Permanence and Globally Asymptotic Stability of Cooperative System Incorporating Harvesting

The stability of a kind of cooperative models incorporating harvesting is considered in this paper. By analyzing the characteristic roots of the models and constructing suitable Lyapunov functions, we prove that nonnegative equilibrium points of the models are globally asymptotically stable. Further, the corresponding nonautonomous cooperative models have a unique asymptotically periodic solution, which is uniformly asymptotically stable. An example is given to illustrate the effectiveness of our results.

Effects of NPY Gene on Total Number of Eggs at 300 Days of Age in Donglan Black-bone Chicken

In this study, PCR-RFLP technique was employed to detect the genetic polymorphism of NPY gene and analyze the effects of various genotypes on the total number of eggs at 300 days of age in 135 Donglan black-bone chicken. According to the results, there were three genotypes （AA, AB and BB） of NPYgene in Donglan black-bone chicken group. Different genotypes exhibited significant effects （P 〈 0. 05 ） on the total number of eggs at 300 days of age. The total number of eggs at 300 days of age of AA genotype was significantly higher than that of BB genotype （P 〈 0. 05）. Therefore, the polymorphic site of NPY gene could be used as a candidate molecular marker that affects egg laying in Donglan black-bone chicken.

Effects of Diet with Picria fel-tarrae Lour Particle on the Growth Performance, Blood Biochemical Indexes, Immune and Antioxidant Function of Hongguang Yellow Chickens

[Objectives]To investigate the effect of diet with Picria fel-tarrae Lour particle(PFLp)on growth performance,blood biochemical indexes,immune and antioxidant function of Hongguang yellow chickens(HYC).[Methods]80 HYC in age of 1 d were divided into 4 groups randomly and each group was assigned to 5 replicates with 24 chicks in each replicate.Group A was control group fed only basal diet.Group B,C and D were treatment groups and fed diets with 0.125%,0.25%and 0.50%of PFLp respectively during the trial of 49 d.Serum samples were taken from 10 chicks in each group in the age of 21,35 and 49 d respectively and analyzed for biochemical,immune and antioxidant parameters in blood.[Results]ADG from group C in 21 d was increased significantly than that from group A,B and D(P<0.01),and ADG in 35 d from group C was also significantly greater than that from group A,B and D(P<0.05),but not much difference was found on ADG among the 4 groups in 49 d(P>0.05);ADFI from group C in 35 d was significantly higher than that from group A,B and D(P<0.05).ADFI from group C in 21 and 49 d were also higher than that from group A(P>0.05).FCR from group C in 21 d was much better than that from the other three groups(P<0.01).Death rate of group C was 50 percent lower than group A;There was no difference occurred in serum biochemical and immune parameters among the 4 groups during the trial(P>0.05).However,the T-AOC from group C and D in 21 d was enhanced significantly than that from group A and B(P<0.01),and the one from group C in 35 d was also increased greatly than that from group A,B and D(P<0.05).GSH from group C and D in 21 d was much higher than that from group A and B(P<0.05),and the ones from group C and D in 35 d were also significantly higher than those from group A and B(P<0.01).T-SOD in three stages trended up also in group C and D(P>0.05).[Conclusions]The diet with 0.25%PFLp in 21 and 35 d could dramatically improve the growth performance,significantly increase the antioxidant capacity and effectively reduce death rate.Diet with 0.25%PFLp is the most appropriate among the three different additions.

Effects of Chinese Herbal Medicine Feed Additives on Growth Performance and Dietary Nutrient Metabolism of Black-bone Chickens

[Objectives]To study the effects of Chinese herbal medicine feed additives on the growth performance and dietary nutrient metabolic rate of black-one chickens.[Methods]480 pieces of 1-day-old Donglan Black-bone Chickens were selected and divided into 4 groups,with 6 replicates in each group,with 20 pieces in each replicate.Among them,group A was the control group and was fed the basal diet;the groups B,C,and D were the experimental groups,which were separately supplemented with 0.25%,0.50%and 1.00%of Chinese herbal medicine additives in the basal diet,and the experimental period was 70 d.At the end of the feeding experiment,24 experimental chickens with similar body weight were selected from each group,and the same design of the feeding experiment was used to continue to feed the original diet for the metabolic experiment to determine the nutrient metabolic rate.[Results]Except the 50-70 d stage,the average daily gain(ADG)of group B in other stages was increased by 5.00%-9.15%(P<0.05),and the average body weight of group B at 70 d was also increased by 4.86%(P<0.05);the ADG of group C at 36-49,1-49 and 1-70 d and the average individual weight at 70 d were also higher than that of group A by 5.90%,2.66%,2.68%and 2.57%,respectively(P>0.05);at 36-49 d,the average daily feed intake(ADFI)of group A was higher than that of group B by 6.04%(P<0.01),and was also higher than that of groups C and D by 5.12%and 4.13%(P<0.05),respectively;at 1-49 d,the ADFI of group A was higher than that of group C by 2.86%(P<0.05),and there was no significant difference between the four groups of experimental chickens at each stage(P>0.05);at 22-35 and 1-70 d,the feed to gain ratio(F/G)of group B was 6.32%and 3.41%lower than that of group A(P<0.05),and at 36-49 and 1-49 d,the F/G of group B was even lower;at 36-49 d,the F/G of group C was 10.15%lower than that of group A(P<0.05),and at 1-49 d,it was also lower than that of group A by 5.29%(P<0.01);there was no significant difference between the two groups at other stages.In terms of nutrient metabolism:the three different amounts of this additive have increased the metabolic rate of DM,CP,CF,NFE,CA,Ca,P,TE and other nutrients in the diet to varying degrees,especially the addition of 0.25%and 0.50%had the significant increase.[Conclusions]The addition of 0.25%Chinese herbal medicine additives in the diet can significantly improve the growth performance and main nutrient metabolic rate of Donglan Black-bone Chickens.

Study on the COVID-19 epidemic in China's Mainland between November 2022 and January 2023,with prediction of its tendency

The prediction system EpiSIX was used to study the COVID-19 epidemic in China's Mainland between November 2022 and January 2023,based on reported data from December 9,2022,to January 30,2023,released by The Chinese Center for Disease Control and Prevention on February 1,2023.Three kinds of reported data were used for model fitting:the daily numbers of positive nucleic acid tests and deaths,and the daily number of hospital beds taken by COVID-19 patients.It was estimated that the overall infection rate was 87.54%and the overall case fatality rate was 0.078%–0.116%(median 0.100%).Assuming that a new COVID-19 epidemic outbreak would start in March or April of 2023,induced by a slightly more infectious mutant strain,we predicted a possible large rebound between September and October 2023,with a peak demand of between 800,000 and 900,000 inpatient beds.If no such new outbreak was induced by other variants,then the current COVID-19 epidemic course in China's Mainland would remain under control until the end of 2023.However,it is suggested that the necessary medical resources be prepared to manage possible COVID-19 epidemic emergencies in the near future,especially for the period between September and October 2023.

COVID-19 transmission driven by age-group mathematical model in Shijiazhuang City of China

Background:A COVID-19 outbreak in the rural areas of Shijiazhuang City was attributed to the complex interactions among vaccination,host,and non-pharmaceutical interventions(NPIs).Herein,we investigated the epidemiological characteristics of all reported symptomatic cases by picking Shijiazhuang City,Hebei Province in Northern China as research objective.In addition,we established an age-group mathematical model to perform the optimal fitting and to investigate the dynamical profiles under three scenarios.Methods:All reported symptomatic cases of Shijiazhuang epidemic(January 2-February 3,2021)were investigated in our study.The cases were classified by gender,age group and location,the distributions were analyzed by epidemiological characteristics.Furthermore,the reported data from Health Commission of Hebei Province was also analyzed by using an age-group mathematical model by two phases and three scenarios.Results:Shijiazhuang epidemic caused by SARS-CoV-2 wild strain was recorded with the peak 84 cases out of 868 reported symptomatic cases on January 11,2021,which was implemented with strong NPIs by local government and referred as baseline situation in this study.The research results showed that R0 under baseline situation ranged from 4.47 to 7.72,and Rt of Gaocheng Distinct took 3.72 with 95%confidence interval from 3.23 to 4.35 on January 9,the declining tendencies of Rt under baseline situation were kept till February 3,the value of Rt reached below 1 on January 19 and remained low value up to February 3 for Gaocheng District and Shijiazhuang City during Shijiazhuang epidemic.This indicated Shijiazhuang epidemic was under control on January 19.However,if the strong NPIs were kept,but remote isolation operated on January 11 was not implemented as of February 9,then the scale of Shijiazhuang epidemic reached 9,482 cases from age group who were 60 years old and over out of 31,017 symptomatic cases.The investigation also revealed that Shijiazhuang epidemic reached 132,648 symptomatic cases for age group who were 60 years old and over(short for G2)under risk-based strategies(Scenario A),58,048 symptomatic cases for G2 under late quarantine strategies(Scenario B)and 207,124 symptomatic cases for G2 under late quarantine double risk strategies(Scenario C),and that the corresponding transmission tendencies of Rt for three scenarios were consistently controlled on Jan 29,2021.Compared with baseline situation,the dates for controlling Rt below 1 under three scenarios were delayed 10 days.Conclusions:Shijiazhuang epidemic was the first COVID-19 outbreak in the rural areas in Hebei Province of Northern China.The targeted interventions adopted in early 2021 were effective to halt the transmission due to the implementation of a strict and village-wide closure.However we found that age group profile and NPIs played critical rules to successfully contain Shijiazhuang epidemic,which should be considered by public health policies in rural areas of China's Mainland during the dynamic zero-COVID policy.

Oscillation characteristics of summer precipitation in the Huaihe River valley and relevant climate background

Based on the summer precipitation data from the Huaihe River valley and the middle and lower reaches of the Yangtze River from 1922 to 2007,we analyzed the interannual and interdecadal oscillation and probability distribution characteristics of summer precipitation in the Huaihe River valley during the same period,using the wavelet transform and generalized extreme distribution methods.Whereby,we studied the climate background of East Asia Summer Monsoon (EASM),Sea Surface Temperature (SST),East Asia telecorrelation circulation,and their relationship with the interannual and interdecadal oscillation of summer precipitation in the Huaihe River valley.We further compared the difference of interdecadal oscillation of summer precipitation and the relevant climate background between the Huaihe River valley and the middle and lower reaches of the Yangtze River.The results show that:1) The intensity change of quasi-biennial oscillation (QBO) of summer precipitation in the Huaihe River valley is consistent with that of interdecadal oscillation.The summer precipitation in the Huaihe River valley has been more than normal since the end of the 1990s,and the QBO is very significant.Meanwhile,the probability of occurrence of extreme heavy rainfall increased obviously.2) The interdecadal oscillation of summer precipitation in the Huaihe River valley has a close relationship with the Pacific Decadal Oscillation (PDO) and interdecadal oscillation of EASM.When PDO is in the cold phase and EASM weakens,the summer precipitation will be greater than normal.3) QBO of summer precipitation in the Huaihe River valley is mainly controlled by that of EASM,and it has a relationship with a circulation pattern of "positive-negative-positive" from the high to the low latitudes in East Asia.4) There is interdecadal phase difference in summer precipitation between the Huaihe River valley and the middle and the lower reaches of the Yangtze River,which is mainly related to the intensity and position of West Pacific subtropical high.

Study on a susceptible—infec ted—vaccina ted model with delay and proportional vaccination

A susceptible-infected-vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper C2-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator R0< 1. Further, if R0> 1, then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator R0> 1.

Study and prediction of the 2022 global monkeypox epidemic

The World Health Organization(WHO)declared monkeypox as a public health emergency of international concern(PHEIC)on July 23,2022,their highest level of alert.This raised concerns about the management of the global monkeypox outbreak,as well as the scientific analysis and accurate prediction of the future course of the epidemic.This study used EpiSIX(an analysis and prediction system for epidemics based on a general SEIR model)to analyze the monkeypox epidemic and to forecast the major tendencies based on data from the USA CDC(https://www.cdc.gov)and the WHO(https://www.who.int/health-topics/monkeypox).The global outbreak of monkeypox started in the UK on May 2,2022,which marked the beginning of an epidemic wave.As of October 28,2022,the cumulative number of reported cases worldwide was 77,115,with 36 deaths.EpiSIX simulations predict that the global monkeypox epidemic will enter a low epidemic status on March 1,2023 with the cumulative number of confirmed cases ranging from 85,000 to 124,000,and the total number of deaths ranging from 60 to 87.Our analysis revealed that the basic reproduction number(R0)of monkeypox virus(MPXV)is near to 3.1 and the percentage of asymptomatic individuals is 13.1%–14.5%,both of which are similar to the data for SARS.The vaccination efficiency against susceptibility(VEs)of individuals who have had monkeypox is~79%,and the vaccination efficiency against infectiousness(VEi)of individuals who have had monkeypox is~76%–82%.The mean incubation period for monkeypox is 8 days.In total,94.7%of infected individuals develop symptoms within 20 days and recover within 2 weeks after the confirmation of symptoms.Simulation results using EpiSIX showed that ring vaccination was remarkably effective against monkeypox.Our findings confirmed that a 20-day isolation for close contacts is necessary.

EFFECTS OF MEDIA COVERAGE AND TEMPORARY IMMUNITY TO A STOCHASTIC SEIR EPIDEMIC MODEL

A type of SEIR epidemic model with media coverage and temporary immunity is investigated in this paper. The existence and uniqueness of the global positive solution with any positive initial value is proved. Under the condition R0s> 1, we prove that the disease is persistent in the mean for a long run. Furthermore, by constructing suitable Lyapunov functions, some sufficient conditions that guarantee the existence of stationary distribution are derived. We also obtain that, if the condition R0e< 1 is satisfied, then the disease is extinct with an exponential rate. As a consequence, some examples and numerical simulation are demonstrated to show the validity and feasibility of the theoretical results.

Globally asymptotic stability of a predator-prey model with stage structure incorporating prey refuge

This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.

EFFECTS OF A TOXICANT ON A SINGLE-SPECIES POPULATION WITH PARTIAL POLLUTION TOLERANCE IN A POLLUTED ENVIRONMENT

We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. The model consists of three ordinary differential equations： one for the population density, one for the amount of toxicant inside the living organisms, and one for the amount of toxicant in the environment. We derive sufficient conditions for the persistence and the extinction of the population depending on the exogenous input rate of the toxicant into the environment and the level of pollution tolerance of the organisms. Numerical simulations are carried out to illustrate our main results.

LONG-TERM DYNAMIC ANALYSIS OF ENDANGERED SPECIES WITH STAGE-STRUCTURE AND MIGRATIONS IN POLLUTED ENVIRONMENTS

We propose a stochastic stage-structured single-species model with migrations and hunting within a polluted environment,where the species is separated into two groups:the immature and the mature,which migrates from one patch to another with different migration rates.By constructing a Lyapunov function,together with stochastic analysis approach,the stochastic single-species model admits a unique global positive solution.We then utilize the comparison theorem of stochastic differential equations to investigate the extinction and persistence of solution to stochastic single-species model.The main results indicate that the species densities all depend on the intensities of random perturbations within both patches.As a consequence,we further provide several strategies for protecting endangered species within protected and unprotected patches.

ANALYSIS OF AN EPIDEMIC MODEL WITH CROWLEY-MARTIN INCIDENCE RATE AND HOLLING TYPE Ⅱ TREATMENT

We propose an epidemic model consisting five compartments within a total population with Crowley-Martin incidence rate and Holling type Ⅱ treatment,where total population is separated by the susceptible, the vaccinated, the exposed, the infected and the removed in this paper. We firstly prove that the epidemic model admits a unique global positive solution by contradiction. We then find out that diseases tend to extinction provided that the basic reproduction number is less than one. Moreover, the sufficient conditions of persistence for infectious diseases are obtained by constructing suitable Lyapunov functions.

DYNAMICAL ANALYSIS OF A SINGLE-SPECIES POPULATION MODEL WITH MIGRATIONS AND HARVEST BETWEEN PATCHES

A single-species population model with migrations and harvest between the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the equilibria. The research points out, under some suitable conditions, the singlespecies population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally asymptotically stable when the harvesting rate exceeds the threshold. Further, we discuss the practical effects of the protection zones and the harvest. The main results indicate that the protective zones indeed eliminate the extinction of the species under some cases, and the theoretical threshold of harvest to the practical management of the endangered species is provided as well. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

PERSISTENCE AND EXTINCTION OF A STOCHASTIC SIS EPIDEMIC MODEL WITH DOUBLE EPIDEMIC HYPOTHESIS

In this paper, we aim at dynamical behaviors of a stochastic SIS epidemic model with double epidemic hypothesis. Sufficient conditions for the extinction and persistence in mean are derived via constructing suitable functions. We obtain a threshold of stochastic SIS epidemic model, which determines how the diseases spread when the white noises are small. Numerical simulations are used to illustrate the efficiency of the main results of this article.

ANALYSIS OF A SUSCEPTIBLE-EXPOSEDINFECTED EPIDEMIC MODEL WITH RANDOM PERTURBATION AND VARYING POPULATION SIZE

In this paper, we study a type of susceptible-exposed-infected（SEI） epidemic model with varying population size and introduce the random perturbation of the constant contact rate into the SEI epidemic model due to the universal existence of fluctuations. Under some moderate conditions, the density of the exposed and the infected individuals exponentially approaches zero almost surely are derived. Furthermore, the stochastic SEI epidemic model admits a stationary distribution around the endemic equilibrium, and the solution is ergodic. Some numerical simulations are carried out to demonstrate the efficiency of the main results.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A BACKWARD STOCHASTIC DIFFERENTIAL EQUATION

A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.

Dynamic evolution of an SVEIR model with variants and non-pharmaceutical interventions for controlling COVID-19

The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant,host,and non-pharmaceutical interventions(NPIs).All reported cases in the Putian epidemic(September 8–October 2,2021,Delta variant B.1.617.2)and Fuzhou epidemic(October 22–November 18,2022,Omicron variant BA.5.2)were classified by sex,age group,occupation,and location in this study.Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention,we established a virus-oriented SVEIR(Susceptible–Vaccinated–Exposed–Infected–Recovered)model to investigate the dynamic evolution features of these two variants and the effects of NPIs.The optimal simulations were carried out with variants and scenario investigations.The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19,and that the Omicron variant was more infectious than the Delta variant.Moreover,the dynamic investigations revealed the increasing tendencies from Delta to Omicron,such as the basic reproduction number,infection rate,percentage of high-risk cases,and the growth rate.Decreasing tendencies were also identified,such as the average recovery period,the awareness delay,and the percentage of symptomatic cases.This study highlighted that NPIs played critical roles in successfully containing the two epidemics.Such interventions are strongly recommended to public health policymakers.