多
The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as w...The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as well as syntactically, and a unified complete theorem is obtained.展开更多
文摘This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R0 is derived as a function of the two contact rates?β1?and β2?. There is a disease free equilibrium point (DFE) of our model. When R0 R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.
基金The author(s)disclosed receipt the financial support for the research and publication of this article from Universidad de Las Americas through their annual general research projects funds.
文摘The growth of COVID-19 pandemic throughout more than 213 countries around the world have put a lot of pressures on governments and health services to try to stop the rapid expansion of the pandemic.During 2009,H1N1 Influenza pandemic,statistical and mathematical methods were used to track how the virus spreads around countries.Most of these models that were developed at the beginning of the XXI century are based on the classical susceptible-infected-recovered(SIR)model developed almost a hundred years ago.The evolution of this model allows us to forecast and compute basic and effective reproduction numbers(R_(t) and R_(0)),measures that quantify the epidemic potential of a pathogen and estimates different scenarios.In this study,we present a traditional estimation technique for R_(0) with statistical distributions by best fitting and a Bayesian approach based on continuous feed of prior distributions to obtain posterior distributions and computing real time R_(t).We use data from COVID-19 officially reported cases in Ecuador since the first confirmed case on February 29th.Because of the lack of data,in the case of R_(0) we compare two methods for the estimation of these parameters below exponential growth and maximum likelihood estimation.We do not make any assumption about the evolution of cases due to limited information and we use previous methods to compare scenarios about R_(0) and in the case of R_(t) we used Bayesian inference to model uncertainty in contagious proposing a new modification to the well-known model of Bettencourt and Ribeiro based on a time window of m days to improve estimations.Ecuadorian R_(0) with exponential growth criteria was 3.45 and with the maximum likelihood estimation method was 2.93.The results show that Guayas,Pichincha and Manabíwere the provinces with the highest number of cases due to COVID-19.Some reasons explain the increased transmissibility in these localities:massive events,population density,cities dispersion patterns,and the delayed time of public health actions to contain pandemic.In conclusion,this is a novel approach that allow us to measure infection dynamics and outbreak distribution when not enough detailed data is available.The use of this model can be used to predict pandemic distribution and to implement data-based effective measures.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA19070104)13th Five-year Informatization Plan of Chinese Academy of Sciences (XXH13505-06)+1 种基金Foundation for Excellent Youth Scholars of Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences (Y851D41)National Natural Science Foundation of China (41801270)。
文摘Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.
基金supported by the National Natural Science Foundation of China(Grant No.19331010).
文摘The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as well as syntactically, and a unified complete theorem is obtained.
