The role of time-varying viral shedding in modelling environmental surveillance for public health: revisiting the 2013 poliovirus outbreak in Israel

Abstract

Environmental pathogen surveillance is a sensitive tool that can detect early-stage outbreaks, and it is being used to track poliovirus and other pathogens. However, interpretation of longitudinal environmental surveillance signals is difficult because the relationship between infection incidence and viral load in wastewater depends on time-varying shedding intensity. We developed a mathematical model of time-varying poliovirus shedding intensity consistent with expert opinion across a range of immunization states. Incorporating this shedding model into an infectious disease transmission model, we analysed quantitative, polymerase chain reaction data from seven sites during the 2013 Israeli poliovirus outbreak. Compared to a constant shedding model, our time-varying shedding model estimated a slower peak (four weeks later), with more of the population reached by a vaccination campaign before infection and a lower cumulative incidence. We also estimated the population shed virus for an average of 29 days (95% CI 28-31), longer than expert opinion had suggested for a population that was purported to have received three or more inactivated polio vaccine (IPV) doses. One explanation is that IPV may not substantially affect shedding duration. Using realistic models of time-varying shedding coupled with longitudinal environmental surveillance may improve our understanding of outbreak dynamics of poliovirus, SARS-CoV-2, or other pathogens.

Keywords: environmental surveillance; infectious disease model; poliovirus; viral shedding; wastewater surveillance.

Figure 1.

We calibrate our shedding model by specifying the number, type, order and mean duration of the compartments, as well as the daily shedding concentrations. A shedding model specifies the latent and infectious subcompartment parameters ${\sigma }_i\hspace{0.17em}$ and ${\gamma }_i\hspace{0.17em}$ and the ratio of low- to high-shedding rates $\lambda$ in our infectious disease model (table 1 and figure 2).

Figure 2.

An SLIR-type model, incorporating vaccination and environmental surveillance. The model represents infection by three strains of poliovirus: WPV1 (subscript w1), OPV1 (subscript o1) and OPV3 (subscript o3). We assume an individual, once infected with either WPV1 or OPV1, is not affected by the other. OPV3 is modelled independently of the other two strains. The latent and infectious compartments have multiple subcompartments, as calibrated in the shedding model. Parameter definitions are given in table 1.

Figure 3.

Mean expert opinion (points) and modelled simulation (lines) for the (a) fraction of the infected population shedding WPV1 and (b) mean faecal shedding concentration among those shedding, both as a function of time since exposure. Simulations are presented for three prior immunization states: fully susceptible (red) and 3+ doses of IPV (blue), at least one dose each of IPV and OPV (yellow). Simulations are determined by specifying compartment duration and shedding concentration in the shedding model in figure 1.

Figure 4.

(a) Modelled fractions of the population that were infected with WPV1, OPV1 and OPV3. The ribbons give the CIs for the maximum-likelihood trajectory using likelihood-based estimates of the 95% confidence parameter region. The grey bars give the approximate periods of the bOPV vaccination campaigns. (b) Epidemic trajectory of WPV1 comparing the best-fit model that incorporates a variable shedding model (solid) to the corresponding best-fit model that assumes constant shedding (dashed).

Figure 5.

qRT-PCR Ct data (points) and model fits (black line) for WPV1 (a), OPV1 (b) and OPV3 (c) strains in wastewater for each of the surveillance sites. The qRT-PCR data and modelled y are scaled by log₂ of their respective site-specific scaling parameter $\kappa$. The ribbons give the CIs for the maximum-likelihood trajectory using likelihood-based estimates of the 95% confidence parameter region. The grey bars give the approximate periods of the bOPV campaigns.