A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

<div><p>Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (MSS), applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, <i>R</i>₀, and <i>R</i>_eff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics.</p></div

Posterior nodes and standard deviations of mixture model parameters describing resistance in treatment-naïve patients.

<p>The four columns following represent the edges and corresponding edge weights associated with tree i. The edge weight is the conditional probability of being resistant to the child node given resistance to the parent node has occurred. If the parent node is the root (WT), the edge weight is the marginal probability of becoming resistant to the child node. Nodes = {WT = wild type, H = isoniazid, R = rifampin, E = ethambutol and S = streptomycin }.</p

Mechanisms of TB drug resistance in treatment-naïve and experienced patients.

<p>The first pathway describes patients who test positive for resistance to anti-TB drugs prior to their first treatment episode. These treatment- naïve patients were initially infected with a drug-resistant strain. The second pathway describes patients who were infected by a drug resistant strain and failed their first course of treatment. After their first course of treatment, they tested positive for resistance to anti-TB drugs. The final pathway describes patients who were infected by a drug susceptible strain and failed their first treatment episode because they acquired resistance via spontaneous mutation.</p

An example of the graphical display of a 2-tree mixture model with three nodes.

<p> is the set of edge weights defined as the conditional probability of the child node given the prior occurrence of the parent event. and are the probability that an individual follows a pathway represented by the first and second tree, respectively.</p

Non-star tree structures from mixture models for treatment-experienced patients.

<p>(a) non-star tree for AFR, FSU, NFSU-EUR, SEAR and WPR. (b) non-star tree for AMR (c) non-star tree for EMR and SEAR.</p

An algorithm for real-time calibration of stochastic compartmental epidemic models.

<p>An algorithm for real-time calibration of stochastic compartmental epidemic models.</p

Sequence of observations during an epidemic.

<p>Sequence of observations during an epidemic.</p

Number of different structures that arose from 30 bootstrap samples fit to naïve and treatment-experienced patients in each region.

<p>The number inside the parenthesis is the percentage of structures which were the same as that of the original sample.</p

Breakdown of data by region.

<p>The first row displays sample size, proportion of the population resistant to any drug and the corresponding confidence interval for treatment-naïve patients and the second row displays this information for patients with a previous treatment history. AFR = African region, AMR = region of the Americas, EMR = Easter Mediterranean region, FSU = Former Soviet Union region, NFSU-EUR = Non-Former Soviet Union European region, SEAR = South-East Asian region, WPR = Western Pacific region.</p

Linear trends in isoniazid resistance (INH-R) among new TB cases.

<p>We estimated trends in the percentage of new TB cases with INH-R and the estimated number of new TB cases with INH-R per 100,000 population. Settings are grouped by any linear trend (p<0.1) found (“down” or “up”) or “no consistent linear trend” if no linear trend was found. RF = Russian Federation.</p