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Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, 17 Xu-Zhou Road, Taipei 100, TaiwanDivision of Infectious Diseases, Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan
The avian influenza A H7N9 virus has an R0 of 1.582 for poultry-to-poultry transmission.
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Without intervention, the H7N9 virus will persist in poultry populations.
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The R0 of H7N9 is only 0.07 for human-to-human transmission.
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Human-to-human transmission of H7N9 is not sustainable.
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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.
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.
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.
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.
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).
Figure 1The two-host model of H7N9 virus transmission in humans and poultry. See text for the definitions of symbols and the dynamic differential equations.
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.
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.
Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases.
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.
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.
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.
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 21
0
12
0
12
Apr 22 – Apr 28
0
1
0
1
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.
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
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
Parameters
Estimated values
Definition (unit)
μp
1/72
Natural turnover rate in poultry (per week)
βp
1.582
Poultry-to-poultry transmission rate (per week)
γp
1
Recovery rate in poultry (per week)
d
1/6, 1/1.3
Rate of screening and culling in poultry (per week)
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 .
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.
Figure 2The exponential growth of human H7N9 virus infection cases in 2013. Before the intervention started in late April 2013 (closing the live poultry markets), the number of new-onset and laboratory-confirmed human H7N9 cases grew exponentially from March 18 to April 14, 2013.
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.
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.
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.
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.
Figure 3Predicted 10-year trend of the H7N9 epidemic in poultry and humans, if none of the interventions are implemented. The x-axis represents time (in weeks) after the initial outbreak of human cases on February 18, 2013. The y-axis represents the proportions of infected humans (red line), infected poultry (blue line), and recovered (seropositive) poultry (pink line) in human and poultry populations. The denominator of the human population is set as 150 000 000 (total population of Shanghai, Zhejiang, and Jiangsu).
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.
Figure 4Predicted 10-year trend of the H7N9 epidemic in poultry and humans, if screening and culling of infected poultry are implemented every 6 weeks The x-axis represents time (in weeks) after the initial outbreak of human cases on February 18, 2013. The y-axis represents the proportions of infected humans (red line), infected poultry (blue line), and recovered (seropositive) poultry (pink line) in human and poultry populations. The denominator of the human population is set as 150 000 000 (total population of Shanghai, Zhejiang, and Jiangsu).
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.
Figure 5Predicted 10-year trend of the H7N9 epidemic in poultry and humans, if screening and culling of infected poultry are implemented every 10 days. The x-axis represents time (in weeks) after the initial outbreak of human cases on February 18, 2013. The y-axis represents the proportions of infected humans (red line), infected poultry (blue line), and recovered (seropositive) poultry (pink line) in human and poultry populations. The denominator of the human population is set as 150 000 000 (total population of Shanghai, Zhejiang, and Jiangsu).
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.
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.
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.
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.
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.
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.
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.
Comparative epidemiology of human infections with avian influenza A H7N9 and H5N1 viruses in China: a population-based study of laboratory-confirmed cases.
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