A nonlocal dispersal and time delayed HIV infection model with general incidences

Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Time Series Models for Short Term Prediction of the Incidence of Japanese Encephalitis in Xianyang City, P R China

Objective To construct a model of Seasonal Autoregressive Integrated Moving Average （SARIMA） for forecasting the epidemic of Japanese encephalitis （JE） in Xianyang, Shaanxi, China, and provide valuable reference information for JE control and prevention. Methods Theoretically epidemiologic study was employed in the research process. Monthly incidence data on JE for the period from Jan 2005 to Sep 2014 were obtained from a passive surveillance system at the Center for Diseases Prevention and Control in Xianyang, Shaanxi province. An optimal SARIMA model was developed for JE incidence from 2005 to 2013 with the Box and Jenkins approach. This SARIMA model could predict JE incidence for the year 2014 and 2015. Results SARIMA （1, 1, 1） （2, 1, 1）12 was considered to be the best model with the lowest Bayesian information criterion, Akaike information criterion, Mean Absolute Error values, the highest R2, and a lower Mean Absolute Percent Error. SARIMA （1, 1, 1） （2, 1, 1）12 was stationary and accurate for predicting JE incidence in Xianyang. The predicted incidence, around 0.3/100 000 from June to August in 2014 with low errors, was higher compared with the actual incidence. Therefore, SARIMA （1, 1, 1） （2, 1, 1）12 appeared to be reliable and accurate and could be applied to incidence prediction. Conclusions The proposed prediction model could provide clues to early identification of the JE incidence that is increased abnormally （≥0.4/100 000）. According to the predicted results in 2014, the JE incidence in Xianyang will decline slightly and reach its peak from June to August.The authors wish to thank the staff from the CDCs from 13 counties of Xianyang, Shaanxi province, China, for their contribution to Japanese encephalitis cases reporting.

Structured Equation Model of Tuberculosis Incidence Based on Its Social Determinants and Risk Factors in Bandar Lampung, Indonesia

World Health Organization through tuberculosis (TB) control averted up to six million deaths and cured thirty-six million people in 1995-2008, but had less success in reducing TB incidence, especially in thirteen high burden countries, including Indonesia. Therefore, TB control will need to have more emphasis on the issues of social determinants, as social determinants affect TB’s incidence directly and/-or through TB’s risk factors. This study aimed to identify a significant effect of social determinants and the risk factors of TB incidence. The research setting was at twenty-seven primary health centers and one hospital that have implemented the Directly Observed Treatment Short Course (DOTS) strategy in Bandar Lampung municipality, Indonesia. Respondents of this research were 238 smear-positive TB patients as case group and 238 patients without TB as control group. Research variables consisted of “social determinants”, “housing condition”, “household food security” and “health access” which were set as latent variables and measured through their indicators. Data had been collected by using questionnaire and then was analyzed with Structural Equation Modeling using SmartPLS 2.0 software. The result showed that “social determinants” through “housing condition” and “household food security” affected “TB incidence”. Moreover, “social determinants”, “housing condition” and “household food security” can be used to explain 34.1% variation of “TB incidence”. In conclusion, the knowledge can be used to support the TB control program, particularly to implement the DOTS strategy together with improving social determinants, housing condition and household food security.

Dynamics of a Nonautonomous SIR Model with Time-Varying Impulsive Release and General Nonlinear Incidence Rate in a Polluted Environment

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.

Stability Analysis of SIQS Epidemic Model with Saturated Incidence Rate

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.

Deterministic and Stochastic Schistosomiasis Models with General Incidence

In this paper, deterministic and stochastic models for schistosomiasis involving four sub-populations are developed. Conditions are given under which system exhibits thresholds behavior. The disease-free equilibrium is globally asymptotically stable if R0 ?and the unique endemic equilibrium is globally asymptotically stable when R0 >?1. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and the stochastic model.

Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates

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.

Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.

Dynamics of a Nonautonomous Plant Disease Model with General Nonlinear Incidence Rate and Time-Varying Impulse

In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive control strategy is proposed and investigated. This novel model could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Using the method of small amplitude perturbation, the sufficient conditions under which guarantee the globally attractive of the disease-free periodic solution and the permanence of the disease are obtained, that is, the disease dies out if R12>1.

Dynamic Analysis for a SIQR Epidemic Model with Specific Nonlinear Incidence Rate

The article investigates a SIQR epidemic model with specific nonlinear incidence rate and stochastic model based on the former, respectively. For deterministic model, we study the existence and stability of the equilibrium points by controlling threshold parameter R0 which determines whether the disease disappears or prevails. Then by using Routh-Hurwitz criteria and constructing suitable Lyapunov function, we get that the disease-free equilibrium is globally asymptotically stable if R0 or unstable if R0>1. In addition, the endemic equilibrium point is globally asymptotically stable in certain region when R0>1. For the corresponding stochastic model, the existence and uniqueness of the global positive solution are discussed and some sufficient conditions for the extinction of the disease and the persistence in the mean are established by defining its related stochastic threshold R0s. Moreover, our analytical results show that the introduction of random fluctuations can suppress disease outbreak. And numerical simulations are used to confirm the theoretical results.

Statistical Modeling of Malaria Incidences in Apac District, Uganda

Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.

Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.

Stability Analysis of an SIR Epidemic Model with Non-Linear Incidence Rate and Treatment

We consider a SIR epidemic model with saturated incidence rate and treatment. We show that if the basic reproduction number, R0 is less than unity and the disease free equilibrium is locally asymptotically stable. Moreover, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end, we give some numerical results to compare our model with existing model and to show the effect of the treatment term on the model.

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

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. .

Modeling and Forecasting Malaria and Dengue Hemorrhagic Fever Incidence and Prevalence in Northern Thailand

Malaria and dengue hemorrhagic fever （DHF） are infectious diseases prevalent in many tropical countries, including Thailand. Thailand is located geographically in a tropical zone and the transmission of malaria and DHF is common, particularly in the upper Northern region of the country. The objective of this study is to identify the patterns of hospital-diagnosed Malaria and DHF incidences by using the previous monthly or quarterly periods of incidences occurring in the upper Northern region of Thailand. The authors use additive plus multiplicative regression models to describe these patterns. The models can be used to forecast malaria and DHF incidences, thus predicting where epidemics are likely to occur. This information can be used to prevent disease outbreaks occurring. Graphical displays showing district and period effects are presented. The results of this study show that historical malaria and DHF incidence rates can be used to provide a useful model for forecasting future epidemics. The graphical display shows the improvement of risk prediction brought about by model. The model, even if based purely on statistical data analysis, can provide a useful basis for allocation of resources for disease prevention.

Evaluation model for freeway incident management system

In order to evaluate the general situation and find special problems of the freeway incident management system, an evaluation model is proposed. First, the expert appraisal approach is used to select the primary evaluation index. As a result, 81 indices and the hierarchical structures of the index such as the object layer, the sub-object layer, the criterion layer and the index layer are determined. Then, based on the fuzzy characteristics of each index layer, the analytical hierarchy process（AHP）and the fuzzy comprehensive evaluation are applied to generate the weight and the satisfaction of the index and the criterion layers. When analyzing the relationship between the sub-object layer and the object layer, it is easy to find that the number of sub-objects is too large and sub-objects are significantly redundant. The partial least square （PLS） is proposed to solve the problems. Finally, an application example, whose result has already been accepted and employed as the indication of a new project in improving incident management, is introduced and the result verifies the feasibility and efficiency of the model.

Changes in Notified Incidence of Pulmonary Tuberculosis in China,2005–2020

Objective To evaluate the trend of notified incidence of pulmonary tuberculosis(PTB)in China at different periods by population and region and to explore the effect of TB prevention and control in recent years.Methods Using pooled data on TB cases reported by the TB Information Management Reporting System(TBIMS)from 2005 to 2020,we calculated the annual percentage change(APC)using the Joinpoint regression model.Results From 2005 to 2020,a total of 16.2 million cases of PTB were reported in China,with an average notified incidence of 75.5 per 100,000 population.The age standardization rate(ASR)continued to decline from 116.9(/100,000)in 2005 to 47.6(/100,000)in 2020,with an average annual decrease of5.6%[APC=-5.6,95%confidence interval(CI):-7.0 to-4.2].The smallest decline occurred in2011–2018(APC=-3.4,95%CI:-4.6 to-2.3)and the largest decrease in 2018–2020(APC=-9.2,95%CI:-16.4 to-1.3).From 2005 to 2020,the ASR in males(159.8 per 100,000 in 2005,72.0 per 100,000 in2020)was higher than that in females(62.2 per 100,000 in 2005,32.3 per 100,000 in 2020),with an average annual decline of 6.0%for male and 4.9%for female.The average notified incidence was the highest among older adults(65 years and over)(182.3/100,000),with an average annual decline of6.4%;children(0–14 years)were the lowest(4.8/100,000),with an average annual decline of 7.3%,but a significant increase of 3.3%between 2014 and 2020(APC=3.3,95%CI:1.4 to 5.2);middle-aged(35–64years)decreased by 5.8%;and youth(15–34 years)decreased by an average annual rate of 4.2%.The average ASR in rural areas(81.3/100,000)is higher than that in urban areas(76.1/100,000).The average annual decline in rural areas was 4.5%and 6.3%in urban areas.South China had the highest average ASR(103.2/100,000),with an average annual decline of 5.9%,while North China had the lowest(56.5/100,000),with an average annual decline of 5.9%.The average ASR in the southwest was 95.3(/100,000),with the smallest annual decline(APC=-4.5,95%CI:-5.5 to-3.5);the average ASR in the Northwest China was 100.1(/100,000),with the largest annual decline(APC=-6.4,95%CI:-10.0 to-2.7);Central,Northeastern,and Eastern China declined by an average of 5.2%,6.2%,and 6.1%per year,respectively.Conclusions From 2005 to 2020,the notified incidence of PTB in China continued to decline,falling by55%.For high-risk groups such as males,older adults,high-burden areas in South,Southwest,and Northwest China,and rural regions,proactive screening should be strengthened to provide timely and effective anti-TB treatment and patient management services for confirmed cases.There is also a necessity to be vigilant about the upward trend of children in recent years,the specific reasons for which need to be further studied.

Modeling of optimal control for urban freeway corridor under incident conditions

Traffic control and management are effective measures to solve the problem of traffic congestion. The optimal control model for freeway corridor is developed under incident conditions, which is in the form of minimization of the sum of the square of the difference between traffic demand and capacity at each intersection and on the freeway bottleneck section. The model optimizes control parameters of phase splits at arterial intersections, off-ramp diversion rates at upstream off-ramps and on-ramp diversion rates at downstream on ramps. Finally, the objective function is discussed and it is showed that the optimal control model is simple and practical.

Incidence trend of nasopharyngeal carcinoma from 1987 to 2011 in Sihui County,Guangdong Province,South China:an age-period-cohort analysis

Introduction:In the past several decades,declining incidences of nasopharyngeal carcinoma(NPC) have been observed in Chinese populations in Hong Kong,Taiwan,Los Angeles,and Singapore.A previous study indicated that the incidence of NPC in Sihui County,South China remained stable until 2002,but whether age,diagnosis period,and birth cohort affect the incidence of NPC remains unknown.Methods:Age-standardized rates(ASRs) of NPC incidence based on the world standard population were examined in both males and females in Sihui County from 1987 to 2011.Joinpoint regression analysis was conducted to quantify the changes in incidence trends.A Poisson regression age-period-cohort model was used to assess the effects of age,diagnosis period,and birth cohort on the risk of NPC.Results:The ASRs of NPC incidence during the study period were 30.29/100,000 for males and 13.09/100,000 for females.The incidence of NPC remained stable at a non-significant average annual percent change of 0.2%for males and-1.6%for females throughout the entire period.A significantly increased estimated annual percent change of 6.8%(95%confidence interval,0.1%-14.0%) was observed from 2003 to 2009 for males.The relative risk of NPC increased with advancing age up to 50-59 and decreased at ages >60 years.The period effect curves on NPC were nearly flat for males and females.The birth cohort effect curve for males showed an increase from the1922 cohort to the 1957 cohort and a decrease thereafter.In females,there was an undulating increase in the relative risk from the 1922 cohort to the 1972 cohort.Conclusions:The incidence trends for NPC remained generally stable in Sihui from 1987 to 2011,with an increase from 2003 to 2009.The relative risks of NPC increased in younger females.