Research Article| Volume 41, P73-78, December 2015

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# A modeling study of human infections with avian influenza A H7N9 virus in mainland China

Open AccessPublished:November 13, 2015

## Highlights

• The avian influenza A H7N9 virus has an R0 of 1.582 for poultry-to-poultry transmission.
• Without intervention, the H7N9 virus will persist in poultry populations.
• The R0 of H7N9 is only 0.07 for human-to-human transmission.
• Human-to-human transmission of H7N9 is not sustainable.
• Intensive screening/culling of infected poultry will rapidly eliminate the H7N9 virus.

## Summary

### Objectives

Since February 2013, more than 400 laboratory-confirmed human cases of avian influenza A H7N9 infection have been reported in mainland China. Little is known of the dynamics of this novel virus in poultry and human populations, which is essential for developing effective long-term control strategies for this zoonosis. The aim of this study was to evaluate the impact of screening and culling of infected poultry on the evolution of the H7N9 epidemic.

### Methods

A mathematical model for transmission dynamics of avian influenza A H7N9 virus in human and poultry populations was constructed. Parameters in the model were estimated using publicly available nationwide surveillance data on animal and human infections.

### Results

By fitting a two-host model, it was shown that screening for H7N9 in poultry and culling could effectively decrease the number of new human H7N9 cases. Furthermore, the elimination of circulating H7N9 virus is possible if an intensive, but technically feasible, poultry screening and culling policy is adopted.

### Conclusions

Screening and culling infected poultry is a critical measure for preventing human H7N9 infections in the long term. This model may provide important insights for decision-making on a national intervention strategy for the long-term control of the H7N9 virus epidemic.

## 1. Introduction

The first case of human infection with a novel influenza A H7N9 virus occurred in mainland China in February 2013.
• Gao R.
• Cao B.
• Hu Y.
• Feng Z.
• Wang D.
• Hu W.
• et al.
Human infection with a novel avian-origin influenza A (H7N9) virus.
• Lam T.T.
• Wang J.
• Shen Y.
• Zhou B.
• Duan L.
• Cheung C.L.
• et al.
The genesis and source of the H7N9 influenza viruses causing human infections in China.
By May 19, 2014, there had been 433 laboratory-confirmed human cases. Fever, cough, sputum, and shortness of breath are the most common clinical presentations.
• Gao H.N.
• Lu H.Z.
• Cao B.
• Du B.
• Shang H.
• Gan J.H.
• et al.
Clinical findings in 111 cases of influenza A (H7N9) virus infection.
More than 80% of cases have involved patients who had been exposed to live poultry.
• Li Q.
• Zhou L.
• Zhou M.
• Chen Z.
• Li F.
• Wu H.
• et al.
Epidemiology of human infections with avian influenza A(H7N9) virus in China.
• Chen Y.
• Liang W.
• Yang S.
• Wu N.
• Gao H.
• Sheng J.
• et al.
Human infections with the emerging avian influenza A H7N9 virus from wet market poultry: clinical analysis and characterisation of viral genome.
Infection with this H7N9 virus frequently leads to severe, life-threatening disease in humans. In contrast, this new type of virus has very low pathogenicity in poultry.
• Yu H.
• Cowling B.J.
• Feng L.
• Lau E.H.
• Liao Q.
• Tsang T.K.
• et al.
Human infection with avian influenza A H7N9 virus: an assessment of clinical severity.
• Cowling B.J.
• Jin L.
• Lau E.H.
• Liao Q.
• Wu P.
• Jiang H.
• et al.
Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases.
To prevent poultry-to-human transmission of this novel reassortant virus, the health authorities closed live poultry markets. The number of new-onset human cases with H7N9 virus infection decreased rapidly.
• Yu H.
• Wu J.T.
• Cowling B.J.
• Liao Q.
• Fang V.J.
• Zhou S.
• et al.
Effect of closure of live poultry markets on poultry-to-person transmission of avian influenza A H7N9 virus: an ecological study.
However, little is known of the dynamics of this novel virus in poultry and human populations, which is essential for developing effective long-term control strategies for this zoonosis.
The aims of this study were to develop a dynamic model for the transmission of H7N9 virus in both poultry and human populations in order to estimate the reproductive numbers (R0) of this virus and to evaluate the impact of the screening and culling of infected poultry on the evolution of the H7N9 epidemic.

## 2. Methods

### 2.1 Study design

A mathematical model to describe the transmission of avian influenza A H7N9 virus among two hosts – humans and poultry – was constructed. Parameters in the model were estimated using publicly available nationwide surveillance data of animal and human infections.

### 2.2 The two-host model

It was assumed that the novel influenza A H7N9 virus can spread rapidly among poultry and can be transmitted easily from poultry to humans, but has only a limited capacity for human-to-human transmission. A SIR modeling approach was used; for each of the two hosts, there are three mutually exclusive states: susceptible (S), infectious (I), and recovered (R) (Figure 1).

### 2.3 The poultry host

The poultry hosts have three states: susceptible poultry (SP), infected poultry (IP), and recovered poultry (RP). It was assumed that the birth rate of poultry (μp) is equal to their natural turnover rate in poultry-raising farms. Susceptible poultry are infected through poultry-to-poultry transmission at a rate of βp. Infected poultry have three alternative outcomes: natural turnover, recovery, or culling (after detection of H7N9 virus in the farm). Parameters γp and d represent the rates of recovery and culling, respectively (Figure 1).

### 2.4 The human host

The human hosts also have three states: susceptible people (Sh), infected people (Ih), and recovered people (Rh). It was assumed that the birth rate (μh) of the human population is equal to the natural death rate, which is estimated by the inverse of life expectancy at birth. Susceptible people become infected through poultry-to-human transmission at a rate of βp−h. Susceptible people can also become infected through human-to-human transmission at a rate of βh. Infected people had three alternative outcomes: H7N9 infection-related death, recovery, or natural death. Parameters m and γh represent the rates of infection-related mortality and recovery, respectively (Figure 1).

### 2.5 The interventions

The effect of screening and culling infected poultry at different levels of intensity was modeled by adjusting the numerical value of the culling rate d. The differential equations that describe the effect of interventions are summarized below; SP, IP, RP, Sh, Ih, and Rh represent proportions of the state among the total host populations, respectively.
$dSpdt=μp−βpSpIp−μpSp,dIpdt=βpSpIp−dIp−γpIp−μpIp,dRpdt=γpIp−μpRp,dShdt=μh−βhShIh−βp-hShIp−μhSh,dIhdt=βhShIh+βp−hShIp−mIh−γhIh−μhIh,dRhdt=γhIh−μhRh,$

### 2.6 Source of data

The information on cases of human infections with influenza A H7N9 virus (Table 1) were obtained from the websites of the Chinese Center for Disease Control and Prevention (CDC) (http://www.chinacdc.cn/) and the National Health and Family Planning Commission (http://www.nhfpc.gov.cn/zhuzhan/). The data included residence, age, sex, and the date of illness onset (or the laboratory confirmation date). The date of illness onset of human cases was estimated from the laboratory confirmation date if the information on the date of onset was missing, based on the average interval of 1 week from illness onset to laboratory confirmation.
• Cowling B.J.
• Jin L.
• Lau E.H.
• Liao Q.
• Wu P.
• Jiang H.
• et al.
Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases.
Table 1Numbers of human influenza A H7N9 infection cases in Shanghai, Zhejiang, and Jiangsu
Time (week)JiangsuZhejiangShanghaiTotal No. of casesNatural logarithm
Natural logarithm transformation of the total numbers of cases.
Feb 18 – Feb 240011
Feb 25 – Mar 30011
Mar 4 – Mar 100000
Mar 11 – Mar 170000
Mar 18 – Mar 2460061.791759
Exponential phase (March 18 to April 14, 2013). The slope of the natural logarithm transformation (for the total numbers of cases) over time is the rate of exponential growth of the H7N9 epidemic in humans.
Mar 25 – Mar 3143292.197225
Exponential phase (March 18 to April 14, 2013). The slope of the natural logarithm transformation (for the total numbers of cases) over time is the rate of exponential growth of the H7N9 epidemic in humans.
Apr 1 – Apr 7389202.995732
Exponential phase (March 18 to April 14, 2013). The slope of the natural logarithm transformation (for the total numbers of cases) over time is the rate of exponential growth of the H7N9 epidemic in humans.
Apr 8 – Apr 147223323.465736
Exponential phase (March 18 to April 14, 2013). The slope of the natural logarithm transformation (for the total numbers of cases) over time is the rate of exponential growth of the H7N9 epidemic in humans.
Apr 15 – Apr 21012012
Apr 22 – Apr 280101
a Natural logarithm transformation of the total numbers of cases.
b Exponential phase (March 18 to April 14, 2013). The slope of the natural logarithm transformation (for the total numbers of cases) over time is the rate of exponential growth of the H7N9 epidemic in humans.
The epidemiological data of human H7N9 cases, including the numbers of family clusters and secondary cases, were obtained from a cross-strait academic conference on H7N9 virus hosted by China and Taiwan.
• Yang W.Z.
• Wu H.Y.
• Xia S.C.
• Lee T.F.
• Shu Y.L.
• Xiang N.J.
The populations of Shanghai, Zhejiang, and Jiangsu were obtained from the Wikipedia website.
The animal surveillance data were obtained from the website of the Chinese Ministry of Agriculture (http://www.moa.gov.cn/). The data included testing results for H7N9 virus among animals in 2013 and 2014 (Table 2).
Table 2H7N9 serological surveillance results in poultry-raising farms of Shanghai, Zhejiang, and Jiangsu, 2013–2014
ShanghaiJiangsuZhejiang
TimeNumber of samplesNumber positivePositive rate (%)Number of samplesNumber positivePositive rate (%)Number of samplesNumber positivePositive rate (%)
April 201316 55430.0263 39010.0087 801160.02
May 2013000.0020 78600.00000.00
June–July 2013440100.0015 62000.00000.00
August 201322500.0084000.00000.00
September 2013318200.0021 12190.04339400.00
November 2013795100.00419600.004051200.49
December 2013125200.00549400.008578.24
Early-January 201413000.0040800.00000.00
Mid-January 2014000.00227800.00000.00
Late-January 2014255600.0010 10100.00986400.00
Early-February 2014000.0062100.00737500.00
Mid-February 201491500.00366600.0089000.00
Late-February 201420700.0010 33400.00271310.04
Early-March 2014000.00321080.2588100.00
Mid-March 2014000.00350500.00000.00
Late-March 2014218167.34746600.00000.00

### 2.7 Parameterization

Table 3 lists the parameters used in the model. The average lifetime of the human is 75 years. Based on this, the value of μh was set as 0.00025641 (per week). The average life span of poultry (at a poultry-raising farm) is 72 weeks, and μp was set as 1/72 (per week). The median duration of illness in human cases is 7 days. A recovery rate of 1 (per week) for both humans and poultry was therefore assumed. The parameters for poultry-to-poultry, poultry-to-human, and human-to-human transmission, infection-related mortality, and poultry screening–culling were estimated using epidemiological surveillance data in human and poultry populations.
Table 3Values of parameter estimations in the mathematical model
ParametersEstimated valuesDefinition (unit)
μp1/72Natural turnover rate in poultry (per week)
βp1.582Poultry-to-poultry transmission rate (per week)
γp1Recovery rate in poultry (per week)
d1/6, 1/1.3Rate of screening and culling in poultry (per week)
μh0.00025641Birth or death rate of humans (per week)
βh0.07Human-to-human transmission rate (per week)
γh1Recovery rate in humans (per week)
βp−h5.3 × 10−6Animal-to-human transmission rate (per week)
m0.563Infection-induced mortality in humans (per week)

## 3. Results

### 3.1 R0 of poultry-to-poultry transmission

Since H7N9 infection is asymptomatic in poultry, the poultry-to-poultry transmission rate βp could not be estimated directly from the animal surveillance data. Instead, βp was estimated from the rate of exponential growth in numbers of human H7N9 cases (Table 1) before the start of interventions. The rate of exponential growth in numbers of human cases provides an unbiased estimate of the rate of exponential growth in numbers of poultry H7N9 infections, because the numbers of human cases are driven by the numbers of poultry infections. The rate of exponential growth of poultry infections was determined by the poultry-to-poultry transmission rate βp minus the poultry recovery rate γp .
• Keeling M.J.
• Rohani P.
Modeling infectious disease in humans and animals.
• Fang C.T.
• Hsu H.M.
• Twu S.J.
• Chen M.Y.
• Chang Y.Y.
• Hwang J.S.
• et al.
Decreased HIV transmission after a policy of providing free access to highly active antiretroviral therapy in Taiwan.
Table 1 and Figure 2 show that the numbers of new-onset and laboratory-confirmed human cases increased exponentially from March 18, 2013 to April 14, 2013 at a rate of 0.582 per week. Since the poultry recovery rate γp is 1 per week, the best estimate for the poultry-to-poultry transmission rate βp is 1.582 per week, and the best estimate for R0 of poultry-to-poultry transmission is 1.582.

### 3.2 R0 of human-to-human transmission

The rate of human-to-human H7N9 transmission was estimated using the method for calculating the reproductive number R when the human-to-human transmission is not sustainable.
• De Serres G.
• Gay N.J.
• Farrington C.P.
Epidemiology of transmissible diseases after elimination.
To support the hypothesis that H7N9 did not cause sustained human-to-human transmission, the epidemiological surveillance data for human H7N9 cases were obtained from the Chinese CDC. As of May 19, 2014, there had been a total of 433 cases of human H7N9 infection in mainland China, including 401 primary cases, 30 secondary cases, and two tertiary cases.
• Yang W.Z.
• Wu H.Y.
• Xia S.C.
• Lee T.F.
• Shu Y.L.
• Xiang N.J.
These surveillance data indicate that human-to-human transmission of H7N9 is not sustainable. The above-stated method was then applied to calculate the R0 of H7N9 in humans from the surveillance data, which was 0.07. Details of the calculation are given in the Appendix. The human-to-human transmission rate βh was then obtained by dividing the reproductive number R by the mean duration of infectiousness (1 week). The best estimate for the human-to-human transmission rate βh is thus 0.07 per week.

### 3.3 Estimation of other key parameters

The case fatality rate of H7N9 infections is 36%,
• Yu H.
• Wu J.T.
• Cowling B.J.
• Liao Q.
• Fang V.J.
• Zhou S.
• et al.
Effect of closure of live poultry markets on poultry-to-person transmission of avian influenza A H7N9 virus: an ecological study.
• Yang W.Z.
• Wu H.Y.
• Xia S.C.
• Lee T.F.
• Shu Y.L.
• Xiang N.J.
which is equivalent to an H7N9 infection-related mortality rate of 0.563 per week (see Appendix for details). It was also estimated that the poultry-to-human transmission rate of H7N9 is 5.3 × 10−6 per week (see Appendix for details). The mean frequency of poultry screening in Shanghai, Zhejiang, and Jiangsu was once every 6 weeks in 2013. The screening frequency increased to once every 1.3 weeks (10 days) in 2014. When poultry infected with the H7N9 virus were detected, they were rapidly culled. Therefore, d was 1/6 (per week) in 2013 and 1/1.3 (per week) in 2014.

### 3.4 Trend in the H7N9 epidemic under different intervention scenarios

By fitting the data to the model, the trend in the H7N9 epidemic under different hypothetical intervention scenarios was simulated.

#### 3.4.1 Scenario 1: No screening and culling of infected poultry

Figure 3 shows that the H7N9 outbreak in humans (red line) is parallel to the H7N9 outbreak among poultry (blue line). After the initial 2013–2014 outbreak, there will be several subsequent outbreaks every 1.5 to 2 years. Eventually, H7N9 will become an endemic disease in both poultry and human populations. The H7N9 seroprevalence rate among poultry (pink line) will stabilize at a level of 35%. H7N9 virus will persist in poultry, with continuing occurrence of human H7N9 cases at a stable frequency in the coming decades.

#### 3.4.2 Scenario 2: Screening and culling of infected poultry every 6 weeks

Figure 4 shows that an intervention with a screening and culling rate of 1/6 (per week) will decrease the peaks of the human outbreak (red line) and poultry outbreak (blue line). The seroprevalence rate among poultry in the endemic stage will also decrease to 22% (pink line). Nevertheless, the H7N9 virus will still persist in poultry, with a continuing occurrence of human H7N9 infection cases.

#### 3.4.3 Scenario 3: Screening and culling of infected poultry every 10 days

Figure 5 shows that a more intensive but technically feasible intervention with a screening and culling rate of 1/1.3 (per week) will prevent subsequent outbreaks of H7N9 in poultry and humans, and rapidly eliminate the H7N9 virus from poultry. The seroprevalence rate among poultry will decrease rapidly to nearly zero in the next 5 years. This will prevent the occurrence of new human H7N9 infection cases.

## 4. Discussion

A dynamic two-host model for the transmission of H7N9 virus in both poultry and human populations was successfully developed. The key transmission parameters in both poultry and human populations were estimated using publicly available nationwide surveillance data of animal and human infections. The simulation results indicate that without interventions, avian influenza A H7N9 will become endemic. The virus will persist in poultry, with a continuing occurrence of human H7N9 infection cases at a stable frequency in the coming decades. On the other hand, an intensive but still technically feasible intervention, with screening and culling of infected poultry every 10 days, will rapidly eliminate the H7N9 virus from both poultry and human populations in the next 5 years.
The closure of live poultry markets is the initial intervention used by health authorities to control H7N9 outbreaks. The closure of live poultry markets works by reducing the contact between people and poultry, and as a result, decreasing the poultry-to-human transmission. The closure of live poultry markets successfully decreased the number of new-onset human H7N9 infection cases in Shanghai, Zhejiang, and Jiangsu.
• Yu H.
• Wu J.T.
• Cowling B.J.
• Liao Q.
• Fang V.J.
• Zhou S.
• et al.
Effect of closure of live poultry markets on poultry-to-person transmission of avian influenza A H7N9 virus: an ecological study.
However, for economic reasons, live poultry markets cannot be shut down permanently. Therefore, other intervention strategies need to be evaluated. The results of this study show that the aggressive screening and culling of infected poultry every 10 days could rapidly eliminate H7N9 virus from both poultry and humans in the long term. This provides an important insight for decision-making on the national intervention strategy for the long-term control of the H7N9 epidemic.
Compared with a previous modeling study on H7N9,
• Xiao Y.
• Sun X.
• Tang S.
• Wu J.
Transmission potential of the novel avian influenza A (H7N9) infection in mainland China.
which also fitted the model to numbers of confirmed human cases, the present study incorporated two additional sources of empirical data to improve the accuracy of parameter estimation. The first was access to epidemiological surveillance data from the Chinese CDC, which allowed the accurate calculation of the reproductive number of H7N9 among humans as 0.07. This in turn led to a more precise estimate for the human-to-human transmission rate βh, one of the key transmission parameters determining the potential of H7N9 to cause outbreaks. The second was access to more comprehensive animal surveillance data from Chinese Ministry of Agriculture. The peak seroprevalence rates in poultry samples from Zhejiang and Shanghai (8.24% and 7.34%, Table 1) support the present model, which predicts that up to 8% of poultry were infected during the peak of the H7N9 outbreak before the implementation of the intervention (Figure 3). This in turn allowed us to obtain a more accurate estimate for the poultry-to-human transmission rate βp−h, another key transmission parameter determining the potential of H7N9 to cause outbreaks in humans.
Two factors make it difficult to obtain a realistic estimate of the poultry-to-poultry transmission rate of H7N9 virus directly from animal surveillance data. First, H7N9 infection is asymptomatic in poultry.
• Cowling B.J.
• Jin L.
• Lau E.H.
• Liao Q.
• Wu P.
• Jiang H.
• et al.
Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases.
This precludes a syndromic surveillance among animals. Second, screening data for asymptomatic poultry is far from comprehensive. However, symptomatic human H7N9 infection case data can provide an unbiased estimate for this important key transmission parameter. This is because, when two different types of host coexist, the number of new infections in the low-risk host (human) will be driven by the epidemic in the high-risk host (poultry). The rate of exponential growth in the numbers of new low-risk host (human) cases will be identical to that of the number of new high-risk host (poultry) cases. Therefore, it was possible to obtain the estimate of the poultry-to-poultry transmission rate from the slope of the natural logarithm-transformed numbers of new human infection cases during the exponential phase, using established methods.
• Keeling M.J.
• Rohani P.
Modeling infectious disease in humans and animals.
• Fang C.T.
• Hsu H.M.
• Twu S.J.
• Chen M.Y.
• Chang Y.Y.
• Hwang J.S.
• et al.
Decreased HIV transmission after a policy of providing free access to highly active antiretroviral therapy in Taiwan.
The rate of human-to-human H7N9 transmission was estimated using the method for calculating the reproductive number R when the human-to-human transmission is not sustainable.
• De Serres G.
• Gay N.J.
• Farrington C.P.
Epidemiology of transmissible diseases after elimination.
This method has been used successfully to estimate R of measles during the elimination phase (1995–1997) in the United States.
• Chiew M.
• Gidding H.F.
• Dey A.
• Wood J.
• Martin N.
• Davis S.
• et al.
Estimating the measles effective reproduction number in Australia from routine notification data.
• Gay N.J.
• De Serres G.
• Farrington C.P.
• Redd S.B.
• Papania M.J.
Assessment of the status of measles elimination from reported outbreaks: United States, 1997-1999.
Just like measles during the elimination phase in the United States, the H7N9 virus did not cause sustained human-to-human transmission in China. Therefore, it was hypothesized that the same method could be used to estimate the rate of human-to-human transmission of H7N9. To support the hypothesis that H7N9 did not cause sustained human-to-human transmission, the epidemiological surveillance data for human H7N9 cases were obtained from the Chinese CDC.
• Yang W.Z.
• Wu H.Y.
• Xia S.C.
• Lee T.F.
• Shu Y.L.
• Xiang N.J.
These surveillance data indicate that human-to-human transmission of H7N9 is not sustainable. The above-stated method was then applied to successfully calculate the R value of H7N9 from the surveillance data as 0.07.
There are several important limitations to this study. First, data of laboratory-confirmed cases with H7N9 virus were used to estimate some parameters. This may have underestimated the size of the epidemic. Second, the animal surveillance data are very likely to be incomplete, which precludes the use of these data to make a valid inference on the range of parameters. Third, several parameters, such as the human and poultry recovery rates, were based on assumptions rather than empirical data. Finally, it was assumed that the screening procedure has a high sensitivity to detect all infected poultry. This assumption may be optimistic, and may therefore have led to an over-estimation for the effect of the screening and culling intervention.
In conclusion, this model shows that screening and culling of infected poultry is the critical measure for preventing human H7N9 infections in the long term. This model may provide an important insight for decision-making on a national intervention strategy for the long-term control of the H7N9 virus epidemic.

## Acknowledgement

The authors acknowledge the financial support provided by the Infectious Diseases Research and Education Center, Ministry of Health and Welfare and National Taiwan University. The funder had no role in the study design, data collection and analysis, or preparation of the manuscript.
Conflict of interest: The authors have no conflicts of interest to declare.

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