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.

Knee Arthroplasty Incidence Rate vs. Revision of Knee Arthroplasty and Its Associated Comorbidities in Colombia

Introduction: Total knee arthroplasty (TKA) has been established as a transformative solution in the treatment of advanced degenerative diseases of the knee, such as osteoarthritis, rheumatoid arthritis, and posttraumatic arthritis. In this sense, TKA surgery, which seeks to replace the damaged joint with prosthetic components, has proven to be highly effective in relieving pain, improving joint function, and, ultimately, significantly increasing patients’ quality of life. The present study describes the TKA and revision knee arthroplasty (RKA) rates and, identifies the associated co morbidities in the Colombian context. Methods: A retrospective cohort study was carried out. It describes demographic and clinical characteristics between two groups of patients, TKA or RKA, and its association with mortality at 30 days, 90 days, or one year after the intervention. Results: The incidence rate of the population undergoing TKA was approximately 11.71 cases per 100,000 inhabitants. Furthermore, the incidence rate for revision knee arthroplasty (RKA) procedures in the same period was around 0.96 per 100,000 inhabitants. In both groups at 30 days postoperatively, a total mortality rate of 0.09%was recorded. When the follow-up was extended to 90 days, it increased to 0.15%;at one year postoperatively, it rose to 0.88%. Conclusion: Mortality after surgery was low in Colombia in 2019. Although RKA is a beneficial procedure, in certain circumstances, it was noted that it carries a higher risk compared to primary TKA. Our results emphasize the importance of careful evaluation of co morbidities and risk factors in patients undergoing these surgical procedures. The application of quality-of-life questionnaires should be considered in future studies on effectiveness and mortality for TKA and RKA in our country.

Incidence and mortality rate of esophageal cancer has decreased during past 40 years in Hebei Province,China

Background： Hebei province is located in North of China with of approximately 6% of whole national population. It is known as a high-risk area for esophageal cancer in China and worldwide. The aim of our study was to estimate the esophageal cancer burden and trend in Hebei Province. Methods： Eight cancer registries in Hebei Province submitted cancer registry data to the Hebei Provincial Cancer Registry Center. All data were qualified and compiled for cancer statistics in 2011. The pooled data were stratified by gender and age group （0, 1-4, 5-9, 10-14...80＋）. Incidence and mortality rates were age-standardized to World Segi＇s population standard and expressed per 100,000 persons. In addition, proportions and cumulative incidence/mortality rates for esophageal cancer were calculated. Esophageal cancer mortality data during the periods 1973-1975, 1990-1992, and 2004-2005 were extracted from the national death surveys. Mortality and incidence rate data from Cixian and Shexian were obtained from population-based cancer registries in each county. Results： The estimated number of newly diagnosed esophageal cancer cases and deaths in 2011 in Hebei Province was 24,318 and 18,226, respectively. The crude incidence rate of esophageal cancer was 33.37/100,000 （males, 42.18/100,000 and females, 24.31/100,000）. The age-standardized rate by world standard population （ASRW） was 28.09/100,000, ranking third among all cancers. The esophageal cancer mortality rate was 25.01/100,000 （males, 31.40/100,000 and females, 18.45/100,000）, ranking third in deaths among all cancers. The mortality rates of esophageal cancer displayed a significant decreasing trend in Hebei Province from 1973-1975 （ASRW =48.69/100,000） to 2004-2005 （ASRW =28.02/100,000）, with a decreased rate of 42.45%. In Cixian, the incidence of esophageal cancer decreased from 250.76/100,000 to 106.74/100,000 in males and from 153.86/100,000 to 75.41/100,000 in females, with annual percentage changes （APC） of 2.13 and 2.16, while the mortality rates declined with an APC of 2.46 for males and 3.10 for females from 1988 to 2011. In Shexian, the incidence rate decreased from 116.90/100,000 to 74.12/100,000 in males and from 46.98/100,000 to 40.64/100,000 in females, while the mortality rates declined, with an APC of 4.89 in males from 2003 to 2011. Conclusions： Although the incidence and mortality rates of esophageal cancer remain high, an obvious decreasing trend has been observed in Hebei Province, as well as in high-risk regions, such as Cixian and Shexian, over the past 40 years.

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.

Evaluation and application of a milk antibody ELISA for assessing the prevalence and incidence of bovine tuberculosis in dairy herds in Hubei Province,China

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.

TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.

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. .

Analysis of the Influence of Operating Room Nursing Care Management on the Incidence Rate of Nosocomial Infection in Orthopedic Surgery Patients

Objective:To analysis the influence of operating room nursing care management on the incidence rate of nosocomial infection in orthopedic surgery patients.Methodology:Fifty six orthopedic surgery patients who admitted into the hospital between January to December 2018 were enrolled into this study and randomly divided into two groups,which were the control group(under general management)and the observation group(under the operating room nursing care management).Further,the incidence rate of nosocomial infections,the incidence rate of irregular nursing care phenomena,the satisfaction score of nursing care management,and the quality of life score were observed and recorded.Result:The incidence rate of nosocomial infection,the incidence rate of irregular nursing care management,the satisfaction score of nursing care management,and the quality of life score of the observation group were compared to that of the control group,and the result showed P<0.05,indicates the statistical significance between the data indicators.Conclusion:The use of operating room nursing care management in patients with orthopedic surgery has shown a significant effect.

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.

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.

Functional Time Series Models to Estimate Future Age-Specific Breast Cancer Incidence Rates for Women in Karachi, Pakistan

Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most populated city of Pakistan, the age-standardized rate of breast cancer was 69.1 per 100,000 women during 1998-2002, which is the highest recorded rate in Asia. The carcinoma of breast in Pakistan is an enormous public health concern. In this study, we examined the recent trends of breast cancer incidence rates among the women in Karachi. Methods： We obtained the secondary data of breast cancer incidence from various hospitals. They included Jinnah Hospital, KIRAN （Karachi Institute of Radiotherapy and Nuclear Medicine）, and Civil hospital, where the data were available for the years 2004-2011. A total of 5331 new cases of female breast cancer were registered during this period. We analyzed the data in 5-year age groups 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75＋. Nonparametric smoothing were used to obtained age-specific incidence curves, and then the curves are decomposed using principal components analysis to fit FTS （functional time series） model. We then used exponential smoothing statspace models to estimate the forecasts of incidence curve and construct prediction intervals. Results： The breast cancer incidence rates in Karachi increased with age for all available years. The rates increased monotonically and are relatively sharp with the age from 15 years to 50 years and then they show variability after the age of 50 years. 10-year forecasts for the female breast cancer incidence rates in Karachi show that the future rates are expected to remain stable for the age-groups 15-50 years, but they will increase for the females of 50-years and over. Hence in future, the newly diagnosed breast cancer cases in the older women in Karachi are expected to increase. Conclusion： Prediction of age related changes in breast cancer incidence rates will provide useful information for controlling the overall burden of cancer in Pakistan and also serve as a resource for health planning in future research. Moreover, these models will be the most useful for modeling and projecting future trends of other cancers and chronic diseases.

Implication of Reported Viral Hepatitis Incidence Rate Change in Hubei Province, China, between 2004-2010

This study examined the change of reported incidence rate for viral hepatitis in Hubei province, China, between 2004 to 2010 to provide scientific evidence for viral hepatitis control. Reported viral hepatitis infection cases were queried from Centre for Disease Control of Hubei Province, China. The incidence of viral hepatitis A decreased steadily across the study period. Viral hepatitis B composed 85% of the viral hepatitis cases. When reported incidence rates for chronic hepatitis B increased, the rates of acute and unclassified cases dropped from 2005 to 2010. The reported viral hepatitis B incidence rate for males was around 1.5-2 times higher than for females. The average annual percentage change of reported viral hepatitis B incidence rates was 4%. The same index for viral hepatitis C was 28%. The reported viral hepatitis B incidence rate of people under 20 years old declined over the period. This decrease was mainly attributed to the recent implementation of vaccination plan. Reported incidence rate of viral hepatitis E also rose in those years. Having a better understanding on reported incidence rates of the present surveillance system is important for developing strategies for further prevention of viral hepatitis. In addition, the data showed that a surveillance system that differentiates new and former infected cases will be more effective in providing evidence for disease control.

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.

National Breast Cancer Mortality and Incidence Rates According to the Human Development Index: An Ecological Study

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.

Trends of incidence and mortality rates of stroke from 1983 to 2000 in Hanzhong rural population

Objective: To explore the trends of incidence and mortality rates of stroke in Hanzhong rural population. Methods: Acting as the WHO MONICA project. Results: The incidence rate of stroke was 152.9/100 000. There was decline trend in male(P<0.05). The mortality rate of stroke was 115.9/100 000. There was no significant decline trend during 18-year period (P<0.05). The incidence and mortality rates of stroke of male were higher than those of female(P<0.05).The incidence and mortality rates were all increased with age(P<0.01). Conclusion: It must stick to the long- term prevention measures to decrease incidence rate, and improve the condition of medical treatment to reduce the mortality rate in rural population.

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.

Geographical mapping and Bayesian spatial modeling of malaria incidence in Sistan and Baluchistan province,Iran

To present the geographical map of malaria and identify some of the important environmental factors of this disease in Sistan and Baluchistan province,Iran.Methods:We used the registered malaria data to compute the standard incidence rates(SIRs) of malaria in different areas of Sislan and Baluchistan province for a nine-sear period(from 2001 to 2009). Statistical analyses consisted of two different pails:geographical mapping of malaria incidence rates,and modeling the environmental(actors.The empirical Bayesian estimates of malaria SIRs were utilized for geographical mapping of malaria and a Poisson random effects model was used for assessing the effect of environmental factors on malaria SIRs.Results:In general.64 926 new cases of malaria were registered in Sistan and Baluchistan Province from 2001 to 2009. Among them.42 695 patients(65.8%) were male and 22 231 patients(34.2%) were female. Modeling the environmental factors showed that malaria incidence rales had positive relationship with humidity,elevation,average minimum temperature and average maximum temperature, while rainfall had negative effect on malaria SIRs in this province.Conclusions:The results of the present Study reveals that malaria is still a serious health problem in Sistan and Baluchistan province.Iran.Geographical map and related environmental factors of malaria can help the health poliey makers to intervene in high risk areas more efficiently and allocate the resources in a proper manner.

Incidence and in-hospital mortality of acute aortic dissection in China： analysis of China Health Insurance Research （CHIRA） Data 2011

ObjectiveAcute 大动脉的解剖(AAD ) 是有高早的死亡率的一个灾难的事件，但是迄今为止，在大陆中国的 AAD 的发生上的数据都不是可得到的。这研究试图在中国估计 AAD 的发生并且描绘临床的侧面，这脉管的 event.MethodsWe 的管理和在里面医院结果使用了中国健康保险研究数据( CHIRA 数据) 2011 它从 25 个城市在到 3,335,000 个随机取样的受益人( 1,718,500 个男人和 1,616,500 个女人)的2011年12月31日的1月一日 2011 的经期期间包括所有住院病人医院记录( 300,886 )并且在大陆中国的不同经济地理的区域的县。有尖锐大动脉的解剖的病人根据疾病 10 I71.0 的 th 修订(ICD-10 ) 。AAD 的估计的发生用方程被计算：估计的发生 = 2.0 ×；（ 40%×；医院承认率)+60%×；医院承认 rate.ResultsThe 医院承认率是 2.0/100,000 (65/3,325,000， 95% CI：1.2-2.8 ) 。AAD 的估计的年度发生是 2.8/100,000 (95% CI：1.9-3.6 ) 并且比在女性在男性是更高的(3.7 对 1.5， P <；0.001 ) 。吝啬的年龄是 58.9 ±；13.4 年。在 23 ± 的吝啬的医院停留期间；6 天，全面在里面医院死亡是 13.9%(9/65 ).ConclusionsOur 学习在中国的大陆显示出相对更低然而并非可以忽略的发生和 AAD 的在里面医院死亡。有用汉语的 AAD 的病人的吝啬的年龄比从西方国家由研究报导了的年轻，当到女发生比率的男性类似于另外的研究报导的那些时。

Incidence and survival of stomach cancer in a high-risk population of Chile

AIM:To study the incidence and survival rate of stomach cancer(SC)and its associated factors in a high risk population in Chile. METHODS:The population-based cancer registry of Valdivia,included in the International Agency for Research on Cancer system,covers 356 396 residents of Valdivia Province,Southern Chile.We studied all SC cases entered in this Registry during 1998-2002 (529 cases).Population data came from the Chilean census(2002).Standardized incidence rates per 100 000 inhabitants(SIR)using the world population, cumulative risk of developing cancer before age 75, and rate ratios by sex,age,ethnicity and social factors were estimated.Relative survival(EdererⅡmethod) and age-standardized estimates(Brenner method) were calculated.Specific survival rates(Kaplan-Meier) were measured at 3 and 5 years and survival curves were analyzed with the Logrank and Breslow tests. Survival was studied in relation to demographics, clinical presentation,laboratory results and medical management of the cases.Those variables significantly associated with survival were later included in a Cox multivariate model. RESULTS:Between 1998 and 2002,529 primary gastric cancers occurred in Valdivia(crude incidence rate 29.2 per 100000 inhabitants).Most cases were male(69.0%), residents of urban areas(57.5%)and Hispanic(83.2%), with a low education level(84.5%<8 school years). SC SIR was higher in men than women(40.8 and 14.8 respectively,P<0.001),risk factors were low education RR 4.4(95%CI:2.9-6.8)and 1.6,(95%CI:1.1-2.1) for women and men respectively and Mapuche ethnicity only significant for women(RR 2.2,95%CI:1.2-3.7).Of all cases,76.4%were histologically confirmed,11.5% had a death certificate only(DCO),56.1%were TNM stageⅣ;445 cases(84.1%)were eligible for survival analysis,all completed five years follow-up;42 remained alive,392 died of SC and 11 died from other causes. Specific 5-year survival,excluding cases with DCO,was 10.6%(95%CI:7.7-13.5);5-year relative survival rate was 12.3%(95%CI:9.1-16.1),men 10.9%(95%CI: 7.4-15.2)and women 16.1%(95%CI:9.5-24.5).Fiveyear specific survival was higher for patients aged<55 years(17.3%),with intestinal type of cancer(14.6%), without metastasis(22.2%),tumor size<4 cm(60.0%), without lymphatic invasion(77.1%),only involvement of the mucous membrane(100%).Statistically significant independent prognostic factors were:TNM staging, diffuse type,metastasis,supraclavicular adenopathy, palpable tumor,and hepatitis or ascites. CONCLUSION:Social determinants are the main risk factors for SC,but not for survival.An advanced clinical stage at consultation is the main cause of poor SC survival.

Trends in the incidence of physician-diagnosed post-traumatic stress disorder among active-duty U.S. military personnel between 1999 and 2008

Background: The impact of combat operations in Iraq and Afghanistan on the incidence of post-traumatic stress disorder(PTSD) in military service members has been poorly quantified. The purpose of this study was to examine trends in the incidence rate of physician-diagnosed PTSD in active-duty military personnel between 1999 and 2008.Methods: We conducted a retrospective cohort study utilizing data extracted from the Defense Medical Surveillance System to identify incident cases of PTSD within the study population. The incidence rate of physician-diagnosed PTSD was the primary outcome of interest. Multivariable Poisson regression was used to analyze the data.Results: The overall incidence rate of PTSD among all active-duty US military personnel was 3.84(95% CI: 3.81, 3.87) cases per 1000 person-years. The adjusted average annual percentage increase in the incidence rate of PTSD prior to the initiation of Operation Iraqi Freedom(OIF) was a modest 5.02%(95% CI: 1.85, 8.29%). Following the initiation of OIF, the average annual percentage increase in the rate of PTSD was 43.03%(95% CI: 40.55, 45.56%). Compared to the baseline period between 1999 and 2002, the incidence rate of PTSD in 2008 was nearly 7 times higher(RR=6.85, 95% CI: 6.49, 7.24). Significant increases in the incidence rate of PTSD were observed following the initiation of OIF regardless of sex, age, race, marital status, military rank, or branch of military service. Notably, the rate of PTSD among females was 6–7 times higher prior to OIF, but there was no difference by gender by 2008.Conclusions: Overall, these data quantify the significant increase in the incidence rate of PTSD following the initiation of combat operations in Iraq and Afghanistan within the active-duty military population during the study period.