To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Le...To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed.At first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions.Then the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested.Next,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked.At last,the correctness of the analytical results is verified by numerical simulations.展开更多
Due to the fact that the emergency medicine distribution is vital to the quick response to urgent demand when an epidemic occurs, the optimal vaccine distribution approach is explored according to the epidemic diffusi...Due to the fact that the emergency medicine distribution is vital to the quick response to urgent demand when an epidemic occurs, the optimal vaccine distribution approach is explored according to the epidemic diffusion rule and different urgency degrees of affected areas with the background of the epidemic outbreak in a given region. First, the SIQR （susceptible, infected, quarantined,recovered） epidemic model with pulse vaccination is introduced to describe the epidemic diffusion rule and obtain the demanded vaccine in each pulse. Based on the SIQR model, the affected areas are clustered by using the self-organizing map （SOM） neutral network to qualify the results. Then, a dynamic vaccine distribution model is formulated, incorporating the results of clustering the affected areas with the goals of both reducing the transportation cost and decreasing the unsatisfied demand for the emergency logistics network. Numerical study with twenty affected areas and four distribution centers is carried out. The corresponding numerical results indicate that the proposed approach can make an outstanding contribution to controlling the affected areas with a relatively high degree of urgency, and the comparison results prove that the performance of the clustering method is superior to that of the non-clustering method on controlling epidemic diffusion.展开更多
COVID-19 epidemic is declared as the public health emergency of international concern by the World Health Organisation in the last week of March 2020.This disease originated from China in December 2019 has already cau...COVID-19 epidemic is declared as the public health emergency of international concern by the World Health Organisation in the last week of March 2020.This disease originated from China in December 2019 has already caused havoc around the world,including India.The first case in India was reported on 30th January 2020,with the cases crossing 4 million on the day paper was written.This pandemic has caused more than 80,000 fatalities with 3 million recoveries.Strict lockdown of the nation for two months,immediate isolation of infected cases and app-based tracing of infected are some of the proactive steps taken by the authorities.For a better understanding of the evolution of COVID-19 in the world,study on evolution and growth of cases in India could not be avoided.To understand the same,one of the compartment model:Susceptible-Infectious-Quarantined-Recovered(SIQR)is used.Recovery rate and doubling rate of the total reported positive cases in the country had crossed 75%and 25 days,respectively.It is also estimated that there is a strong positive correlation between testing rate and detection of new cases up to 6 million tests per day.Using the SIQR modelling effective reproduction number,epidemic doubling rate and infected to quarantined ratio is determined to check the temporal evolution of the pandemic in the country.Effective reproduction number that was at its peak during first half of the April is gradually converging to 1.It is also estimated using this model that with each detected cases in India,there could be 10-50 undetected cases.Like every mathematical model,this model also has some assumptions.To make this model more robust,a technique with weighted parameter that can avoid a person with a strong immune system to be equally vulnerable to the infection,can be worked out.Machine learning algorithms can also be used to train our model with the data of other countries to make the analysis and prediction more precise and accurate.展开更多
The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compart...The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compartments;susceptible individuals(S),infected individuals at large(I),quarantined patients(Q)and recovered individuals(R),and the time evolution of the pandemic is described by a set of ordinary differential equations.It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases,from which the number of infected individuals can be estimated.The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government.The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR(Polymerase Chain Reaction)testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population.An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.展开更多
基金supported by the Natural Science Foundation of Ningxia(Grant 2021AAC03030).
文摘To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed.At first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions.Then the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested.Next,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked.At last,the correctness of the analytical results is verified by numerical simulations.
基金The National Natural Science Foundation of China (No.70671021)
文摘Due to the fact that the emergency medicine distribution is vital to the quick response to urgent demand when an epidemic occurs, the optimal vaccine distribution approach is explored according to the epidemic diffusion rule and different urgency degrees of affected areas with the background of the epidemic outbreak in a given region. First, the SIQR （susceptible, infected, quarantined,recovered） epidemic model with pulse vaccination is introduced to describe the epidemic diffusion rule and obtain the demanded vaccine in each pulse. Based on the SIQR model, the affected areas are clustered by using the self-organizing map （SOM） neutral network to qualify the results. Then, a dynamic vaccine distribution model is formulated, incorporating the results of clustering the affected areas with the goals of both reducing the transportation cost and decreasing the unsatisfied demand for the emergency logistics network. Numerical study with twenty affected areas and four distribution centers is carried out. The corresponding numerical results indicate that the proposed approach can make an outstanding contribution to controlling the affected areas with a relatively high degree of urgency, and the comparison results prove that the performance of the clustering method is superior to that of the non-clustering method on controlling epidemic diffusion.
文摘COVID-19 epidemic is declared as the public health emergency of international concern by the World Health Organisation in the last week of March 2020.This disease originated from China in December 2019 has already caused havoc around the world,including India.The first case in India was reported on 30th January 2020,with the cases crossing 4 million on the day paper was written.This pandemic has caused more than 80,000 fatalities with 3 million recoveries.Strict lockdown of the nation for two months,immediate isolation of infected cases and app-based tracing of infected are some of the proactive steps taken by the authorities.For a better understanding of the evolution of COVID-19 in the world,study on evolution and growth of cases in India could not be avoided.To understand the same,one of the compartment model:Susceptible-Infectious-Quarantined-Recovered(SIQR)is used.Recovery rate and doubling rate of the total reported positive cases in the country had crossed 75%and 25 days,respectively.It is also estimated that there is a strong positive correlation between testing rate and detection of new cases up to 6 million tests per day.Using the SIQR modelling effective reproduction number,epidemic doubling rate and infected to quarantined ratio is determined to check the temporal evolution of the pandemic in the country.Effective reproduction number that was at its peak during first half of the April is gradually converging to 1.It is also estimated using this model that with each detected cases in India,there could be 10-50 undetected cases.Like every mathematical model,this model also has some assumptions.To make this model more robust,a technique with weighted parameter that can avoid a person with a strong immune system to be equally vulnerable to the infection,can be worked out.Machine learning algorithms can also be used to train our model with the data of other countries to make the analysis and prediction more precise and accurate.
文摘The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compartments;susceptible individuals(S),infected individuals at large(I),quarantined patients(Q)and recovered individuals(R),and the time evolution of the pandemic is described by a set of ordinary differential equations.It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases,from which the number of infected individuals can be estimated.The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government.The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR(Polymerase Chain Reaction)testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population.An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.
