Evaluation of animal-to-human and human-to-human transmission of influenza A (H7N9) virus in China, 2013–15

A novel avian-origin influenza A(H7N9) virus emerged in China in March 2013 and by 27 September 2017 a total of 1533 laboratory-confirmed cases have been reported. Occurrences of animal-to-human and human-to-human transmission have been previously identified, and the force of human-to-human transmission is an important component of risk assessment. In this study, we constructed an ecological model to evaluate the animal-to-human and human-to-human transmission of H7N9 during the first three epidemic waves in spring 2013, winter/spring 2013–2014 and winter/spring 2014–2015 in China based on 149 laboratory-confirmed urban cases. Our analysis of patterns in incidence in major cities allowed us to estimate a mean incubation period in humans of 2.6 days (95% credibility interval, CrI: 1.4–3.1) and an effective reproduction number Re of 0.23 (95% CrI: 0.05–0.47) for the first wave, 0.16 (95% CrI: 0.01–0.41) for the second wave, and 0.16 (95% CrI: 0.01–0.45) for the third wave without a significant difference between waves. There was a significant decrease in the incidence of H7N9 cases after live poultry market closures in various major cities. Our analytic framework can be used for continued assessment of the risk of human to human transmission of A(H7N9) virus as human infections continue to occur in China.


Market hazard model: animal-to-human transmission
First we defined: -Npre,t,i is the average number of people who visited LPMs in area i before closure.
-Nost,t,i is the average number of people who visited LPM in area i after closure (95% reduction of visits number was considered).
-pre,i is the constant force of infection in the area i in LPM before closure -post,i is the constant force of infection in the area i in LPM after closure.
-F(t) is the CDF of the incubation period of H7N9 following a Weibull distribution with parameters (a,b).
-Ai is the date on which the first case was anounced in area i.
-Bi = Ai − 4 and Ti are the start and end of time horizon for area i.
The 4 days adjustment was made to account for any potential errors associated with variations in symptoms definition, patient recall of symptoms onset and incubation period.
-Xt,i is the number of confirmed cases with onset on day t in area i.
-C i,j is the date of LPM closure in area i.
We assumed that the population visiting LPM in each area i was subject to a daily per capita force of infection pre,i before any live poultry market (LPM) was closed and post,i after all LPMs were closed.

Ci (LPM closure)
New infections in area i occurred according to a Poisson process such that the number of infections on day t was Poisson distributed with mean pre,i Npre,t,i for t ∈[Ai, Ci -1] and post,i Npost,t,i for t ∈[Ci, T].
We assumed that the incubation period followed the same (cumulative) probability Weibull distribution F with scale a and shape b for all cities.
Under these assumptions, the number of cases with onset on day t in area i was Poisson distributed with mean :

Human-to-human transmission model:
We defined the human-to-human transmission, assuming that an infected individual has an infectiousness profile, i.e. the serial interval of H7N9, following a Poisson distribution with mean Sp. Using the effective reproduction number Re, i.e. the number of new infections generated by each infectious individual, we defined hH(t) the expected number of new human cases with onset on day t in area i: where : -k is the maximum value of the serial interval (we arbitrarily fixed k=14 days).
-N(t) is the number of newly infected individuals at time t.
-S p is the mean serial interval.
for Ait  for Ci tTi -Re is the effective reproduction number assumed to be constant over time and in the different areas.
The likelihood for the time series of observed human cases in all the LPM observed in this study was defined using the PDF of Poisson distribution : where hi(t)=ha,i(t)+hH,i(t), the sum of animal-to-human and human-to-human H7N9 cases at each day t.
We estimated the pre-and post-LPM closure constant force of infection, the parameters of the incubation period distribution and Re by fitting the model to the epidemic curve data in the different areas using MCMC methods.
We assumed a semi-informative prior (normal distribution with mean 0 and standard deviation 10) for a and non-informative flat priors for all other parameters. We drew 10,000 samples from the posterior distributions after a burn-in of 5,000 iterations.

Sensitivity analysis
To assess the impact of unreported primary cases, we simulated epidemics based on the ecological data we collected and on the assumption that on a given day, the number of reported cases is defined as: = , where q is the proportion of reported cases, Mt the number of reported cases and Nt the real number of cases each given day. Under this assumption, we simulated epidemics by adding the ecological data with the number of unreported cases estimated each day, using a binomial distribution with parameters p, i.e the probability of unreporting (1-q) and n the number of reported cases that given day.
We simulated 1,000 epidemics for each value of p and we fitted the model to each of this simulated epidemic. We finally merged all the posterior distributions to get the estimates of each parameter.