Understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models

Abstract

The nature and role of re-infection and partial immunity are likely to be important determinants of the transmission dynamics of human respiratory syncytial virus (hRSV). We propose a single model structure that captures four possible host responses to infection and subsequent reinfection: partial susceptibility, altered infection duration, reduced infectiousness and temporary immunity (which might be partial). The magnitude of these responses is determined by four homotopy parameters, and by setting some of these parameters to extreme values we generate a set of eight nested, deterministic transmission models. In order to investigate hRSV transmission dynamics, we applied these models to incidence data from eight international locations. Seasonality is included as cyclic variation in transmission. Parameters associated with the natural history of the infection were assumed to be independent of geographic location, while others, such as those associated with seasonality, were assumed location specific. Models incorporating either of the two extreme assumptions for immunity (none or solid and lifelong) were unable to reproduce the observed dynamics. Model fits with either waning or partial immunity to disease or both were visually comparable. The best fitting structure was a lifelong partial immunity to both disease and infection. Observed patterns were reproduced by stochastic simulations using the parameter values estimated from the deterministic models.

Fig. 1

A diagram of the parent model (Model 8) of the nested set. The boxes represent the state variables of the model for each of which there is an ordinary differential equation. The arrows represent the flow between the states of the model.

Fig. 2

A diagram showing the relationships of the nested models. An arrow from Model A to Model B indicates that A can be transformed to B by explicitly including the labelled parameters.

Fig. 3

The fit of Model 6 to the eight data sets. For each location, the model prediction of the incidence (line) is plotted with the monthly cases for that location (crosses).

Fig. 4

West Midlands RSV data with Model 6 prediction. The model prediction of the incidence (line) plotted with the weekly cases from the West Midlands (crosses).

Fig. 5

Bar charts showing the results of 50 simulations of the stochastic version of Model 6 for (a) closed populations (ξ = 0) and (b) populations where there is random influx of infections (ξ = 2 × 10⁻⁷).

Fig. 6

Graph showing the predicted number of (primary and repeat) infections by Model 6 without seasonal forcing using parameter values estimated from the Finland data set for different values of basic reproduction number including the reinfection threshold (bold dotted) and the estimated lower and upper seasonal limits (dashed).