Economic factors influencing zoonotic disease dynamics: demand for poultry meat and seasonal transmission of avian influenza in Vietnam

While climate is often presented as a key factor influencing the seasonality of diseases, the importance of anthropogenic factors is less commonly evaluated. Using a combination of methods – wavelet analysis, economic analysis, statistical and disease transmission modelling – we aimed to explore the influence of climatic and economic factors on the seasonality of H5N1 Highly Pathogenic Avian Influenza in the domestic poultry population of Vietnam. We found that while climatic variables are associated with seasonal variation in the incidence of avian influenza outbreaks in the North of the country, this is not the case in the Centre and the South. In contrast, temporal patterns of H5N1 incidence are similar across these 3 regions: periods of high H5N1 incidence coincide with Lunar New Year festival, occurring in January-February, in the 3 climatic regions for 5 out of the 8 study years. Yet, daily poultry meat consumption drastically increases during Lunar New Year festival throughout the country. To meet this rise in demand, poultry production and trade are expected to peak around the festival period, promoting viral spread, which we demonstrated using a stochastic disease transmission model. This study illustrates the way in which economic factors may influence the dynamics of livestock pathogens.

With γ being the rate of depopulation, and with δ being the rate of restocking and t R the number of depopulated farms at time t.
Transmission was density-dependent. Moreover, we assumed homogeneous mixing, and ignored spatial heterogeneity in the transmission process, to ensure that the model is as parsimonious as possible while allowing exploration of the temporal variations in viral spread.

Supplementary Method S3. Characteristics of the Approximate Bayesian computation algorithm 1.Selection criteria used in the Approximate Bayesian Computation (ABC) algorithm
A proposed particle was selected if it meets the three following criteria: 1. Kolmogorov-Smirnov distance between simulated and observed cumulated distributions of waiting times between AIOs 1 needed to be lower than a pre-defined threshold 2 . 0 = T . Further reduction of this threshold did not affect the shape of the posterior distribution.
2. The maximum proportion of removed farms needed to be below 25% at any time step. A higher proportion appears rather unrealistic as it means that poultry production would be majorly disrupted, which has never been observed since the first AI epizootic 3. AIOs must be reported during the last year, i.e. the disease must be maintained throughout the study period.

3.Resulting selection rate
With the abovementioned selection criteria and prior intervals, it took on average 60 to 4580 iterations to select a particle (i. The duration of periods spent by birds in the E and I compartments were not exponentially distributed. Instead, these periods were the sum of a fixed minimum duration and an additional stochastic integer duration generated from a binomial distribution. Further details are provided in 2 .
It was assumed that detection occurs when reaching a certain cumulative mortality threshold T over a 2 days' period, i.e. when

Data
The number of birds per farm was supposed to vary from 20 to 1,000 3,4 . The latent and infectious period of individual birds were taken from 5 . The latent period distribution ranged from 3 to 11 hours with a mean of 6 hours. The infectious period ranged from 43 to 55 hours with a mean of 48 hours. Estimates of intra-flock reproduction numbers were taken from 5 and 6 . The legal definition of a suspicion of H5N1 in a poultry flock in Vietnam is 5% cumulated mortality over 2 consecutive days 7 . We considered a threshold of 10% cumulated mortality in 2 consecutive days as it constitutes a more realistic assumption. It is particularly true in the case of smallholder farms with a limited number of birds which represent more than 90% of poultry farms of Viet Nam 3 .

Results
For each set of parameters, the estimation of the detection period was based on 1000 simulations.
The minimum and maximum estimates are presented in the following table:

Recovery period
As no precise data was available, the length of the recovery period was estimated based on the authors' knowledge of Vietnamese poultry production. It was assumed that the period during which farms remained depopulated was unlikely to be lower than 15 days, as farmers feared reinfection caused by virus survival in the environment, but it was very unlikely to be higher than 45 days, as farmers tended to resume their production as quickly as possible for economic reasons.

Supplementary Table S1
Values of posterior rates of infectious contacts during and outside the defined at-risk period and their ratio selected through Approximate Bayesian Computation in the three pre-defined climatic regions of Vietnam (Median, minimum and maximum).