Posterior results for FMD-ILM using the spatial stratification method.

<p>Posterior means and 95% credible intervals for all parameters of the data augmented FMD-ILM under the spatial stratification method. We sampled <i>ρ</i> = 0.50 from each stratum. The results are compared to the full model.</p

Posterior results for full MCMC and SRS methods.

<p>Posterior means and 95% credible intervals for <i>α</i>, <i>β</i>, and <i>λ</i>_<i>z</i> for the full MCMC and SRS methods for 10 different epidemics simulated from the data augmented spatial ILM with varying sampling proportions. The dashed, horizontal lines represent the true parameter values: <i>α</i> = 1.4, <i>β</i> = 2.3, and <math><mrow><msub><mo>λ</mo><mi>z</mi></msub><mo>=</mo><mn>1</mn><mn>3</mn></mrow></math>, with a population of size <i>n</i> = 625.</p

Average infectious period under the simulation study.

<p>Illustration of the average infectious period under the simulation study. The average incubation period is 3 days, and the average delay to disease recovery and removal from the population is 4 days. The ‘S’ symbol indicates the individual is susceptible to the disease at that time point and the ‘R’ symbol indicates the individual has recovered from the disease and has been removed from the population at that time point.</p

Posterior results for FMD-ILM using the SRS method.

<p>Posterior means and 95% credible intervals for all parameters of the data augmented FMD-ILM under the SRS method. The results are compared to the full model to assess accuracy.</p

Full posterior results for full MCMC and spatial stratification methods.

<p>Posterior means and 95% credible intervals for <i>α</i>, <i>β</i>, and <i>λ</i>_<i>z</i> for the full MCMC and spatial stratification methods for 10 different epidemics simulated from the data augmented spatial ILM with varying values for <i>m</i> and <i>ρ</i>. The dashed, horizontal lines represent the true parameter values: <i>α</i> = 1.4, <i>β</i> = 2.3, and <math><mrow><msub><mo>λ</mo><mi>z</mi></msub><mo>=</mo><mn>1</mn><mn>3</mn></mrow></math>, with a population of size <i>n</i> = 625.</p

Predictive accuracy evaluated via the root mean square error (RMSE) of autoregressive integrated moving average (ARIMA), generalized linear autoregressive moving average (GLARMA), and random forest (RF) time series models.

<p>Predictive accuracy evaluated via the root mean square error (RMSE) of autoregressive integrated moving average (ARIMA), generalized linear autoregressive moving average (GLARMA), and random forest (RF) time series models.</p

Assessment of autoregressive integrated moving average (ARIMA), generalized linear autoregressive moving average (GLARMA), and random forest (RF) time series regression models for predicting influenza A virus frequency in swine in Ontario, Canada

<div><p>Influenza A virus commonly circulating in swine (IAV-S) is characterized by large genetic and antigenic diversity and, thus, improvements in different aspects of IAV-S surveillance are needed to achieve desirable goals of surveillance such as to establish the capacity to forecast with the greatest accuracy the number of influenza cases likely to arise. Advancements in modeling approaches provide the opportunity to use different models for surveillance. However, in order to make improvements in surveillance, it is necessary to assess the predictive ability of such models. This study compares the sensitivity and predictive accuracy of the autoregressive integrated moving average (ARIMA) model, the generalized linear autoregressive moving average (GLARMA) model, and the random forest (RF) model with respect to the frequency of influenza A virus (IAV) in Ontario swine. Diagnostic data on IAV submissions in Ontario swine between 2007 and 2015 were obtained from the Animal Health Laboratory (University of Guelph, Guelph, ON, Canada). Each modeling approach was examined for predictive accuracy, evaluated by the root mean square error, the normalized root mean square error, and the model’s ability to anticipate increases and decreases in disease frequency. Likewise, we verified the magnitude of improvement offered by the ARIMA, GLARMA and RF models over a seasonal-naïve method. Using the diagnostic submissions, the occurrence of seasonality and the long-term trend in IAV infections were also investigated. The RF model had the smallest root mean square error in the prospective analysis and tended to predict increases in the number of diagnostic submissions and positive virological submissions at weekly and monthly intervals with a higher degree of sensitivity than the ARIMA and GLARMA models. The number of weekly positive virological submissions is significantly higher in the fall calendar season compared to the summer calendar season. Positive counts at weekly and monthly intervals demonstrated a significant increasing trend. Overall, this study shows that the RF model offers enhanced prediction ability over the ARIMA and GLARMA time series models for predicting the frequency of IAV infections in diagnostic submissions.</p></div

Residuals plots.

<p>The residuals were obtained after fitting with simulated prospective autoregressive integrated moving average (ARIMA), generalized linear autoregressive moving average (GLARMA), and random forest (RF) model predicted counts at weekly and monthly intervals.</p

Retrospective predicted counts of weekly and monthly submissions and positive submissions for IAV.

<p>The autoregressive integrated moving average (ARIMA) is shown in red, the generalized linear autoregressive moving average (GLARMA) in blue, and the random forest (RF) in green. The actual observations are represented by black lines.</p

Normal Quantile-|Quantile (Q-Q) plots of the residuals.

<p>Residuals were obtained after fitting with simulated prospective autoregressive integrated moving average (ARIMA), generalized linear autoregressive moving average (GLARMA), and random forest (RF) model predicted counts at weekly and monthly intervals.</p