To evaluate the HIV pandemic in Chongqing,the pooled PCR,Ig G‐capture BED enzyme immunoassay(BED‐CEIA),and cohort observations were used to estimate the HIV incidences among men who have sex with men(MSM).617 MSM su...To evaluate the HIV pandemic in Chongqing,the pooled PCR,Ig G‐capture BED enzyme immunoassay(BED‐CEIA),and cohort observations were used to estimate the HIV incidences among men who have sex with men(MSM).617 MSM subjects completed the survey at a voluntary counseling and testing(VCT)site.The observed HIV incidence was 12.5 per 100 P‐Ys(95%CI=9.1‐15.7).The annual acute HIV infection(AHI)incidence estimated by pooled PCR was 14.展开更多
A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium ...A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
Background: This study aimed to identify the role of human development index (HDI) in the incidence and mortality rates of breast cancer (BC) worldwide. Methods: Data on the age-standardized incidence and mortality ra...Background: This study aimed to identify the role of human development index (HDI) in the incidence and mortality rates of breast cancer (BC) worldwide. Methods: Data on the age-standardized incidence and mortality rates of BC for 184 countries were obtained from the GLOBOCAN. Data about the HDI and other indices were obtained from the World Bank Report 2013. Linear regression model was used for assessment the effect of HDI on BC occurrence rates. Results: In 2012, BCs were estimated to have affected a total of 1,671,149 individuals (crude rate: 47.8 per 100,000 individuals), and caused 521,907 deaths worldwide (crude rate: 14.7 per 100,000 individuals). Nearly half of total female BC cases (46.3%) with the highest risk of incidence (age-standardized Rate (ASR): 128 per 100,000) had occurred in very high HDI regions. The most proportion of the mortality burden was in low HDI and medium HDI areas. Linear regression analyses showed a direct significant correlation between the incidence of BC and HDI at the global level (B = 104.5, P < 0.001). The mortality rate of BC was not significantly associated with HDI (B = 3.26, P = 0.160). Conclusion: Our study showed that the burden of female BC is enormous in very high HDI and low HID regions. Targeted interventions have the ability to reduce this number significantly through resource-dependent interventions. Moreover, further reductions in mortality could be brought about by increasing access to curative treatment for patients with BC.展开更多
在这份报纸，我们涉及反应 -- 有在一个连续围住的空间领域的非线性的发生率和非局部的延期效果的散开先生流行模型。我们由下一代操作员的想法介绍模型的基本繁殖号码 R <sub>0</sub> 。借助于动态系统和一致坚持的理论，...在这份报纸，我们涉及反应 -- 有在一个连续围住的空间领域的非线性的发生率和非局部的延期效果的散开先生流行模型。我们由下一代操作员的想法介绍模型的基本繁殖号码 R <sub>0</sub> 。借助于动态系统和一致坚持的理论，我们以 R <sub>0</sub> 调查模型的全球动力学。最后，我们实现数字模拟显示出我们的结果的可行性并且探索一些流行病学的卓见。展开更多
In this paper,a reaction-diffusion SEI epidemic model with nonlinear incidence rate is proposed.The well-posedness of solutions is studied,including the existence of positive and unique classical solution and the exis...In this paper,a reaction-diffusion SEI epidemic model with nonlinear incidence rate is proposed.The well-posedness of solutions is studied,including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions.The basic reproduction numbers are given in both heterogeneous and homogeneous environments.For spatially heterogeneous environment,by the comparison principle of the diffusion system,the infection-free steady state is proved to be globally asymptotically stable if R_(0)<1,if R_(0)>1,the system will be persistent and admit at least one positive steady state.For spatially homogenous environment,by constructing a Lyapunov function,the infect ion-free steady state is proved to be globally asymptotically stable if,R_(0)<1,and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if R_(0)>1.Finally,two examples are given via numerical simulations,and then some control strategies are also presented by the sensitive analysis.展开更多
In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqu...In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.展开更多
In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individual...In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individuals after detection, and separation of somesusceptible individuals from the rest to avoid the infection, without an increase in thenumber of classes. We find that the system has a unique disease-free equilibrium (DFE)which is locally asymptotically stable when the reproduction number is less than unity.The multiple endemic equilibria may exist irrespective of the basic reproduction number.The existence of bistability is encountered. Supercritical transcritical (forward), as wellas subcritical transcritical (backward) bifurcation, may occur at R0 = 1 where contactrate, β = β∗ acts as the bifurcation parameter. Therefore, DFE need not be globallystable. The conditions for the existence of Andronov–Hopf bifurcation are deduced withmaximum treatment capacity, c = c0 as the bifurcation parameter. The impacts of isolation of confirmed infected cases and separation of some susceptible from rest are studiednumerically as well as the effect of saturation in treatment. The existence of chaoticbehavior is deduced by showing the maximum Lyapunov exponent to be positive as wellas the sensitivity to initial conditions. The computation of the Kalpan–Yorke dimensionto be fractional confirms the existence of fractal-type strange attractor. The positiveKolmogorov–Sinai entropy further strengthens the claim of the existence of chaos.展开更多
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 vaccinat...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.展开更多
Bovine tuberculosis(bTB)is a chronic zoonotic disease that is endemic in China.Current in-vitro tests for bTB are mainly based on blood assays.Collection of samples results in some stress to the sampled cattle and ass...Bovine tuberculosis(bTB)is a chronic zoonotic disease that is endemic in China.Current in-vitro tests for bTB are mainly based on blood assays.Collection of samples results in some stress to the sampled cattle and associated economic losses for the herd owner.This study was designed to investigate the relationship between milk and serum antibody tests for bTB in dairy cows using 85 cows with milk and corresponding blood samples.Totally 4,395 milk samples were used to assesse the apparent(test)prevalence and incidence of bTB using the milk antibody ELISA.The association between levels of bTB milk antibody and milk quality was also evaluated.Milk and serum antibody tests showed a good correlation with a 87.5%(95%CI:61.7%,98.4)positive agreement and 98.7%(95%CI:95.4,99.8)negative agreement.The animal level lactoprevalence ranged from 0.3%(95%CI:0,1.2)to 33.3%(95%CI:26.6,40.6)in different farms and the incidence rate ranged from 0 head/cow-month(95%CI:0,0.02)to 0.04 head/cow-month(95%CI:0.02,0.07).Twenty percent of sampled farms met the criteria for bTB control in China.The prevalence on large-scale farms was lower(p<0.001)than on small farms.The bTB milk antibody levels had a negative correlation with milk yield and a positive correlation with somatic cell count(SCC),milk protein percentage(MPP)and percentage of total solids(TS).According to this research,milk ELISA could be used as a supplement of blood samples to assist in the surveillance for bTB and for alerting control and eradication of bTB.展开更多
This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz crit...This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .展开更多
This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. ...This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
Objective: To predict the daily incidence and fatality rates based on long short-term memory(LSTM) in 4 age groups of COVID-19 patients in Mazandaran Province, Iran.Methods: To predict the daily incidence and fatality...Objective: To predict the daily incidence and fatality rates based on long short-term memory(LSTM) in 4 age groups of COVID-19 patients in Mazandaran Province, Iran.Methods: To predict the daily incidence and fatality rates by age groups, this epidemiological study was conducted based on the LSTM model. All data of COVID-19 disease were collected daily for training the LSTM model from February 22, 2020 to April 10, 2021 in the Mazandaran University of Medical Sciences. We defined 4 age groups, i.e., patients under 29, between 30 and 49, between 50 and 59, and over 60 years old. Then, LSTM models were applied to predict the trend of daily incidence and fatality rates from 14 to 40 days in different age groups. The results of different methods were compared with each other.Results: This study evaluated 5 0826 patients and 5 109 deaths with COVID-19 daily in 20 cities of Mazandaran Province. Among the patients, 25 240 were females(49.7%), and 25 586 were males(50.3%). The predicted daily incidence rates on April 11, 2021 were 91.76, 155.84, 150.03, and 325.99 per 100 000 people, respectively;for the fourteenth day April 24, 2021, the predicted daily incidence rates were 35.91, 92.90, 83.74, and 225.68 in each group per 100 000 people. Furthermore, the predicted average daily incidence rates in 40 days for the 4 age groups were 34.25, 95.68, 76.43, and 210.80 per 100 000 people, and the daily fatality rates were 8.38, 4.18, 3.40, 22.53 per 100 000 people according to the established LSTM model. The findings demonstrated the daily incidence and fatality rates of 417.16 and 38.49 per 100 000 people for all age groups over the next 40 days. Conclusions: The results highlighted the proper performance of the LSTM model for predicting the daily incidence and fatality rates. It can clarify the path of spread or decline of the COVID-19 outbreak and the priority of vaccination in age groups.展开更多
In this paper,a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler’s method.The existence and stability of fixed points in this model are well studied....In this paper,a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler’s method.The existence and stability of fixed points in this model are well studied.The center manifold theorem and bifurcation theory are applied to analyze the bifurcation properties by using the discrete time step and the intervention level as control parameters.We discuss in detail some codimension-one bifurcations such as transcritical,period-doubling and Neimark–Sacker bifurcations,and a codimension-two bifurcation with 1:2 resonance.In addition,the phase portraits,bifurcation diagrams and maximum Lyapunov exponent diagrams are drawn to verify the correctness of our theoretical analysis.It is found that the numerical results are consistent with the theoretical analysis.More interestingly,we also found other bifurcations in the model during the numerical simulation,such as codimension-two bifurcations with 1:1 resonance,1:3 resonance and 1:4 resonance,generalized period-doubling and fold-flip bifurcations.The results show that the dynamics of the discrete-time model are richer than that of the continuous-time SIR epidemic model.Such a discrete-time model may not only be widely used to detect the pathogenesis of infectious diseases,but also make a great contribution to the prevention and control of infectious diseases.展开更多
This study aimed to examine the association between the use of H1-antihistamines(AHs)and head and neck cancer(HNC)risk in patients with type 2 diabetes mellitus(T2DM).Data from the National Health Insurance Research D...This study aimed to examine the association between the use of H1-antihistamines(AHs)and head and neck cancer(HNC)risk in patients with type 2 diabetes mellitus(T2DM).Data from the National Health Insurance Research Database of Taiwan were analyzed for the period from 2008 to 2018.A propensity-score-matched cohort of 54,384 patients each in the AH user and nonuser groups was created and analyzed using Kaplan-Meier method and Cox proportional hazards regression.The results showed that the risk of HNC was significantly lower in AH users(adjusted hazard ratio:0.55,95%CI:0.48 to 0.64)and the incidence rate was also lower(5.16 vs.8.10 per 100,000 person-years).The lower HNC incidence rate in AH users(95%CI:0.63;0.55 to 0.73)suggests that AH use may reduce the risk of HNC in T2DM patients.展开更多
Background: The COVID-19 pandemic continues to be a major worldwide health problem. The present study aims to contribute to surveillance of the immune and clinical response of vaccines to SARS-CoV-2. Methods: Observat...Background: The COVID-19 pandemic continues to be a major worldwide health problem. The present study aims to contribute to surveillance of the immune and clinical response of vaccines to SARS-CoV-2. Methods: Observational medication study on acquired immunity and effectiveness of vaccines. Population: 620 workers in the health service of Almansa (Spain). Representative sample of 150 individuals. Sociodemographic, clinical, and epidemiological data and samples were recorded to determine anti-SARS-CoV-2 serum IgG levels 6 and 9 months after vaccination with Pfizer. Results: Mean age 46.45 years;76% women;85.1% working in a hospital. 19.3% had had COVID-19 in the year prior to vaccination. 96.7% were fully vaccinated with Pfizer/BioNTech. At 6 months, 100% seropositivity and mean IgG levels of 3017.2 AU/ml. Significant variations in IgG levels in individuals with prior COVID-19 infection and smokers. At 9 months, 99.3% remained seropositive;2.8% infected after vaccination. The repeated measures analysis showed a difference in means of 669.0 AU/ml (significant decrease in IgG levels of 28.9%). Conclusion: Antibody levels remained positive 6 and 9 months after vaccination, although IgG levels were found to decay.展开更多
This paper presents the mathematical analysis of the dynamical system for avian influenza.The proposed model considers a nonlinear dynamical model of birds and human.The half-saturated incidence rate is used for the t...This paper presents the mathematical analysis of the dynamical system for avian influenza.The proposed model considers a nonlinear dynamical model of birds and human.The half-saturated incidence rate is used for the transmission of avian influenza infection.Rigorous mathematical results are presented for the proposed models.The local and global dynamics of each model are presented and proven that when R0<1,then the disease-free equilibrium of each model is stable both locally and globally,and when R0>1,then the endemic equilibrium is stable both locally and globally.The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.展开更多
Objective:To identify the incidence rate,relative risk,hotspot regions and incidence trend of COVID-19 in Qom province,northwest part of Iran in the first stage of the pandemic.Methods:The study included 1125 official...Objective:To identify the incidence rate,relative risk,hotspot regions and incidence trend of COVID-19 in Qom province,northwest part of Iran in the first stage of the pandemic.Methods:The study included 1125 officially reported PCR-confirmed cases of COVID-19 from 20 February 2020 to 20 April 2020 in 90 regions in Qom city,Iran.The Bayesian hierarchical spatial model was used to model the relative risk of COVID-19 in Qom city,and the segmented regression model was used to estimate the trend of COVID-19 incidence rate.The Poisson distribution was applied for the observed number of COVID-19,and independent Gamma prior was used for inference on log-relative risk parameters of the model.Results:The total incidence rate of COVID-19 was estimated at 89.5 per 100000 persons in Qom city(95%CI:84.3,95.1).According to the results of the Bayesian hierarchical spatial model and posterior probabilities,43.33%of the regions in Qom city have relative risk greater than 1;however,only 11.11%of them were significantly greater than 1.Based on Geographic Information Systems(GIS)spatial analysis,10 spatial clusters were detected as active and emerging hotspot areas in the south and central parts of the city.The downward trend was estimated 10 days after the reporting of the first case(February 7,2020);however,the incidence rate was decreased by an average of 4.24%per day(95%CI:−10.7,−3.5).Conclusions:Spatial clusters with high incidence rates of COVID-19 in Qom city were in the south and central regions due to the high population density.The GIS could depict the spatial hotspot clusters of COVID-19 for timely surveillance and decision-making as a way to contain the disease.展开更多
In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotica...In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.展开更多
基金supported by the Department of Health and Family Counseling,Chongqing[2016HBRC009,2017ZDXM001]
文摘To evaluate the HIV pandemic in Chongqing,the pooled PCR,Ig G‐capture BED enzyme immunoassay(BED‐CEIA),and cohort observations were used to estimate the HIV incidences among men who have sex with men(MSM).617 MSM subjects completed the survey at a voluntary counseling and testing(VCT)site.The observed HIV incidence was 12.5 per 100 P‐Ys(95%CI=9.1‐15.7).The annual acute HIV infection(AHI)incidence estimated by pooled PCR was 14.
文摘A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘Background: This study aimed to identify the role of human development index (HDI) in the incidence and mortality rates of breast cancer (BC) worldwide. Methods: Data on the age-standardized incidence and mortality rates of BC for 184 countries were obtained from the GLOBOCAN. Data about the HDI and other indices were obtained from the World Bank Report 2013. Linear regression model was used for assessment the effect of HDI on BC occurrence rates. Results: In 2012, BCs were estimated to have affected a total of 1,671,149 individuals (crude rate: 47.8 per 100,000 individuals), and caused 521,907 deaths worldwide (crude rate: 14.7 per 100,000 individuals). Nearly half of total female BC cases (46.3%) with the highest risk of incidence (age-standardized Rate (ASR): 128 per 100,000) had occurred in very high HDI regions. The most proportion of the mortality burden was in low HDI and medium HDI areas. Linear regression analyses showed a direct significant correlation between the incidence of BC and HDI at the global level (B = 104.5, P < 0.001). The mortality rate of BC was not significantly associated with HDI (B = 3.26, P = 0.160). Conclusion: Our study showed that the burden of female BC is enormous in very high HDI and low HID regions. Targeted interventions have the ability to reduce this number significantly through resource-dependent interventions. Moreover, further reductions in mortality could be brought about by increasing access to curative treatment for patients with BC.
基金Supported by the Science and Technology Planed Projects of Gansu Province(18JR3RA217)Science Research Foundation for Higher Education Institutions of Gansu Province(2018B-032)
文摘在这份报纸，我们涉及反应 -- 有在一个连续围住的空间领域的非线性的发生率和非局部的延期效果的散开先生流行模型。我们由下一代操作员的想法介绍模型的基本繁殖号码 R <sub>0</sub> 。借助于动态系统和一致坚持的理论，我们以 R <sub>0</sub> 调查模型的全球动力学。最后，我们实现数字模拟显示出我们的结果的可行性并且探索一些流行病学的卓见。
基金supported by the National Natural Science Foundation of China(Grant No.11871475)the Hunan Provincial Innovation Foundation for Postgraduate(Grant No.CX20200096)the Fundamental Research Funds for the Central Universities of Central South University(Grant No.2020zzts024).
文摘In this paper,a reaction-diffusion SEI epidemic model with nonlinear incidence rate is proposed.The well-posedness of solutions is studied,including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions.The basic reproduction numbers are given in both heterogeneous and homogeneous environments.For spatially heterogeneous environment,by the comparison principle of the diffusion system,the infection-free steady state is proved to be globally asymptotically stable if R_(0)<1,if R_(0)>1,the system will be persistent and admit at least one positive steady state.For spatially homogenous environment,by constructing a Lyapunov function,the infect ion-free steady state is proved to be globally asymptotically stable if,R_(0)<1,and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if R_(0)>1.Finally,two examples are given via numerical simulations,and then some control strategies are also presented by the sensitive analysis.
基金This work is supported by the National Natural Science Foundation of China(Nos.12001090 and 11871473)Shandong Provincial Natural Science Foundation(No.ZR2019MA010)the Fundamental Research Funds for the Central Universitiesof China(No.2412020QD024).
文摘In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.
文摘In this paper, we construct an SIR epidemic model with a modified Beddington–DeAngelis type incidence rate and saturated treatment rate. We modify the incidence rateto incorporate the isolation of infected individuals after detection, and separation of somesusceptible individuals from the rest to avoid the infection, without an increase in thenumber of classes. We find that the system has a unique disease-free equilibrium (DFE)which is locally asymptotically stable when the reproduction number is less than unity.The multiple endemic equilibria may exist irrespective of the basic reproduction number.The existence of bistability is encountered. Supercritical transcritical (forward), as wellas subcritical transcritical (backward) bifurcation, may occur at R0 = 1 where contactrate, β = β∗ acts as the bifurcation parameter. Therefore, DFE need not be globallystable. The conditions for the existence of Andronov–Hopf bifurcation are deduced withmaximum treatment capacity, c = c0 as the bifurcation parameter. The impacts of isolation of confirmed infected cases and separation of some susceptible from rest are studiednumerically as well as the effect of saturation in treatment. The existence of chaoticbehavior is deduced by showing the maximum Lyapunov exponent to be positive as wellas the sensitivity to initial conditions. The computation of the Kalpan–Yorke dimensionto be fractional confirms the existence of fractal-type strange attractor. The positiveKolmogorov–Sinai entropy further strengthens the claim of the existence of chaos.
基金supported by NSFC under grants 11201075 and 11601085。
文摘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.
基金the Natural Science Foundation of China(U21A20259)National Key Research and Development Program of Ningxia Hui Autonomous Region(2021BEF02028)+1 种基金the Natural Science Foundation of Hubei Province(2021CFA016)China Agriculture Research System of MOF and MARA and Basic and technical innovation team for prevention and control of bovine disease.
文摘Bovine tuberculosis(bTB)is a chronic zoonotic disease that is endemic in China.Current in-vitro tests for bTB are mainly based on blood assays.Collection of samples results in some stress to the sampled cattle and associated economic losses for the herd owner.This study was designed to investigate the relationship between milk and serum antibody tests for bTB in dairy cows using 85 cows with milk and corresponding blood samples.Totally 4,395 milk samples were used to assesse the apparent(test)prevalence and incidence of bTB using the milk antibody ELISA.The association between levels of bTB milk antibody and milk quality was also evaluated.Milk and serum antibody tests showed a good correlation with a 87.5%(95%CI:61.7%,98.4)positive agreement and 98.7%(95%CI:95.4,99.8)negative agreement.The animal level lactoprevalence ranged from 0.3%(95%CI:0,1.2)to 33.3%(95%CI:26.6,40.6)in different farms and the incidence rate ranged from 0 head/cow-month(95%CI:0,0.02)to 0.04 head/cow-month(95%CI:0.02,0.07).Twenty percent of sampled farms met the criteria for bTB control in China.The prevalence on large-scale farms was lower(p<0.001)than on small farms.The bTB milk antibody levels had a negative correlation with milk yield and a positive correlation with somatic cell count(SCC),milk protein percentage(MPP)and percentage of total solids(TS).According to this research,milk ELISA could be used as a supplement of blood samples to assist in the surveillance for bTB and for alerting control and eradication of bTB.
文摘This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .
文摘This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
文摘Objective: To predict the daily incidence and fatality rates based on long short-term memory(LSTM) in 4 age groups of COVID-19 patients in Mazandaran Province, Iran.Methods: To predict the daily incidence and fatality rates by age groups, this epidemiological study was conducted based on the LSTM model. All data of COVID-19 disease were collected daily for training the LSTM model from February 22, 2020 to April 10, 2021 in the Mazandaran University of Medical Sciences. We defined 4 age groups, i.e., patients under 29, between 30 and 49, between 50 and 59, and over 60 years old. Then, LSTM models were applied to predict the trend of daily incidence and fatality rates from 14 to 40 days in different age groups. The results of different methods were compared with each other.Results: This study evaluated 5 0826 patients and 5 109 deaths with COVID-19 daily in 20 cities of Mazandaran Province. Among the patients, 25 240 were females(49.7%), and 25 586 were males(50.3%). The predicted daily incidence rates on April 11, 2021 were 91.76, 155.84, 150.03, and 325.99 per 100 000 people, respectively;for the fourteenth day April 24, 2021, the predicted daily incidence rates were 35.91, 92.90, 83.74, and 225.68 in each group per 100 000 people. Furthermore, the predicted average daily incidence rates in 40 days for the 4 age groups were 34.25, 95.68, 76.43, and 210.80 per 100 000 people, and the daily fatality rates were 8.38, 4.18, 3.40, 22.53 per 100 000 people according to the established LSTM model. The findings demonstrated the daily incidence and fatality rates of 417.16 and 38.49 per 100 000 people for all age groups over the next 40 days. Conclusions: The results highlighted the proper performance of the LSTM model for predicting the daily incidence and fatality rates. It can clarify the path of spread or decline of the COVID-19 outbreak and the priority of vaccination in age groups.
基金supported by the NSF of Shandong Province(ZR2021MA016,ZR2019MA034,ZR2018BF018)the China Postdoctoral Science Foundation(2019M652349)the Youth Creative Team Sci-Tech Program of Shandong Universities(2019KJI007).
文摘In this paper,a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler’s method.The existence and stability of fixed points in this model are well studied.The center manifold theorem and bifurcation theory are applied to analyze the bifurcation properties by using the discrete time step and the intervention level as control parameters.We discuss in detail some codimension-one bifurcations such as transcritical,period-doubling and Neimark–Sacker bifurcations,and a codimension-two bifurcation with 1:2 resonance.In addition,the phase portraits,bifurcation diagrams and maximum Lyapunov exponent diagrams are drawn to verify the correctness of our theoretical analysis.It is found that the numerical results are consistent with the theoretical analysis.More interestingly,we also found other bifurcations in the model during the numerical simulation,such as codimension-two bifurcations with 1:1 resonance,1:3 resonance and 1:4 resonance,generalized period-doubling and fold-flip bifurcations.The results show that the dynamics of the discrete-time model are richer than that of the continuous-time SIR epidemic model.Such a discrete-time model may not only be widely used to detect the pathogenesis of infectious diseases,but also make a great contribution to the prevention and control of infectious diseases.
基金Lo-Hsu Medical Foundation,LotungPoh-Ai Hospital,supports Szu-Yuan Wu’s work(Funding Numbers:10908,10909,11001,11002,11003,11006,and 11013).
文摘This study aimed to examine the association between the use of H1-antihistamines(AHs)and head and neck cancer(HNC)risk in patients with type 2 diabetes mellitus(T2DM).Data from the National Health Insurance Research Database of Taiwan were analyzed for the period from 2008 to 2018.A propensity-score-matched cohort of 54,384 patients each in the AH user and nonuser groups was created and analyzed using Kaplan-Meier method and Cox proportional hazards regression.The results showed that the risk of HNC was significantly lower in AH users(adjusted hazard ratio:0.55,95%CI:0.48 to 0.64)and the incidence rate was also lower(5.16 vs.8.10 per 100,000 person-years).The lower HNC incidence rate in AH users(95%CI:0.63;0.55 to 0.73)suggests that AH use may reduce the risk of HNC in T2DM patients.
文摘Background: The COVID-19 pandemic continues to be a major worldwide health problem. The present study aims to contribute to surveillance of the immune and clinical response of vaccines to SARS-CoV-2. Methods: Observational medication study on acquired immunity and effectiveness of vaccines. Population: 620 workers in the health service of Almansa (Spain). Representative sample of 150 individuals. Sociodemographic, clinical, and epidemiological data and samples were recorded to determine anti-SARS-CoV-2 serum IgG levels 6 and 9 months after vaccination with Pfizer. Results: Mean age 46.45 years;76% women;85.1% working in a hospital. 19.3% had had COVID-19 in the year prior to vaccination. 96.7% were fully vaccinated with Pfizer/BioNTech. At 6 months, 100% seropositivity and mean IgG levels of 3017.2 AU/ml. Significant variations in IgG levels in individuals with prior COVID-19 infection and smokers. At 9 months, 99.3% remained seropositive;2.8% infected after vaccination. The repeated measures analysis showed a difference in means of 669.0 AU/ml (significant decrease in IgG levels of 28.9%). Conclusion: Antibody levels remained positive 6 and 9 months after vaccination, although IgG levels were found to decay.
基金The corresponding authors extend their appreciation to the Deanship of Scientific Research,University of Hafr Al Batin for funding this work through the research group project no.(G-108-2020).
文摘This paper presents the mathematical analysis of the dynamical system for avian influenza.The proposed model considers a nonlinear dynamical model of birds and human.The half-saturated incidence rate is used for the transmission of avian influenza infection.Rigorous mathematical results are presented for the proposed models.The local and global dynamics of each model are presented and proven that when R0<1,then the disease-free equilibrium of each model is stable both locally and globally,and when R0>1,then the endemic equilibrium is stable both locally and globally.The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.
文摘Objective:To identify the incidence rate,relative risk,hotspot regions and incidence trend of COVID-19 in Qom province,northwest part of Iran in the first stage of the pandemic.Methods:The study included 1125 officially reported PCR-confirmed cases of COVID-19 from 20 February 2020 to 20 April 2020 in 90 regions in Qom city,Iran.The Bayesian hierarchical spatial model was used to model the relative risk of COVID-19 in Qom city,and the segmented regression model was used to estimate the trend of COVID-19 incidence rate.The Poisson distribution was applied for the observed number of COVID-19,and independent Gamma prior was used for inference on log-relative risk parameters of the model.Results:The total incidence rate of COVID-19 was estimated at 89.5 per 100000 persons in Qom city(95%CI:84.3,95.1).According to the results of the Bayesian hierarchical spatial model and posterior probabilities,43.33%of the regions in Qom city have relative risk greater than 1;however,only 11.11%of them were significantly greater than 1.Based on Geographic Information Systems(GIS)spatial analysis,10 spatial clusters were detected as active and emerging hotspot areas in the south and central parts of the city.The downward trend was estimated 10 days after the reporting of the first case(February 7,2020);however,the incidence rate was decreased by an average of 4.24%per day(95%CI:−10.7,−3.5).Conclusions:Spatial clusters with high incidence rates of COVID-19 in Qom city were in the south and central regions due to the high population density.The GIS could depict the spatial hotspot clusters of COVID-19 for timely surveillance and decision-making as a way to contain the disease.
基金Supported by the National Natural Science Foundation of China(11101323)Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)Supported by the Xi’an Polytechnic University Innovation Fund for Graduate Students(CX201608)
文摘In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.
