Epidemiological characteristics and transmissibility of HPV infection: A long-term retrospective study in Hokkien Golden Triangle, China, 2013-2021.

OBJECTIVE: Multiple human papillomavirus (HPV)-associated diseases have put a significant disease burden on the world. Therefore, we conducted a study to explore the epidemiological characteristics of HPV and the transmissibility of its genotypes. METHODS: HPV testing data was collected from Hospital. A transmission dynamics model of HPV was constructed to simulate and compare the transmissibility of different HPV genotypes, which was quantitatively described by the basic reproduction number (R0). RESULTS: The collected HPV subjects were mainly from Xiamen City, Zhangzhou City and Quanzhou City, together, they are known as the Hokkien golden triangle. There were variations in the distribution of HPV infections by age groups. Among all HPV genotypes, 13 of them had R0 > 1, with 10 of them being high-risk types. The top five were HPV56, 18, 58, 52 and 53, among which, HPV56, 18, 58 and 42 were of high risk, whereas HPV53 was not, and the R0 values for the five were 3.35 (CI: 0.00-9.99), 3.20 (CI: 0.00-6.46), 3.19 (CI: 1.27-6.94), 3.19 (CI: 1.01-8.42) and 2.99 (CI: 0.00-9.39), respectively. In addition, HPV52 had R0 > 1 for about 51 months, which had the longest duration. CONCLUSION: Most high-risk HPV types in the Hokkien golden triangle could transmit among the population. Therefore, there is a need of further optimization for developing HPV vaccines and better detection methods in the region.

Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate.

A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R 0. Specifically, it shows that the disease-free equilibrium E 0 is globally asymptotically stable (GAS) for R 0 < 1, and globally attractive (GA) for R 0 = 1, while the endemic equilibrium E* is GAS and E 0 is unstable for R 0 > 1. Especially, to obtain the global stability of the equilibrium E* for R 0 > 1, the weak persistence of the model is proved by some analysis techniques.

The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy.

The global spread of COVID-19 has not been effectively controlled. It poses a significant threat to public health and global economic development. This paper uses a mathematical model with vaccination and isolation treatment to study the transmission dynamics of COVID-19. In this paper, some basic properties of the model are analyzed. The control reproduction number of the model is calculated and the stability of the disease-free and endemic equilibria is analyzed. The parameters of the model are obtained by fitting the number of cases that were detected as positive for the virus, dead, and recovered between January 20 and June 20, 2021, in Italy. We found that vaccination better controlled the number of symptomatic infections. A sensitivity analysis of the control reproduction number has been performed. Numerical simulations demonstrate that reducing the contact rate of the population and increasing the isolation rate of the population are effective non-pharmaceutical control measures. We found that if the isolation rate of the population is reduced, a short-term decrease in the number of isolated individuals can lead to the disease not being controlled at a later stage. The analysis and simulations in this paper may provide some helpful suggestions for preventing and controlling COVID-19.

Shigellosis seasonality and transmission characteristics in different areas of China: A modelling study.

Objective: In China, the burden of shigellosis is unevenly distributed, notably across various ages and geographical areas. Shigellosis temporal trends appear to be seasonal. We should clarify seasonal warnings and regional transmission patterns. Method: This study adopted a Logistic model to assess the seasonality and a dynamics model to compare the transmission in different areas. The next-generation matrix was used to calculate the effective reproduction number (R eff) to quantify the transmissibility. Results: In China, the rate of shigellosis fell from 35.12 cases per 100,000 people in 2005 to 7.85 cases per 100,000 people in 2017, peaking in June and August. After simulation by the Logistic model, the 'peak time' is mainly concentrated from mid-June to mid-July. China's 'early warning time' is primarily focused on from April to May. We predict the 'peak time' of shigellosis is the 6.30th month and the 'early warning time' is 3.87th month in 2021. According to the dynamics model results, the water/food transfer pathway has been mostly blocked off. The transmissibility of different regions varies greatly, such as the mean R eff of Longde County (3.76) is higher than Xiamen City (3.15), higher than Chuxiong City (2.52), and higher than Yichang City (1.70). Conclusion: The 'early warning time' for shigellosis in China is from April to May every year, and it may continue to advance in the future, such as the early warning time in 2021 is in mid-March. Furthermore, we should focus on preventing and controlling the person-to-person route of shigellosis and stratified deploy prevention and control measures according to the regional transmission.

The transmission dynamics of Middle East Respiratory Syndrome coronavirus.

BACKGROUND: In this study, we aimed to quantify the contribution of different transmission routes of the Middle East respiratory syndrome (MERS) and determine its transmissibility. METHODS: Based on the natural history and transmission features of MERS in different countries, a susceptible-exposed-symptomatic-asymptomatic-recovered/death (SEIARD) model and a multi-route dynamic model (MMDM). The SEIARD model and MMDM were adopted to simulate MERS in South Korea and Saudi Arabia, respectively. Data on reported MERS cases in the two countries were obtained from the World Health Organization. Thereafter, the next generation matrix method was employed to derive the equation for the basic reproduction number (R0), and the model fitting procedure was adopted to calculate the R0 values corresponding to these different countries. RESULTS: In South Korea, 'Person-to-Person' transmission was identified as the main mode of MERS transmission in healthcare settings, while in Saudi Arabia, in addition to 'Person-to-Person' transmission, 'Host-to-Host' and 'Host-to-Person' transmission also occurred under certain scenarios, with camels being the main host. Further, the fitting results showed that the SEIARD model and MMDM fitted the data well. The mean R0 value was 8.59 (95% confidence interval [CI]: 0-28.02) for MERS in South Korea, and for MERS in Saudi Arabia, it was 1.15 and 1.02 (95% CI: 0.86-1.44) for the 'Person-to-Person' and 'Camel-to-Camel' transmission routes, respectively. CONCLUSIONS: The SEIARD and MMDM model can be used to simulate the transmission of MERS in different countries. Additionally, in Saudi Arabia, the transmissibility of MERS was almost the same among hosts (camels) and humans.

A kinetic model considering the decline of antibody level and simulation about vaccination effect of COVID-19.

We build a model that consider the falling antibody levels and vaccination to assess the impact of falling antibody levels and vaccination on the spread of the COVID-19 outbreak, and simulate the influence of vaccination rates and failure rates on the number of daily new cases in England. We get that the lower the vaccine failure rate, the fewer new cases. Over time, vaccines with low failure rates are more effective in reducing the number of cases than vaccines with high failure rates and the higher the vaccine efficiency and vaccination rate, the lower the epidemic peak. The peak arrival time is related to a boundary value. When the failure rate is less than this boundary value, the peak time will advance with the decrease of failure rate; when the failure rate is greater than this boundary value, the peak time is delayed with the decrease of failure rate. On the basis of improving the effectiveness of vaccines, increasing the vaccination rate has practical significance for controlling the spread of the epidemic.

Epidemiological Characteristics and Transmissibility of Human Immunodeficiency Virus in Nanning City, China, 2001-2020.

Background: Human immunodeficiency virus (HIV) is a single-stranded RNA virus that can weaken the body's cellular and humoral immunity and is a serious disease without specific drug management and vaccine. This study aimed to evaluate the epidemiologic characteristics and transmissibility of HIV. Methods: Data on HIV follow-up were collected in Nanning City, Guangxi Zhuang Autonomous, China. An HIV transmission dynamics model was built to simulate the transmission of HIV and estimate its transmissibility by comparing the effective reproduction number (Reff ) at different stages: the rapid growth period from January 2001 to March 2005, slow growth period from April 2005 to April 2011, and the plateau from May 2011 to December 2019 of HIV in Nanning City. Results: High-risk areas of HIV prevalence in Nanning City were mainly concentrated in suburbs. Furthermore, high-risk groups were those of older age, with lower income, and lower education levels. The Reff in each stage (rapid growth, slow growth, and plateau) were 2.74, 1.62, and 1.15, respectively, which suggests the transmissibility of HIV in Nanning City has declined and prevention and control measures have achieved significant results. Conclusion: Over the past 20 years, the HIV incidence in Nanning has remained at a relatively high level, but its development trend has been curbed. Transmissibility was reduced from 2.74 to 1.15. Therefore, the prevention and treatment measures in Nanning City have achieved significant improvement.

The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China.

This study aimed at estimating the transmissibility of hepatitis C. The data for hepatitis C cases were collected in six districts in Xiamen City, China from 2004 to 2018. A population-mixed susceptible-infectious-chronic-recovered (SICR) model was used to fit the data and the parameters of the model were calculated. The basic reproduction number (R0) and the number of newly transmitted cases by a primary case per month (MNI) were adopted to quantitatively assess the transmissibility of hepatitis C virus (HCV). Eleven curve estimation models were employed to predict the trends of R0 and MNI in the city. The SICR model fits the reported HCV data well (P < 0.01). The median R0 of each district in Xiamen is 0.4059. R0 follows the cubic model curve, the compound curve and the power function curve. The median MNI of each district in Xiamen is 0.0020. MNI follows the cubic model curve, the compound curve and the power function curve. The transmissibility of HCV follows a decreasing trend, which reveals that under the current policy for prevention and control, there would be a high feasibility to eliminate the transmission of HCV in the city.

A five-compartment model of age-specific transmissibility of SARS-CoV-2.

BACKGROUND: The novel coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, also called 2019-nCoV) causes different morbidity risks to individuals in different age groups. This study attempts to quantify the age-specific transmissibility using a mathematical model. METHODS: An epidemiological model with five compartments (susceptible-exposed-symptomatic-asymptomatic-recovered/removed [SEIAR]) was developed based on observed transmission features. Coronavirus disease 2019 (COVID-19) cases were divided into four age groups: group 1, those ≤ 14 years old; group 2, those 15 to 44 years old; group 3, those 45 to 64 years old; and group 4, those ≥ 65 years old. The model was initially based on cases (including imported cases and secondary cases) collected in Hunan Province from January 5 to February 19, 2020. Another dataset, from Jilin Province, was used to test the model. RESULTS: The age-specific SEIAR model fitted the data well in each age group (P < 0.001). In Hunan Province, the highest transmissibility was from age group 4 to 3 (median: ß43 = 7.71 × 10- 9; SAR43 = 3.86 × 10- 8), followed by group 3 to 4 (median: ß34 = 3.07 × 10- 9; SAR34 = 1.53 × 10- 8), group 2 to 2 (median: ß22 = 1.24 × 10- 9; SAR22 = 6.21 × 10- 9), and group 3 to 1 (median: ß31 = 4.10 × 10- 10; SAR31 = 2.08 × 10- 9). The lowest transmissibility was from age group 3 to 3 (median: ß33 = 1.64 × 10- 19; SAR33 = 8.19 × 10- 19), followed by group 4 to 4 (median: ß44 = 3.66 × 10- 17; SAR44 = 1.83 × 10- 16), group 3 to 2 (median: ß32 = 1.21 × 10- 16; SAR32 = 6.06 × 10- 16), and group 1 to 4 (median: ß14 = 7.20 × 10- 14; SAR14 = 3.60 × 10- 13). In Jilin Province, the highest transmissibility occurred from age group 4 to 4 (median: ß43 = 4.27 × 10- 8; SAR43 = 2.13 × 10- 7), followed by group 3 to 4 (median: ß34 = 1.81 × 10- 8; SAR34 = 9.03 × 10- 8). CONCLUSIONS: SARS-CoV-2 exhibits high transmissibility between middle-aged (45 to 64 years old) and elderly (≥ 65 years old) people. Children (≤ 14 years old) have very low susceptibility to COVID-19. This study will improve our understanding of the transmission feature of SARS-CoV-2 in different age groups and suggest the most prevention measures should be applied to middle-aged and elderly people.

Risk estimation and prediction of the transmission of coronavirus disease-2019 (COVID-19) in the mainland of China excluding Hubei province.

BACKGROUND: In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. METHODS: A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (Rc), as well as the effective daily reproduction ratio- Re(t), of the disease transmission in the mainland of China excluding Hubei province. RESULTS: The estimation outcomes indicate that Rc is 3.36 (95% CI: 3.20-3.64) and Re(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. CONCLUSIONS: To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.

A mathematical model for simulating the phase-based transmissibility of a novel coronavirus.

BACKGROUND: As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020. The virus was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020. This study aimed to develop a mathematical model for calculating the transmissibility of the virus. METHODS: In this study, we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection. Since the Bats-Hosts-Reservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market (reservoir) to people, we simplified the model as Reservoir-People (RP) transmission network model. The next generation matrix approach was adopted to calculate the basic reproduction number (R0) from the RP model to assess the transmissibility of the SARS-CoV-2. RESULTS: The value of R0 was estimated of 2.30 from reservoir to person and 3.58 from person to person which means that the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population was 3.58. CONCLUSIONS: Our model showed that the transmissibility of SARS-CoV-2 was higher than the Middle East respiratory syndrome in the Middle East countries, similar to severe acute respiratory syndrome, but lower than MERS in the Republic of Korea.

Asymptomatic transmission shifts epidemic dynamics.

Asymptomatic transmission of infectious diseases has been recognized recently in several epidemics or pandemics. There is a great need to incorporate asymptomatic transmissions into traditional modeling of infectious diseases and to study how asymptomatic transmissions shift epidemic dynamics. In this work, we propose a compartmental model with asymptomatic transmissions for waterborne infectious diseases. We conduct a detailed analysis and numerical study with shigellosis data. Two parameters, the proportion $p$ of asymptomatic infected individuals and the proportion $k$ of asymptomatic infectious individuals who can asymptomatically transmit diseases, play major rules in the epidemic dynamics. The basic reproduction number $\mathscr{R}_{0}$ is a decreasing function of parameter $p$ when parameter $k$ is smaller than a critical value while $\mathscr{R}_{0}$ is an increasing function of $p$ when $k$ is greater than the critical value. $\mathscr{R}_{0}$ is an increasing function of $k$ for any value of $p$. When $\mathscr{R}_{0}$ passes through 1 as $p$ or $k$ varies, the dynamics of epidemics is shifted. If asymptomatic transmissions are not counted, $\mathscr{R}_{0}$ will be underestimated while the final size may be overestimated or underestimated. Our study provides a theoretical example for investigating other asymptomatic transmissions and useful information for public health measurements in waterborne infectious diseases.

Influence of asymptomatic infections for the effectiveness of facemasks during pandemic influenza.

In this paper, the SEIR model is generalized by introducing an asymptomatic class to quantify the influence of wearing N95 facemasks in reducing the spread of influenza H1N1. What's more, we explain the control reproduction number Rc according to the biological meaning reasonably. Without any intervention, the basic reproduction number R0=1.83 and there will be a large outbreak of infectious diseases. If N95 facemasks are 50% effective in reducing susceptibility and infectivity, 50% of population wear them on the first day, the basic reproduction number will be decreased from 1.83 to 1.17 and the final size reduced from 73% to 2%.

Influence of media intervention on AIDS transmission in MSM groups.

To explore the effects of propaganda and education on the prevention and control of AIDS infection, a model of AIDS transmission in MSM population is proposed and theoretically analyzed by introducing media impact factors. The basic reproduction number of AIDS transmission in MSM group without media intervention R0 = 1.5447 is obtained. Based on the comparison of the implementation of three different detection and treatment measures, it can be concluded that the promotion of condom use is more effective than other strategies, and using condoms with a fixed partner can reduce the value of R0 more quickly.

Incidence dynamics and investigation of key interventions in a dengue outbreak in Ningbo City, China.

BACKGROUND: The reported incidence of dengue fever increased dramatically in recent years in China. This study aimed to investigate and to assess the effectiveness of intervention implemented in a dengue outbreak in Ningbo City, Zhejiang Province, China. METHODS: Data of a dengue outbreak were collected in Ningbo City in China by a field epidemiological survey according to a strict protocol and case definition. Serum specimens of all cases were collected for diagnosis and the virological characteristics were detected by using polymerase chain reaction (PCR) and gene sequencing. Vector surveillance was implemented during the outbreak to collect the larva and adult mosquito densities to calculate the Breteau Index (BI) and human biting rate (HBR), respectively. Data of monthly BI and light-trap density in 2018 were built to calculate the seasonality of the vector. A transmission mathematical model was developed to dynamic the incidence of the disease. The parameters of the model were estimated by the data of the outbreak and vector surveillance data in 2018. The effectiveness of the interventions implemented during the outbreak was assessed by the data and the modelling. RESULTS: From 11 August to 8 September, 2018, a dengue outbreak was reported with 27 confirmed cases in a population of 5536-people community (community A) of Ningbo City. Whole E gene sequences were obtained from 24 cases and were confirmed as dengue virus type 1 (DENV-1). The transmission source of the outbreak was origin from community B where a dengue case having the same E gene sequence was onset on 30 July. Aedes albopictus was the only vector species in the area. The value of BI and HBR was 57.5 and 12 per person per hour respectively on 18 August, 2018 and decreased dramatically after interventions. The transmission model fitted well (χ2 = 6.324, P = 0.388) with the reported cases data. With no intervention, the total simulated number of the cases would be 1728 with a total attack rate (TAR) of 31.21% (95%CI: 29.99%- 32.43%). Case isolation and larva control (LC) have almost the same TAR and duration of outbreak (DO) as no intervention. Different levels of reducing HBR (rHBR) had different effectiveness with TARs ranging from 1.05% to 31.21% and DOs ranging from 27 days to 102 days. Adult vector control (AVC) had a very low TAR and DO. "LC+AVC" had a similar TAR and DO as that of AVC. "rHBR100%+LC", "rHBR100%+AVC", "rHBR100%+LC+AVC" and "rHBR100%+LC+AVC+Iso" had the same effectiveness. CONCLUSIONS: Without intervention, DENV-1 could be transmitted rapidly within a short period of time and leads to high attack rate in community in China. AVC or rHBR should be recommended as primary interventions to control rapid transmission of the dengue virus at the early stage of an outbreak.

Multiple infection leads to backward bifurcation for a schistosomiasis model.

Based on years of experience in schistosomiasis prevention and treatment, one of the typical features of schistosomiasis is multiple infection of a human host by parasites, which may dramatically a ect the host's infectivity. In this paper we establish a schistosomiasis model that takes into consideration multiple infection by separating humans with single and multiple infectious. The disease free equilibrium is shown to be globally asymptotically stable under certain condition. The model analysis suggests that a backward bifurcation may occur if the transmission rate from multiple infected humans to snails is high. This conclusion has not been seen in previous models of schistosomiasis. Such backward bifurcation is not possible without considering multiple infections. This conclusion may provide a new threshold theory for the prevention and treatment of schistosomiasis. Furthermore, numerical simulations suggest that e ective treatment of humans with multiple infection is important to control schistosomiasis. Especially, prevention of multiple infection may be critical.

Schistosomiasis Transmission Model and its Control in Anhui Province.

National Bureau of Statistics of China reports that the incidence of schistosomiasis has been increasing in recent years. To study dynamic behaviors of schistosomiasis transmission, based on practical experience of staff in Anhui Institute of Schistosomiasis, a mathematical schistosomiasis model with reinfection of recovered people is established in this paper. Metzler matrix theory and center manifold theorem are used to analyze stability of equilibria. Parameter estimation has been performed by combining model and monitoring data. It is found that the basic reproduction number is different every year. The most concern of Institute of Schistosomiasis is whether or when to kill snails every year. To answer this question, threshold value of snail density can be obtained. Once the snail density exceeds the threshold, the staff will need to kill snails. To find the best control measures, sensitivity analysis is used to find out sensitive parameters, and then control measures can be obtained by optimization control measures. The results show that combination of spraying molluscicide, publicity and education, improving the health facilities, and large-scale treatment of patient groups have the best effect. In additional, it is found that the number of patients does not change much when the reinfection rate of recovered people is very small. However, when the reinfection rate is slightly larger, the number of patients will suddenly increase to a large value.

Effects of isolation and slaughter strategies in different species on emerging zoonoses.

Zoonosis is the kind of infectious disease transmitting among different species by zoonotic pathogens. Different species play different roles in zoonoses. In this paper, we established a basic model to describe the zoonotic pathogen transmission from wildlife, to domestic animals, to humans. Then we put three strategies into the basic model to control the emerging zoonoses. Three strategies are corresponding to control measures of isolation, slaughter or similar in wildlife, domestic animals and humans respectively. We analyzed the effects of these three strategies on control reproductive numbers and equilibriums and we took avian influenza epidemic in China as an example to show the impacts of the strategies on emerging zoonoses in different areas at beginning.

Effect of Intermediate Hosts on Emerging Zoonoses.

Most emerging zoonotic pathogens originate from animals. They can directly infect humans through natural reservoirs or indirectly through intermediate hosts. As a bridge, an intermediate host plays different roles in the transmission of zoonotic pathogens. In this study, we present three types of pathogen transmission to evaluate the effect of intermediate hosts on emerging zoonotic diseases in human epidemics. These types are identified as follows: TYPE 1, pathogen transmission without an intermediate host for comparison; TYPE 2, pathogen transmission with an intermediate host as an amplifier; and TYPE 3, pathogen transmission with an intermediate host as a vessel for genetic variation. In addition, we established three mathematical models to elucidate the mechanisms underlying zoonotic disease transmission according to these three types. Stability analysis indicated that the existence of intermediate hosts increased the difficulty of controlling zoonotic diseases because of more difficult conditions to satisfy for the disease to die out. The human epidemic would die out under the following conditions: TYPE 1: [Formula: see text] and [Formula: see text]; TYPE 2: [Formula: see text], [Formula: see text], and [Formula: see text]; and TYPE 3: [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] Simulation with similar parameters demonstrated that intermediate hosts could change the peak time and number of infected humans during a human epidemic; intermediate hosts also exerted different effects on controlling the prevalence of a human epidemic with natural reservoirs in different periods, which is important in addressing problems in public health. Monitoring and controlling the number of natural reservoirs and intermediate hosts at the right time would successfully manage and prevent the prevalence of emerging zoonoses in humans.

The Evolutionary Dynamics of Stochastic Epidemic Model with Nonlinear Incidence Rate.

A stochastic SIRS epidemic model with nonlinear incidence rate and varying population size is formulated to investigate the effect of stochastic environmental variability on inter-pandemic transmission dynamics of influenza A. Sufficient conditions for extinction and persistence of the disease are established. In the case of persistence, the existence of endemic stationary distribution is proved and the distance between stochastic solutions and the endemic equilibrium of the corresponding deterministic system in the time mean sense is estimated. Based on realistic parameters of influenza A in humans, numerical simulations have been performed to verify/extend our analytical results. It is found that: (i) the deterministic threshold of the influenza A extinction R(S)0 may exist and the threshold parameter will be overestimated in case of neglecting the impaction of environmental noises; (ii) the presence of environmental noises is capable of supporting the irregular recurrence of influenza epidemic, and the average level of the number of infected individuals I(t) always decreases with the increase in noise intensity; and (iii) if R(S)0 > 1, the volatility of I(t) increases with the increase of noise intensity, while the volatility of I(t) decreases with the increase in noise intensity if R(S)0 < 1.