Community-based measures for mitigating the 2009 H1N1 pandemic in China

Relationships between building attributes and COVID-19 infection in London

In the UK, all domestic COVID-19 restrictions have been removed since they were introduced in March 2020. After illustrating the spatial-temporal variations in COVID-19 infection rates across London, this study then particularly aimed to examine the relationships of COVID-19 infection rates with building attributes, including building density, type, age, and use, since previous studies have shown that the built environment plays an important role in public health. Multisource data from national health services and the London Geomni map were processed with GIS techniques and statistically analysed. From March 2020 to April 2022, the infection rate of COVID-19 in London was 3,159.28 cases per 10,000 people. The spatial distribution across London was uneven, with a range from 1,837.88 to 4,391.79 per 10,000 people. During this period, it was revealed that building attributes played a significant role in COVID-19 infection. It was noted that higher building density areas had lower COVID-19 infection rates in London. Moreover, a higher percentage of historic or flat buildings tended to lead to a decrease in infection rates. In terms of building use, the rate of COVID-19 infection tended to be lower in public buildings and higher in residential buildings. Variations in the infection rate were more sensitive to building type; in particular, the percentage of residents living in flats contributed the most to variations in COVID-19 infection rates, with a value of 2.3%. This study is expected to provide support for policy and practice towards pandemic-resilient architectural design.

Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.

Transformation of urban mobility during COVID-19 pandemic - Lessons for transportation planning

INTRODUCTION

The coronavirus disease (COVID-19) pandemic is a global threat that started in Wuhan, China, in 2019 and spread rapidly to the globe. To reduce the spread of the COVID-19, different non-pharmacological control measures have been conducted in different countries, which include social distancing, distance working, and stay-at-home mandates. These control measures had affected global transportation and mobility significantly. This study investigated the short-term changes in urban mobility, tropospheric air pollution, and fuel consumption in two major cities of Saudi Arabia, namely, Riyadh and Jeddah.

METHODS

In this study, the dynamics of the number of trips and trip purposes in different provinces of the country were analyzed, focusing on the pandemic period and the lockdown program. These changes impacted fuel consumption and, consequently, air pollutants. The quantity of fuel consumption and its trend was projected considering a few possible fuel consumption and emission scenarios. It is also expected that fuel price plays a role in fuel consumption. The spatial and temporal distributions of the remote sensed tropospheric Nitrogen Dioxide (NO2) levels in different provinces were presented to depict the short 19 and long-term impact on the air quality due to the changes in mobility.

RESULTS

The significant reduction in urban mobility has been observed since the beginning of the first partial curfew in March 2020 compared to that in 2019. The air pollutant levels (such as NO2) in 2020 after the pandemic were generally less than those of 2019. The fuel consumption has been following a decreasing trend in 2020 starting from January due to dynamic fuel price and the additional influence of pandemic. Based on the current online shopping pattern, it is argued that there will be some permanent behavioral changes in urban mobility, which will decrease some shopping trips at least immediately after the recovery from the pandemic.

CONCLUSIONS

This study concluded that the availability of global urban mobility data, remote sensed based tropospheric air pollution data, and global fuel consumption database are important sources of information to investigate the impact of COVID pandemic, especially for the developing countries which suffer from scarcity of pertinent urban mobility information. It seems that, at least in the study area, the spread of COVID-19 is a complex phenomenon in which several exogenous factors, in addition to the curfew protocols, affect the spread of the virus.

Review of fractional epidemic models

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

Expectations of citizens from the government in response to COVID-19 pandemic: a cross-sectional study in Iran

Background

The government is the main body in charge of controlling epidemics; hence, expectations from the intention and capacities of the government would affect the flexibility and behaviors of citizens. Given the severity of COVID-19 pandemic and the urgent need for cooperation of people in the prevention and combat processes, understanding the public perspectives would be crucial and instructive. This study aimed to explore such perspectives towards the current pandemic among the Iranian. Indeed, we sought to provide a favorable platform for effective policies in the face of the COVID-19 pandemic through recognizing public expectations.

Methods

This cross-sectional survey used an open-ended online questionnaire to investigate the common perspectives of the Iranian towards the response of government to COVID-19 pandemic. The participants were selected using snowball and convenient sampling techniques across the country. The collected data were analyzed and described using a thematic analysis.

Results

In general, 2547 participants agreed to participate in this study and completed the online questionnaire. According to the findings, the Iranian exhibited several expectations regarding the response of the government to COVID-19 pandemic. Three main themes were extracted based on these expectations: (1) health-related expectations, (2) policy-related expectations, and (3) Information-related expectations. In this study, a majority of participants highlighted the need to consider and follow-up the patients and their families, providing the financial and hygiene support during the pandemic, applying strict restrictions, and using close monitoring and controlling procedures. Furthermore, they mentioned that authorities and news agencies should observe the principals honesty and transparency.

Conclusions

Our findings revealed that people expect the government and other responsible institutions to minimize the burden of this pandemic through adopting effective policies. Also, they could help policy-makers become aware of the expectations of people and develop better strategies.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-021-10722-y.

Joint impacts of media, vaccination and treatment on an epidemic Filippov model with application to COVID-19

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects

BACKGROUND

Many countries worldwide are faced with the choice between the (re)surgence of COVID-19 and endangering the economic and mental well-being of their citizens. While infection numbers are monitored and measures adjusted, a systematic strategy for balancing contact restrictions and socioeconomic life in the absence of a vaccine is currently lacking.

METHODS

In a mathematical model, we determine the efficacy of regional containment strategies, where contact restrictions are triggered locally in individual regions upon crossing critical infection number thresholds. Our stochastic meta-population model distinguishes between contacts within a region and cross-regional contacts. We use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, including the effects of their individual national lockdowns, and county population sizes obtained from census data to define individual regions. As a performance measure, we determine the number of days citizens will experience contact restrictions over the next 5 years ('restriction time') and compare it to an equivalent national lockdown strategy. To extract crucial parameters, we vary the proportion of cross-regional contacts (between 0% and 100%), the thresholds for initiating local measures (between 5 and 20 active infections per 100,000 inhabitants) as well as their duration after infection numbers have returned below the threshold (between 7 and 28 days). We compare performance across the five different countries and test how further subdivision of large counties into independently controlled regions of up to 100,000 or 200,000 inhabitants affects the results.

FINDINGS

Our numerical simulations show a substantially reduced restriction time for regional containment, if the effective reproduction number of SARS-CoV-2 without restrictions, R 0, is only slightly larger than 1 and the proportion of cross-regional contacts (the so-called leakiness) is low. In Germany, specifically, for R 0=1.14, a leakiness of 1% is sufficiently low to reduce the mean restriction time from 468 days (s.d. 3 days) for the national containment strategy to 43 days (s.d. 3 days across simulations) for the regional strategy, when local measures are initiated at 10 infections per 100,000 inhabitants in the past 7 days. For R 0=1.28, the allowed leakiness for minimal restriction time reduces to approximately 0.3%. The dependence of the restriction time on the leakiness is threshold-like only for regional containment, due to cooperative effects. It rises to levels similar to the national containment strategy for a leakiness > 10% (517 days national vs. 486 days regional for leakiness 32% and R 0=1.14). We find a strong correlation between the population size of each region and the experienced restriction time. For countries with large counties, this can result in only a mild reduction in restriction time for regional containment, which can only be partly compensated by lower thresholds for initiating local measures and increasing their duration. In contrast, further subdividing large counties into smaller units can ensure a strong reduction of the restriction time for the regional strategy.

INTERPRETATION

The leakiness, i.e. the proportion of cross-regional contacts, and the regional structure itself were crucial parameters for the performance of the regional strategy. Therefore, regional strategies could offer an adaptive way to contain the epidemic with fewer overall restrictions, if cross-regional infections can be kept below the critical level, which could be achieved without affecting local socioeconomic freedom. Maintaining general hygiene and contact tracing, testing should be intensified to ensure regional measures can be initiated at low infection thresholds, preventing the spread of the disease to other regions before local elimination. While such tight control could lead to more restrictions in the short run, restrictions necessary for long-term containment could be reduced by up to a factor of 10. Our open-source simulation code is freely available and can be readily adapted to other countries.

FUNDING

This work was supported by the Max Planck Society.

Early mandated social distancing is a strong predictor of reduction in peak daily new COVID-19 cases

OBJECTIVES

Mandated social distancing has been applied globally to reduce the spread of coronavirus disease 2019 (COVID-19). However, the beneficial effects of this community-based intervention have not been proven or quantified for the COVID-19 pandemic.

STUDY DESIGN

This is a regional population-level observational study.

METHODS

Using publicly available data, we examined the effect of timing of mandated social distancing on the rate of COVID-19 cases in 119 geographic regions, derived from 41 states within the United States and 78 other countries. The highest number of new COVID-19 cases per day recorded within a geographic unit was the primary outcome. The total number of COVID-19 cases in regions where case numbers had reached the tail end of the outbreak was an exploratory outcome.

RESULTS

We found that the highest number of new COVID-19 cases per day per million persons was significantly associated with the total number of COVID-19 cases per million persons on the day before mandated social distancing (β = 0.66, P < 0.0001). These findings suggest that if mandated social distancing is not initiated until the number of existing COVID-19 cases has doubled, the eventual peak would result in 58% more COVID-19 cases per day. Subgroup analysis on those regions where the highest number of new COVID-19 cases per day has peaked showed increase in β values to 0.85 (P < 0.0001). The total number of cases during the outbreak in a region was strongly predicted by the total number of COVID-19 cases on the day before mandated social distancing (β = 0.97, P < 0.0001).

CONCLUSIONS

Initiating mandated social distancing when the numbers of COVID-19 cases are low within a region significantly reduces the number of new daily COVID-19 cases and perhaps also reduces the total number of cases in the region.

Global dynamics for a Filippov epidemic system with imperfect vaccination

Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formulated Filippov system, we examine the sliding mode dynamics, the boundary equilibrium bifurcations, and the global dynamics. Our main results show that it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depend on the threshold value and other parameter values. The global stability of the disease-free equilibrium or pseudo-equilibrium reveals that we may eradicate the disease or maintain the number of infected individuals at a previously given value. Further, the bi-stability and tri-stability imply that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. This emphasizes the importance of threshold policy and challenges in the control of infectious diseases if without perfect vaccines.

The effect of control measures on COVID-19 transmission in Italy: Comparison with Guangdong province in China

BACKGROUND

COVID-19 has spread all around the world. Italy is one of the worst affected countries in Europe. Although there is a trend of relief, the epidemic situation hasn't stabilized yet. This study aims to investigate the dynamics of the disease spread in Italy and provide some suggestions on containing the epidemic.

METHODS

We compared Italy's status at the outbreak stage and control measures with Guangdong Province in China by data observation and analysis. A modified autonomous SEIR model was used to study the COVID-19 epidemic and transmission potential during the early stage of the outbreak in Italy. We also utilized a time-dependent dynamic model to study the future disease dynamics in Italy. The impact of various non-pharmaceutical control measures on epidemic was investigated through uncertainty and sensitivity analyses.

RESULTS

The comparison of specific measures implemented in the two places and the time when the measures were initiated shows that the initial prevention and control actions in Italy were not sufficiently timely and effective. We estimated parameter values based on available cumulative data and calculated the basic reproduction number to be 4.32 before the national lockdown in Italy. Based on the estimated parameter values, we performed numerical simulations to predict the epidemic trend and evaluate the impact of contact limitation, detection and diagnosis, and individual behavior change due to media coverage on the epidemic.

CONCLUSIONS

Italy was in a severe epidemic status and the control measures were not sufficiently timely and effective in the beginning. Non-pharmaceutical interventions, including contact restrictions and improvement of case recognition, play an important role in containing the COVID-19 epidemic. The effect of individual behavior changes due to media update of the outbreak cannot be ignored. For policy-makers, early and strict blockade measures, fast detection and improving media publicity are key to containing the epidemic.

A study of SARS-CoV-2 epidemiology in Italy: from early days to secondary effects after social distancing

BACKGROUND

The outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 101,739 confirmed cases, in Italy, as of March 30th, 2020. While the analogous event in China appears to be under control at the moment, the outbreaks in western countries are still at an early stage of development. Italy, at present, is playing a major role in understanding the transmission dynamics of these new infections and evaluating the effectiveness of control measures in a western social context.

METHODS

We combined a quarantined model with early-stage development data in Italy (during the period February 20th-March 30th) to predict longer-term progression (from March 30th, till June 25th, 2020 in a long-term view) with different control measures. Due to significant variations in the control strategies, which have been changing over time, and thanks to the introduction of detection technologies leading to faster confirmation of the SARS-CoV-2 infections, we made use of time-dependent contact and diagnosis rates to estimate when the effective daily reproduction ratio can fall below 1. Within the same framework, we analyze the possible secondary infection event after relaxing the isolation measures.

OUTCOMES AND INTERPRETATION

We study two simplified scenarios compatible with the observation data and the effects of two stringent measures on the evolution of the epidemic. On one side, the contact rate must be kept as low as possible, but it is also clear that, in a modern developed country, it cannot fall under certain minimum levels and for a long time. The complementary parameter tuned is the transition rate of the symptomatic infected individuals to the quarantined class, a parameter δ I I connected with the time t _I = 1/δ_I   needed to perform diagnostic tests. Within the conditions of the outbreak in Italy, this time must fall under 12-8 h in order to make the reproduction number less than 1 to minimize the case numbers. Moreover, we show how the same parameter plays an even more important role in mitigating the effects of a possible secondary infection event.

Modelling the Measles Outbreak at Hong Kong International Airport in 2019: A Data-Driven Analysis on the Effects of Timely Reporting and Public Awareness

Background

Measles, a highly contagious disease, still poses a huge burden worldwide. Lately, a trend of resurgence threatened the developed countries. A measles outbreak occurred in the Hong Kong International Airport (HKIA) between March and April 2019, which infected 29 airport staff. During the outbreak, multiple measures were taken including daily situation updates, setting up a public enquiry platform on March 23, and an emergent vaccination program targeting unprotected staff. The outbreak was put out promptly. The effectiveness of these measures was unclear.

Methods

We quantified the transmissibility of outbreak in HKIA by the effective reproduction number, R_eff(t), and basic reproduction number, R₀(t). The reproduction number was modelled as a function of its determinants that were statistically examined, including lags in hospitalization, situation update, and level of public awareness. Then, we considered a hypothetical no-measure scenario when improvements in reporting and public enquiry were absent and calculated the number of infected airport staff.

Results

Our estimated average R₀ is 10.09 (95% CI: 1.73−36.50). We found that R₀(t) was positively associated with lags in hospitalization and situation update, while negatively associated with the level of public awareness. The average predicted basic reproduction number, r₀, was 14.67 (95% CI: 9.01−45.32) under the no-measure scenario, which increased the average R₀ by 77.57% (95% CI: 1.71−111.15). The total number of infected staff would be 179 (IQR: 90−339, 95% CI: 23−821), namely the measure induced 8.42-fold (95% CI: 0.21−42.21) reduction in the total number of infected staff.

Conclusion

Timely reporting on outbreak situation and public awareness measured by the number of public enquiries helped to control the outbreak.

Phase-adjusted estimation of the COVID-19 outbreak in South Korea under multi-source data and adjustment measures: a modelling study

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (C_rI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R₀ of COVID-19 to be 4.79(95% C_rI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R_c ≈ 0.32(95% C_rI 0.19 - 0.47) at the second phase from February 25 to March 2 because of the voluntary lockdown measures. At the third phase from March 3 to March 9, we estimate R_c to be 0.27 (95% C_rI 0.14 - 0.42). We predict that the final size of the COVID-19 outbreak in South Korea is 9661 (95% C_rI 8660 - 11100) and the whole epidemic will be over by late April. It is found that reducing contact rate and enhancing the testing speed will have the impact on the peak value and the peak time.

Coupling the Macroscale to the Microscale in a Spatiotemporal Context to Examine Effects of Spatial Diffusion on Disease Transmission

There are many challenges to coupling the macroscale to the microscale in temporal or spatial contexts. In order to examine effects of an individual movement and spatial control measures on a disease outbreak, we developed a multiscale model and extended the semi-stochastic simulation method by linking individual movements to pathogen’s diffusion, linking the slow dynamics for disease transmission at the population level to the fast dynamics for pathogen shedding/excretion at the individual level. Numerical simulations indicate that during a disease outbreak individuals with the same infection status show the property of clustering and, in particular, individuals’ rapid movements lead to an increase in the average reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, the final size and the peak value of the outbreak. It is interesting that a high level of aggregation the individuals’ movement results in low new infections and a small final size of the infected population. Further, we obtained that either high diffusion rate of the pathogen or frequent environmental clearance lead to a decline in the total number of infected individuals, indicating the need for control measures such as improving air circulation or environmental hygiene. We found that the level of spatial heterogeneity when implementing control greatly affects the control efficacy, and in particular, an uniform isolation strategy leads to low a final size and small peak, compared with local measures, indicating that a large-scale isolation strategy with frequent clearance of the environment is beneficial for disease control.

A discrete stochastic model of the COVID-19 outbreak: Forecast and control

The novel Coronavirus (COVID-19) is spreading and has caused a large-scale infection in China since December 2019. This has led to a significant impact on the lives and economy in China and other countries. Here we develop a discrete-time stochastic epidemic model with binomial distributions to study the transmission of the disease. Model parameters are estimated on the basis of fitting to newly reported data from January 11 to February 13, 2020 in China. The estimates of the contact rate and the effective reproductive number support the efficiency of the control measures that have been implemented so far. Simulations show the newly confirmed cases will continue to decline and the total confirmed cases will reach the peak around the end of February of 2020 under the current control measures. The impact of the timing of returning to work is also evaluated on the disease transmission given different strength of protection and control measures.

Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions

Since the emergence of the first cases in Wuhan, China, the novel coronavirus (2019-nCoV) infection has been quickly spreading out to other provinces and neighboring countries. Estimation of the basic reproduction number by means of mathematical modeling can be helpful for determining the potential and severity of an outbreak and providing critical information for identifying the type of disease interventions and intensity. A deterministic compartmental model was devised based on the clinical progression of the disease, epidemiological status of the individuals, and intervention measures. The estimations based on likelihood and model analysis show that the control reproduction number may be as high as 6.47 (95% CI 5.71-7.23). Sensitivity analyses show that interventions, such as intensive contact tracing followed by quarantine and isolation, can effectively reduce the control reproduction number and transmission risk, with the effect of travel restriction adopted by Wuhan on 2019-nCoV infection in Beijing being almost equivalent to increasing quarantine by a 100 thousand baseline value. It is essential to assess how the expensive, resource-intensive measures implemented by the Chinese authorities can contribute to the prevention and control of the 2019-nCoV infection, and how long they should be maintained. Under the most restrictive measures, the outbreak is expected to peak within two weeks (since 23 January 2020) with a significant low peak value. With travel restriction (no imported exposed individuals to Beijing), the number of infected individuals in seven days will decrease by 91.14% in Beijing, compared with the scenario of no travel restriction.

Public awareness, news promptness and the measles outbreak in Hong Kong from March to April, 2019

Background: Globally, a resurgence of measles during the last decade may be attributed to many factors. An unexpected measles outbreak occurred in Hong Kong, and infected 29 airport staff between March and April 2019. The authority updated public on new cases daily, a public enquiry telephone/online platform was set up on March 23, and an emergent vaccination programme was launched targeting unvaccinated airport staff. We aimed to study this measles outbreak and its related factors.Methods: We quantified the transmissibility of the outbreak by the time-varying effective reproduction number, R_eff(t), and inferred the time-varying basic reproduction number, R₀(t). We examined the statistical associations between local public awareness or reporting delay and the R₀(t).Results: Our estimated average R₀ is 10.7 with 95% CI of 6.0-29.2. We found that R₀(t) was negatively associated with the level of public awareness and the level of promptness of situation updates on new cases.Conclusion: Public awareness via situation updates helped to control the outbreak. The medical effects of the vaccination programme was not soon enough to cause the immediate shutting down of the outbreak, but it boosted herd immunity to prevent future airport outbreaks in the next few years.

Large-scale Lassa fever outbreaks in Nigeria: quantifying the association between disease reproduction number and local rainfall

Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017–18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018–19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017–18 (1.33 with 95% CI 1.29–1.37) was significantly higher than those for 2016–17 (1.23 with 95% CI: (1.22, 1.24)) and 2018–19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%–1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.

Comparison of methods to Estimate Basic Reproduction Number (R 0) of influenza, Using Canada 2009 and 2017-18 A (H1N1) Data

Background

The basic reproduction number (R ₀) has a key role in epidemics and can be utilized for preventing epidemics. In this study, different methods are used for estimating R ₀'s and their vaccination coverage to find the formula with the best performance.

Materials and Methods

We estimated R ₀ for cumulative cases count data from April 18 to July 6, 2009 and 35-2017 to 34-2018 weeks in Canada: maximum likelihood (ML), exponential growth rate (EG), time-dependent reproduction numbers (TD), attack rate (AR), gamma-distributed generation time (GT), and the final size of the epidemic. Gamma distribution with mean and standard deviation 3.6 ± 1.4 is used as GT.

Results

The AR method obtained a R _{0 (}95% confidence interval [CI]) value of 1.116 (1.1163, 1.1165) and an EG (95%CI) value of 1.46 (1.41, 1.52). The R ₀ (95%CI) estimate was 1.42 (1.27, 1.57) for the obtained ML, 1.71 (1.12, 2.03) for the obtained TD, 1.49 (1.0, 1.97) for the gamma-distributed GT, and 1.00 (0.91, 1.09) for the final size of the epidemic. The minimum and maximum vaccination coverage were related to AR and TD methods, respectively, where the TD method has minimum mean squared error (MSE). Finally, the R ₀ (95%CI) for 2018 data was 1.52 (1.11, 1.94) by TD method, and vaccination coverage was estimated as 34.2%.

Conclusion

For the purposes of our study, the estimation of TD was the most useful tool for computing the R ₀, because it has the minimum MSE. The estimation R ₀ > 1 indicating that the epidemic has occurred. Thus, it is required to vaccinate at least 41.5% to prevent and control the next epidemic.

Analysis of an Epidemic System with Two Response Delays in Media Impact Function

A functional differential model of SEIS-M type with two time delays, representing the response time for mass media to cover the current infection and for individuals' behavior changes to media coverage, was proposed to examine the delayed media impact on the transmission dynamics of emergent infectious diseases. The threshold dynamics were established in terms of the basic reproduction number [Formula: see text]. When there are no time delays, we showed that if the media impact is low, the endemic equilibrium is globally asymptotically stable for [Formula: see text], while the endemic equilibrium may become unstable and Hopf bifurcation occurs for some appropriate conditions by taking the level of media impact as bifurcation parameter. With two time delays, we comprehensively investigated the local and global bifurcation by considering the summation of delays as a bifurcation parameter, and theoretically and numerically examined the onset and termination of Hopf bifurcations from the endemic equilibrium. Main results show that either the media described feedback cycle, from infection to the level of mass media and back to disease incidence, or time delays can induce Hopf bifurcation and result in periodic oscillations. The findings indicate that the delayed media impact leads to a richer dynamics that may significantly affect the disease infections.

Unraveling R0: Considerations for Public Health Applications

We assessed public health use of R 0, the basic reproduction number, which estimates the speed at which a disease is capable of spreading in a population. These estimates are of great public health interest, as evidenced during the 2009 influenza A (H1N1) virus pandemic.

We reviewed methods commonly used to estimate R 0, examined their practical utility, and assessed how estimates of this epidemiological parameter can inform mitigation strategy decisions.

In isolation, R 0 is a suboptimal gauge of infectious disease dynamics across populations; other disease parameters may provide more useful information. Nonetheless, estimation of R 0 for a particular population is useful for understanding transmission in the study population. Considered in the context of other epidemiologically important parameters, the value of R 0 may lie in better understanding an outbreak and in preparing a public health response.

Stochastic Modelling of Air Pollution Impacts on Respiratory Infection Risk

The impact of air pollution on people's health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6 year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi'an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm. The intervals between changes in a sequence indicate when the air pollution becomes increasingly serious. Also, the inflow rate of pollutants during the main pollution periods each year has an increasing trend. This study used a stochastic SEIS model associated with the AQI to explore the impact of air pollution on respiratory infections. Good fits to both the AQI data and the numbers of influenza-like illness cases were obtained by stochastic numerical simulation of the model. Based on the model's dynamics, the AQI time series and the daily number of respiratory infection cases under various government intervention measures and human protection strategies were forecasted. The AQI data in the last 15 months verified that government interventions on vehicles are effective in controlling air pollution, thus providing numerical support for policy formulation to address the haze crisis.

Measuring the impact of air pollution on respiratory infection risk in China

China is now experiencing major public health challenges caused by air pollution. Few studies have quantified the dynamics of air pollution and its impact on the risk of respiratory infection. We conducted an integrated data analysis to quantify the association among air quality index (AQI), meteorological variables and respiratory infection risk in Shaanxi province of China in the period of November 15th, 2010 to November 14th, 2016. Our analysis illustrated a statistically significantly positive correlation between the number of influenza-like illness (ILI) cases and AQI, and the respiratory infection risk has increased progressively with increased AQI with a time lag of 0-3 days. We also developed mathematical models for the AQI trend and respiratory infection dynamics, incorporating AQI-dependent incidence and AQI-based behaviour change interventions. Our combined data and modelling analysis estimated the basic reproduction number for the respiratory infection during the studying period to be 2.4076, higher than the basic reproduction number of the 2009 pandemic influenza in the same province. Our modelling-based simulations concluded that, in terms of respiratory infection risk reduction, the persistent control of emission in the China's blue-sky programme is much more effective than substantial social-economic interventions implemented only during the smog days.

Impact of individual behaviour change on the spread of emerging infectious diseases

Human behaviour plays an important role in the spread of emerging infectious diseases, and understanding the influence of behaviour changes on epidemics can be key to improving control efforts. However, how the dynamics of individual behaviour changes affects the development of emerging infectious disease is a key public health issue. To develop different formula for individual behaviour change and introduce how to embed it into a dynamic model of infectious diseases, we choose A/H1N1 and Ebola as typical examples, combined with the epidemic reported cases and media related news reports. Thus, the logistic model with the health belief model is used to determine behaviour decisions through the health belief model constructs. Furthermore, we propose 4 candidate infectious disease models without and with individual behaviour change and use approximate Bayesian computation based on sequential Monte Carlo method for model selection. The main results indicate that the classical compartment model without behaviour change and the model with average rate of behaviour change depicted by an exponential function could fit the observed data best. The results provide a new way on how to choose an infectious disease model to predict the disease prevalence trend or to evaluate the influence of intervention measures on disease control. However, sensitivity analyses indicate that the accumulated number of hospital notifications and deaths could be largely reduced as the rate of behaviour change increases. Therefore, in terms of mitigating emerging infectious diseases, both media publicity focused on how to guide people's behaviour change and positive responses of individuals are critical.

Global hopf bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease

We proposed a delay differential model, associated with the response time for individuals to the current infection, to examine the media impact on the transmission dynamics of infectious diseases. We investigated the global bifurcation by considering the delay as a bifurcation parameter and examined the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical studies to identify ranges of parameters for coexisting multiple periodic solutions are guided by the bifurcation analysis and the Matlab package DDE-BIFTOOL developed by Engelborghs et al. Further, we parameterized the proposed model on the basis of the 2009 A/H1N1 pandemic influenza data in Shaanxi province, China, and estimated the basic reproduction number to be 1.79 [95% CI (1.77-1.80)] and the time delay to be 2.94 days [95% CI (2.56-3.24)]. Our main results indicated that media impact with time delay significantly influenced the transmission dynamics of infectious diseases.

Efficient Vaccine Distribution Based on a Hybrid Compartmental Model

To effectively and efficiently reduce the morbidity and mortality that may be caused by outbreaks of emerging infectious diseases, it is very important for public health agencies to make informed decisions for controlling the spread of the disease. Such decisions must incorporate various kinds of intervention strategies, such as vaccinations, school closures and border restrictions. Recently, researchers have paid increased attention to searching for effective vaccine distribution strategies for reducing the effects of pandemic outbreaks when resources are limited. Most of the existing research work has been focused on how to design an effective age-structured epidemic model and to select a suitable vaccine distribution strategy to prevent the propagation of an infectious virus. Models that evaluate age structure effects are common, but models that additionally evaluate geographical effects are less common. In this paper, we propose a new SEIR (susceptible-exposed-infectious šC recovered) model, named the hybrid SEIR-V model (HSEIR-V), which considers not only the dynamics of infection prevalence in several age-specific host populations, but also seeks to characterize the dynamics by which a virus spreads in various geographic districts. Several vaccination strategies such as different kinds of vaccine coverage, different vaccine releasing times and different vaccine deployment methods are incorporated into the HSEIR-V compartmental model. We also design four hybrid vaccination distribution strategies (based on population size, contact pattern matrix, infection rate and infectious risk) for controlling the spread of viral infections. Based on data from the 2009-2010 H1N1 influenza epidemic, we evaluate the effectiveness of our proposed HSEIR-V model and study the effects of different types of human behaviour in responding to epidemics.

Media coverage and hospital notifications: Correlation analysis and optimal media impact duration to manage a pandemic

News reporting has the potential to modify a community's knowledge of emerging infectious diseases and affect peoples' attitudes and behavior. Here we developed a quantitative approach to evaluate the effects of media on such behavior. Statistically significant correlations between the number of new hospital notifications, during the 2009 A/H1N1 influenza epidemic in the Shaanxi province of China, and the number of daily news items added to eight major websites were found from Pearson correlation and cross-correlation analyses. We also proposed a novel model to examine the implication for transmission dynamics of these correlations. The model incorporated the media impact function into the intensity of infection, and enhanced the traditional epidemic SEIR model with the addition of media dynamics. We used a nonlinear least squares estimation to identify the best-fit parameter values in the model from the observed data. We also carried out the uncertainty and sensitivity analyses to determine key parameters during early phase of the disease outbreak for the final outcome of the outbreak with media impact. The findings confirm the importance of responses by individuals to the media reports, with behavior changes having important consequence for the emerging infectious disease control. Therefore, for mitigating emerging infectious diseases, media reports should be focused on how to guide people's behavioral changes, which are critical for limiting the spread of disease.

Model Selection and Evaluation Based on Emerging Infectious Disease Data Sets including A/H1N1 and Ebola

The aim of the present study is to apply simple ODE models in the area of modeling the spread of emerging infectious diseases and show the importance of model selection in estimating parameters, the basic reproduction number, turning point, and final size. To quantify the plausibility of each model, given the data and the set of four models including Logistic, Gompertz, Rosenzweg, and Richards models, the Bayes factors are calculated and the precise estimates of the best fitted model parameters and key epidemic characteristics have been obtained. In particular, for Ebola the basic reproduction numbers are 1.3522 (95% CI (1.3506, 1.3537)), 1.2101 (95% CI (1.2084, 1.2119)), 3.0234 (95% CI (2.6063, 3.4881)), and 1.9018 (95% CI (1.8565, 1.9478)), the turning points are November 7,November 17, October 2, and November 3, 2014, and the final sizes until December 2015 are 25794 (95% CI (25630, 25958)), 3916 (95% CI (3865, 3967)), 9886 (95% CI (9740, 10031)), and 12633 (95% CI (12515, 12750)) for West Africa, Guinea, Liberia, and Sierra Leone, respectively. The main results confirm that model selection is crucial in evaluating and predicting the important quantities describing the emerging infectious diseases, and arbitrarily picking a model without any consideration of alternatives is problematic.

An Epidemic Patchy Model with Entry-Exit Screening

A multi-patch SEIQR epidemic model is formulated to investigate the long-term impact of entry-exit screening measures on the spread and control of infectious diseases. A threshold dynamics determined by the basic reproduction number R₀ is established: The disease can be eradicated if R₀ < 1, while the disease persists if R₀ > 1. As an application, six different screening strategies are explored to examine the impacts of screening on the control of the 2009 influenza A (H1N1) pandemic. We find that it is crucial to screen travelers from and to high-risk patches, and it is not necessary to implement screening in all connected patches, and both the dispersal rates and the successful detection rate of screening play an important role on determining an effective and practical screening strategy.

Media impact switching surface during an infectious disease outbreak

There are many challenges to quantifying and evaluating the media impact on the control of emerging infectious diseases. We modeled such media impacts using a piecewise smooth function depending on both the case number and its rate of change. The proposed model was then converted into a switching system, with the switching surface determined by a functional relationship between susceptible populations and different subgroups of infectives. By parameterizing the proposed model with the 2009 A/H1N1 influenza outbreak data in the Shaanxi province of China, we observed that media impact switched off almost as the epidemic peaked. Our analysis implies that media coverage significantly delayed the epidemic's peak and decreased the severity of the outbreak. Moreover, media impacts are not always effective in lowering the disease transmission during the entire outbreak, but switch on and off in a highly nonlinear fashion with the greatest effect during the early stage of the outbreak. The finding draws the attention to the important role of informing the public about 'the rate of change of case numbers' rather than 'the absolute number of cases' to alter behavioral changes, through a self-adaptive media impact switching on and off, for better control of disease transmission.

Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature

BACKGROUND

The potential impact of an influenza pandemic can be assessed by calculating a set of transmissibility parameters, the most important being the reproduction number (R), which is defined as the average number of secondary cases generated per typical infectious case.

METHODS

We conducted a systematic review to summarize published estimates of R for pandemic or seasonal influenza and for novel influenza viruses (e.g. H5N1). We retained and summarized papers that estimated R for pandemic or seasonal influenza or for human infections with novel influenza viruses.

RESULTS

The search yielded 567 papers. Ninety-one papers were retained, and an additional twenty papers were identified from the references of the retained papers. Twenty-four studies reported 51 R values for the 1918 pandemic. The median R value for 1918 was 1.80 (interquartile range [IQR]: 1.47-2.27). Six studies reported seven 1957 pandemic R values. The median R value for 1957 was 1.65 (IQR: 1.53-1.70). Four studies reported seven 1968 pandemic R values. The median R value for 1968 was 1.80 (IQR: 1.56-1.85). Fifty-seven studies reported 78 2009 pandemic R values. The median R value for 2009 was 1.46 (IQR: 1.30-1.70) and was similar across the two waves of illness: 1.46 for the first wave and 1.48 for the second wave. Twenty-four studies reported 47 seasonal epidemic R values. The median R value for seasonal influenza was 1.28 (IQR: 1.19-1.37). Four studies reported six novel influenza R values. Four out of six R values were <1.

CONCLUSIONS

These R values represent the difference between epidemics that are controllable and cause moderate illness and those causing a significant number of illnesses and requiring intensive mitigation strategies to control. Continued monitoring of R during seasonal and novel influenza outbreaks is needed to document its variation before the next pandemic.

Transmission characteristics of different students during a school outbreak of (H1N1) pdm09 influenza in China, 2009

Many outbreaks of A(H1N1)pdm09 influenza have occurred in schools with a high population density. Containment of school outbreaks is predicted to help mitigate pandemic influenza. Understanding disease transmission characteristics within the school setting is critical to implementing effective control measures. Based on a school outbreak survey, we found almost all (93.7%) disease transmission occurred within a single grade, only 6.3% crossed grades. Transmissions originating from freshmen exhibited a star-shaped network; other grades exhibited branch- or line-shaped networks, indicating freshmen have higher activity and are more likely to cause infection. R₀ for freshmen, calculated as 2.04, estimated as 2.76, was greater than for other grades (P < 0.01). Without intervention, the estimated number of cases was much greater when the outbreak was initiated by freshmen than by other grades. Furthermore, the estimated number of cases required to be under quarantine and isolation for freshmen was less than that of equivalent other grades. So we concluded that different grades have different transmission mode. Freshmen were the main facilitators of the spread of A(H1N1)pdm09 influenza during this school outbreak, so control measures (e.g. close contact isolation) priority used for freshmen would likely have effectively reduced spread of influenza in school settings.

Investigation of key interventions for shigellosis outbreak control in China

Shigellosis is a major public health concern in China, where waterborne disease outbreaks are common. Shigellosis-containing strategies, mostly single or multiple interventions, are implemented by primary-level health departments. Systematic assessment of the effectiveness of these measures is scarce. To estimate the efficacy of commonly used intervention strategies, we developed a Susceptible–Exposed–Infectious/Asymptomatic–Recovered–Water model. No intervention was predicted to result in a total attack rate (TAR) of 90% of the affected population (95% confidence interval [CI]: 86.65–92.80) and duration of outbreak (DO) of 89 days, and the use of single-intervention strategies can be futile or even counter-productive. Prophylactics and water disinfection did not improve TAR or DO. School closure for up to 3 weeks did not help but only increased DO. Isolation alone significantly increased DO. Only antibiotics treatment could shorten the DO to 35 days with TAR unaffected. We observed that these intervention effects were additive when in combined usage under most circumstances. Combined intervention “Isolation+antibiotics+prophylactics+water disinfection” was predicted to result in the lowest TAR (41.9%, 95%CI: 36.97–47.04%) and shortest DO (28 days). Our actual Shigellosis control implementation that also included school closure for 1 week, attained comparable results and the modeling produced an epidemic curve of Shigellosis highly similar to our actual outbreak data. This lends a strong support to the reality of our model that provides a possible reference for public health professionals to evaluate their strategies towards Shigellosis control.

THE STUDY OF HIV INFECTION IN CHINESE ANTIRETROVIRAL THERAPY PATIENTS

Analysis of changes in viral load after initiation of treatment with potent antiretroviral agents has provided substantial insights into the dynamics of human immunodeficiency virus type 1. We built a simple mathematics model to study the effect of latent-infected resting memory CD4+ T cells during the HIV infection and highly active anti-retroviral therapy (HAART). Through analysis of eight patients who received HAART in China, we have an insight into the mechanisms of resting memory CD4+ T cells in HIV infection. Simulations show that new infections still exist in the eight patients even under the HAART. Also, because of the long half-life of resting infected memory CD4+ T cells, removal of HIV from patient could take considerably longer time or be unattainable.

A Filippov system describing media effects on the spread of infectious diseases

A Filippov epidemic model with media coverage is proposed to describe the real characteristics of media/psychological impact in the spread of an infectious disease. We extend the existing models by incorporating a piecewise continuous transmission rate to describe that the media coverage exhibits its effect once the number of infected individuals exceeds a certain critical level. Mathematical and bifurcation analyses with regard to the local, global stability of equilibria and local sliding bifurcations are performed. Our main results show that the system stabilizes at either the equilibrium points of the two subsystems or the new endemic state induced by the on–off media effect, depending on the threshold levels. The finding suggests that a previously chosen level of the desired number of infected individuals can be reached when the threshold policy and other parameters are chosen properly.

Unraveling R0: considerations for public health applications

We assessed public health use of R0, the basic reproduction number, which estimates the speed at which a disease is capable of spreading in a population. These estimates are of great public health interest, as evidenced during the 2009 influenza A (H1N1) virus pandemic. We reviewed methods commonly used to estimate R0, examined their practical utility, and assessed how estimates of this epidemiological parameter can inform mitigation strategy decisions. In isolation, R0 is a suboptimal gauge of infectious disease dynamics across populations; other disease parameters may provide more useful information. Nonetheless, estimation of R0 for a particular population is useful for understanding transmission in the study population. Considered in the context of other epidemiologically important parameters, the value of R0 may lie in better understanding an outbreak and in preparing a public health response.

Bayesian estimation of the effective reproduction number for pandemic influenza A H1N1 in Guangdong Province, China

PURPOSE

During the course of a pandemic, it is necessary to understand its transmissibility, which is often summarized by the effective reproduction number. Accurate estimation of the effective reproduction number (R) is of vital significance in real-time decision making for coping with pandemic influenza.

METHODS

We used daily case notification data in Guangdong Province, China, in conjunction with Bayesian inference of two different stochastic susceptible, infectious, recovered (SIR) models to estimate the effective reproduction number. The duration of infectiousness was taken from published literature, and the proportion of imported cases was obtained from individual-level data.

RESULTS

At the initial epidemic phase, 40% of the first 261 cases were not locally acquired. Explicitly accounting for imported cases and different infectious periods, the possible range of basic reproduction number was preliminarily estimated to be between 1.05 and 1.46. We showed how the daily case reports provided valuable information to estimate the effective reproduction number. We also found the potential delay in reporting had a relatively minor impact on estimating R.

CONCLUSIONS

Our proposed models and findings provide a relevant contribution towards establishing a basis for monitoring the evolution of emerging infectious diseases in real time and understanding the characteristics of pandemic influenza A H1N1 in Guangdong Province.

Was mandatory quarantine necessary in China for controlling the 2009 H1N1 pandemic?

The Chinese government enforced mandatory quarantine for 60 days (from 10 May to 8 July 2009) as a preventative strategy to control the spread of the 2009 H1N1 pandemic. Such a prevention strategy was stricter than other non-pharmaceutical interventions that were carried out in many other countries. We evaluated the effectiveness of the mandatory quarantine and provide suggestions for interventions against possible future influenza pandemics. We selected one city, Beijing, as the analysis target. We reviewed the epidemiologic dynamics of the 2009 H1N1 pandemic and the implementation of quarantine measures in Beijing. The infectious population was simulated under two scenarios (quarantined and not quarantined) using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. The basic reproduction number R0 was adjusted to match the epidemic wave in Beijing. We found that mandatory quarantine served to postpone the spread of the 2009 H1N1 pandemic in Beijing by one and a half months. If mandatory quarantine was not enforced in Beijing, the infectious population could have reached 1,553 by 21 October, i.e., 5.6 times higher than the observed number. When the cost of quarantine is taken into account, mandatory quarantine was not an economically effective intervention approach against the 2009 H1N1 pandemic. We suggest adopting mitigation methods for an influenza pandemic with low mortality and morbidity.

Modelling HIV/AIDS epidemic among men who have sex with men in China

A compartmental model with antiviral therapy was proposed to identify the important factors that influence HIV infection among gay men in China and suggest some effective control strategies. We proved that the disease will be eradicated if the reproduction number is less than one. Based on the number of annual reported HIV/AIDS among MSM we used the Markov-Chain Monte-Carlo (MCMC) simulation to estimate the unknown parameters. We estimated a mean reproduction number of 3.88 (95% CI: 3.69-4.07). The estimation results showed that there were a higher transmission rate and a lower diagnose rate among MSM than those for another high-risk population. We compared the current treatment policy and immediate therapy once people are diagnosed with HIV, and numerical studies indicated that immediate antiviral therapy would lead to few HIV new infections conditional upon relatively low infectiousness; otherwise the current treatment policy would result in low HIV new infection. Further, increasing treatment coverage rate may lead to decline in HIV new infections and be beneficial to disease control, depending on the infectiousness of the infected individuals with antiviral therapy. The finding suggested that treatment efficacy (directly affecting infectiousness), behavior changes, and interventions greatly affect HIV new infection; strengthening intensity will contribute to the disease control.

Deviations in influenza seasonality: odd coincidence or obscure consequence?

In temperate regions, influenza typically arrives with the onset of colder weather. Seasonal waves travel over large spaces covering many climatic zones in a relatively short period of time. The precise mechanism for this striking seasonal pattern is still not well understood, and the interplay of factors that influence the spread of infection and the emergence of new strains is largely unknown. The study of influenza seasonality has been fraught with problems. One of these is the ever-shifting description of illness resulting from influenza and the use of both the historical definitions and new definitions based on actual isolation of the virus. The compilation of records describing influenza oscillations on a local and global scale is massive, but the value of these data is a function of the definitions used. In this review, we argue that observations of both seasonality and deviation from the expected pattern stem from the nature of this disease. Heterogeneity in seasonal patterns may arise from differences in the behaviour of specific strains, the emergence of a novel strain, or cross-protection from previously observed strains. Most likely, the seasonal patterns emerge from interactions of individual factors behaving as coupled resonators. We emphasize that both seasonality and deviations from it may merely be reflections of our inability to disentangle signal from noise, because of ambiguity in measurement and/or terminology. We conclude the review with suggestions for new promising and realistic directions with tangible consequences for the modelling of complex influenza dynamics in order to effectively control infection.

Modeling the initial transmission dynamics of influenza A H1N1 in Guangdong Province, China

BACKGROUND

The novel influenza A H1N1 (2009) virus, identified in mid-2009, spread rapidly in Guangdong Province. The accurate estimation of epidemiological parameters is of vital significance in decision-making for coping with pandemic influenza.

METHODS

We used influenza A H1N1 epidemic data from local cases in Guangdong Province, China, in conjunction with a complex SEIR model (susceptible, exposed, infectious, recovered) to estimate the basic reproduction number. The transmission rate was obtained by fitting the model to the cumulative number of local daily infected cases using the nonlinear ordinary least squares method. The latent period and duration of infectiousness were obtained from the published literature, and the proportion of symptomatic infected cases was obtained from the serological survey conducted by the Center for Disease Control and Prevention of Guangdong Province. We determined the variance of model parameters via a simulation study.

RESULTS

The model was in keeping with the observed epidemic data (coefficient of determination=0.982). The basic reproduction number was estimated preliminarily to be R0=1.525 (95% confidence interval 1.448-1.602), with the possible range of true R0 being 1.30-1.85. We estimated the transmission rate β to be between 0.390 and 0.432.

CONCLUSIONS

With the help of the serological survey, useful estimates of key epidemiological parameters for the influenza A H1N1 outbreak in Guangdong Province were obtained. The sensitivity analysis suggests that different latent periods and infectious periods, which specify different mean durations of generation time, have a significant impact on R0. Our proposed model and findings provide a relevant contribution towards understanding the characteristics of influenza A H1N1 in Guangdong Province.

Predicting the HIV/AIDS epidemic and measuring the effect of mobility in mainland China

HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube Sampling were used to estimate the basic reproductive ratio and its sensitivity to parameter variations. We estimated a mean reproduction number of 1.708 (95% CI 1.440-1.977). Our analysis using national surveillance data indicates that HIV-positive individuals most likely move from economically developed regions to regions with more numerous HIV cases, while mobility of AIDS patients likely flows in the opposite direction, due to the current policy that AIDS patients must return to their registered residence to receive free antiretroviral therapy. Our results based on a spatially stratified population dynamical model show increasing mobility rates of HIV/AIDS cases can have a significant effect on the number of HIV/AIDS cases per province and has the potential to decrease the overall number of HIV/AIDS cases in the country. We recommend that the community-based HIV/AIDS support and care program should be implemented by some local governments (especially in epidemically severe areas) to mitigate HIV infections in China.

MODELING STRATEGIES FOR CONTROLLING H1N1 OUTBREAKS IN CHINA

There has been a global attack of A/H1N1 virus in 2009, which widely affected the world's normal stability and economic development. Since the emergence of the first diagnosed A/H1N1 influenza infected person in 11 May 2009 in China, very strict policy including quarantine and isolation measures were widely implemented to control the spread of this disease before the vaccine appeared. We propose a compartmental model that mimics the infection process of A/H1N1 under control strategies taken in mainland China. Apart from theoretical analysis, using the statistic data of Shaanxi Province, we estimated the unknown epidemiological parameters of this disease in Shaanxi via least-squares fitting method. The estimated control reproductive number of H1N1 for its first peak was [Formula: see text] (95% CI: 2.362–2.748) and that for the second peak was [Formula: see text] (95% CI: 1.765–2.001). Our findings in this paper suggest that neither quarantine nor isolation measures could be relaxed, and the implementation of these interventions can reduce the pandemic outbreak of A/H1N1 pandemic significantly.

TRANSMISSION DYNAMICS AND OPTIMAL CONTROL OF AN INFLUENZA MODEL WITH QUARANTINE AND TREATMENT

We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic reproduction number [Formula: see text], the disease-free equilibrium (DFE) is globally asymptotically stable, if [Formula: see text], the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treatment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin's maximum principle is used to characterize the optimal levels of the three controls. Numerical simulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.

Campus quarantine (Fengxiao) for curbing emergent infectious diseases: lessons from mitigating A/H1N1 in Xi'an, China

During the 2009 A/H1N1 influenza pandemic, very strict interventions including campus quarantine (Fengxiao) (restrictions on the movements of university personnel) were taken in mainland China to slow down the initial spread of the disease from the university network to a wider community. The decision for implementation and/or relaxation of Fengxiao depends on the assessment of the level of infection within the university network compared with that in the wider community and on the degree of interruption of normal academic activities and the associated social/economic costs. However, the most important consideration influencing the decision is whether the initiation and termination of Fengxiao can alter the pattern of disease spread in the entire community for effective prevention and control of the emerging disease. Here we formulate and analyze a dynamic model to evaluate the effectiveness of Fengxiao as a social distance measure for curbing the outbreak in major cities of China. Using data from the initial laboratory-confirmed cases admitted to the 8th Hospital of Xi'an (the capital city of the Shaanxi Province), we estimated the reproduction number for the period under consideration in the range 1.273-1.784 and concluded that the population's mobility, combined with the suspension of the Fengxiao strategy, was a key factor contributing to a subsequent epidemic wave. Fengxiao in China is a reversal of the usual strategy of school closures adopted in many other countries, but the lessons learnt from it may be useful for disease management in other countries where restrictions on the movements across a facility boundary and close monitoring of the infection within the facility are feasible in the long term.

Risk factors for pandemic (H1N1) 2009 seroconversion among adults, Singapore, 2009

A total of 828 community-dwelling adults were studied during the course of the pandemic (H1N1) 2009 outbreak in Singapore during June-September 2009. Baseline blood samples were obtained before the outbreak, and 2 additional samples were obtained during follow-up. Seroconversion was defined as a >4-fold increase in antibody titers to pandemic (H1N1) 2009, determined by using hemagglutination inhibition. Men were more likely than women to seroconvert (mean adjusted hazards ratio [HR] 2.23, mean 95% confidence interval [CI] 1.26-3.93); Malays were more likely than Chinese to seroconvert (HR 2.67, 95% CI 1.04-6.91). Travel outside Singapore during the study period was associated with seroconversion (HR 1.76, 95% CI 1.11-2.78) as was use of public transport (HR 1.81, 95% CI 1.05-3.09). High baseline antibody titers were associated with reduced seroconversion. This study suggests possible areas for intervention to reduce transmission during future influenza outbreaks.

Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review

Please cite this paper as: Boëlle P‐Y et al. (2011) Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review. Influenza and Other Respiratory Viruses 5(5), 306–316.

Background  The new influenza virus A/H1N1 (2009), identified in mid‐2009, rapidly spread over the world. Estimating the transmissibility of this new virus was a public health priority.

Methods  We reviewed all studies presenting estimates of the serial interval or generation time and the reproduction number of the A/H1N1 (2009) virus infection.

Results  Thirteen studies documented the serial interval from household or close‐contact studies, with overall mean 3 days (95% CI: 2·4, 3·6); taking into account tertiary transmission reduced this estimate to 2·6 days. Model‐based estimates were more variable, from 1·9 to 6 days. Twenty‐four studies reported reproduction numbers for community‐based epidemics at the town or country level. The range was 1·2–3·1, with larger estimates reported at the beginning of the pandemic. Accounting for under‐reporting in the early period of the pandemic and limiting variation because of the choice of the generation time interval, the reproduction number was between 1·2 and 2·3 with median 1·5.

Discussion  The serial interval of A/H1N1 (2009) flu was typically short, with mean value similar to the seasonal flu. The estimates of the reproduction number were more variable. Compared with past influenza pandemics, the median reproduction number was similar (1968) or slightly smaller (1889, 1918, 1957).