Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartmen...We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.展开更多
Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction...Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction number of general population epidemic model is obtained.Based on the epidemic model of general population,the epidemic model of general population and college population is further established,and the control reproduction number is also obtained.Methods For the established epidemic model,firstly,the expression of the control reproduc-tion number is obtained by using the next generation matrix.Secondly,the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model,and the parameters in the model are estimated by least square method and MCMC.Thirdly,the Latin hypercube sampling method and partial rank correlation coefficient(PRCC)are adopted to analyze the sensitivity of the model.Conclusions The control reproduction number remained at 3 from January 23 to January 31,then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China.In order to further control the spread of the epidemic,the following measures can be taken:(i)reducing infection by wearing masks,paying attention to personal hygiene and limiting travel;(i)improving isolation of suspected patients and treatment of symptomatic individuals.In particular,the epidemic model of the collge population and the general population is estab-lished,and the control reproduction number is given,which will provide theoretical basis for the prevention and control of the epidemic in the colleges.展开更多
We reexamined sexual dimorphism and female reproduction in the Many-Lined Sun Skink Eutropis multifasciata from Hainan,China. Our data confirm that adults are sexually dimorphic in body size and shape,with males being...We reexamined sexual dimorphism and female reproduction in the Many-Lined Sun Skink Eutropis multifasciata from Hainan,China. Our data confirm that adults are sexually dimorphic in body size and shape,with males being the larger sex and larger in head size but shorter in abdomen length than females of the same snoutvent length(SVL). The rate at which head width increased with SVL was greater in males as opposed to the previous conclusion that the rate does not differ between the sexes. Maternal size was the main determinant of reproductive investment,with larger females generally producing more,as well as larger,offspring. Females produced up to nine offspring per litter as opposed to the previously reported 2–7. Most females gave birth between March and August,a time period approximately four months longer than that(May–June) reported previously. Females with a higher fecundity tended to produce smaller offspring as opposed to the previous conclusion that females do not tradeoff offspring size against number. Litter size,neonate mass and litter mass remained remarkably constant among years,and litter mass was more tightly related to female body size than litter size or neonate mass. Smaller females could produce relatively heavier litters without a concomitant reduction in postpartum body condition.展开更多
We studied relations between natural seedling reproduction and above ground environment in a longleaf pine ecosystem. Forty-eight 0.05 ha circular plots were sampled under single-tree selection, group-tree selection a...We studied relations between natural seedling reproduction and above ground environment in a longleaf pine ecosystem. Forty-eight 0.05 ha circular plots were sampled under single-tree selection, group-tree selection and control stands in three main longleaf pine areas in south Alabama, USA. We measured six above-ground environment factors, viz. canopy closure, stand density, basal area, average tree height, understory cover and PAR under canopy. We employed forward, back-ward and stepwise selection regression to produce one model. Three main variables：canopy closure, stand density and basal area, were left in the model; light, PAR and understory cover were not incorporated into the model at the 0.10 significance level. Basal area was a positive pa-rameter, while canopy closure and stand density were negative parame-ters. Canopy closure was the main parameter in the model. The model proved to be meaningful, and has potential to provide useful guidance for future work.展开更多
This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delay...This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.展开更多
This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was ...This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.展开更多
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
基金The work has been supported by a grant received from the Ministry of Education,Government of India under the Scheme for the Promotion of Academic and Research Collaboration(SPARC)(ID:SPARC/2019/1396).
文摘We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.
基金Supported by the Fundamental Research Funds for the Central Universities,CHD(300102129201)the Nat ural Science Basic Research Plan in Shaanxi Province of China(2018JM1011)the National Natural Science Foundation of China(11701041)。
文摘Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction number of general population epidemic model is obtained.Based on the epidemic model of general population,the epidemic model of general population and college population is further established,and the control reproduction number is also obtained.Methods For the established epidemic model,firstly,the expression of the control reproduc-tion number is obtained by using the next generation matrix.Secondly,the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model,and the parameters in the model are estimated by least square method and MCMC.Thirdly,the Latin hypercube sampling method and partial rank correlation coefficient(PRCC)are adopted to analyze the sensitivity of the model.Conclusions The control reproduction number remained at 3 from January 23 to January 31,then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China.In order to further control the spread of the epidemic,the following measures can be taken:(i)reducing infection by wearing masks,paying attention to personal hygiene and limiting travel;(i)improving isolation of suspected patients and treatment of symptomatic individuals.In particular,the epidemic model of the collge population and the general population is estab-lished,and the control reproduction number is given,which will provide theoretical basis for the prevention and control of the epidemic in the colleges.
基金Acknowledgements This work was assisted through participation in ＂Optimal Control and Optimization for Individual- based and Agent-based Models＂ Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.
基金supported by the grants from the National Natural Science Foundation of China (30670281 and 31060064)the Priority Academic Program Development of Jiangsu Higher Education Institutions (CXLX11_0885)the Hainan Key Program of Science and Technology (ZDXM20110008)
文摘We reexamined sexual dimorphism and female reproduction in the Many-Lined Sun Skink Eutropis multifasciata from Hainan,China. Our data confirm that adults are sexually dimorphic in body size and shape,with males being the larger sex and larger in head size but shorter in abdomen length than females of the same snoutvent length(SVL). The rate at which head width increased with SVL was greater in males as opposed to the previous conclusion that the rate does not differ between the sexes. Maternal size was the main determinant of reproductive investment,with larger females generally producing more,as well as larger,offspring. Females produced up to nine offspring per litter as opposed to the previously reported 2–7. Most females gave birth between March and August,a time period approximately four months longer than that(May–June) reported previously. Females with a higher fecundity tended to produce smaller offspring as opposed to the previous conclusion that females do not tradeoff offspring size against number. Litter size,neonate mass and litter mass remained remarkably constant among years,and litter mass was more tightly related to female body size than litter size or neonate mass. Smaller females could produce relatively heavier litters without a concomitant reduction in postpartum body condition.
文摘We studied relations between natural seedling reproduction and above ground environment in a longleaf pine ecosystem. Forty-eight 0.05 ha circular plots were sampled under single-tree selection, group-tree selection and control stands in three main longleaf pine areas in south Alabama, USA. We measured six above-ground environment factors, viz. canopy closure, stand density, basal area, average tree height, understory cover and PAR under canopy. We employed forward, back-ward and stepwise selection regression to produce one model. Three main variables：canopy closure, stand density and basal area, were left in the model; light, PAR and understory cover were not incorporated into the model at the 0.10 significance level. Basal area was a positive pa-rameter, while canopy closure and stand density were negative parame-ters. Canopy closure was the main parameter in the model. The model proved to be meaningful, and has potential to provide useful guidance for future work.
基金supported via funding from Prince Sattam bin Abdulaziz University Project Number(PSAU/2023/R/1444)The first author is partially supported by the University Research Fellowship(PU/AD-3/URF/21F37237/2021 dated 09.11.2021)of PeriyarUniversity,SalemThe second author is supported by the fund for improvement of Science and Technology Infrastructure(FIST)of DST(SR/FST/MSI-115/2016).
文摘This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62266030 and 61863025)International S & T Cooperation Projects of Gansu province (Grant No.144WCGA166)Longyuan Young Innovation Talents and the Doctoral Foundation of LUT。
文摘This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.
