Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Combining statistical and dynamic modelling approaches to within-host analysis of Porcine Reproductive and Respiratory Syndrome (PRRS) virus infections
Zeenath Islam, Stephen C Bishop, Nicholas J Savil, Raymond R. R. Rowland, Joan K Lunney, Benjamin Trible, Andrea Doeschl-Wilson

Last modified: 2014-03-31


Porcine reproductive and respiratory syndrome (PRRS) is one of the most economically significant viral diseases facing the global swine industry. Viremia profiles of PRRS virus challenged pigs reflect the severity and progression of infection within the host and provide crucial information for subsequent control measures. In this study we analyse the largest available longitudinal PRRS viremia dataset from an in-vivo experiment. The primary objective was to provide a suitable mathematical description of viremia profiles with biologically meaningful parameters for quantitative analysis of profile characteristics. The Wood’s function, a gamma-type function, and a biphasic extended Wood’s function were fit to the individual profiles using Bayesian inference with a likelihood framework. Using maximum likelihood inference and numerous fit criteria, we established that the broad spectrum of viremia trends could be adequately represented by either uni- or biphasic Wood’s functions. Three viremic categories emerged: cleared (uni-modal and below detection within 42 days post infection(dpi)), persistent (transient experimental persistence over 42 dpi) and rebound (biphasic within 42 dpi). The convenient biological interpretation of the model parameters estimates, allowed us not only to quantify inter-host variation, but also to establish common viremia curve characteristics and their predictability. Statistical analysis of the profile characteristics revealed that persistent profiles were distinguishable within 21 dpi, whereas it is not possible to predict the onset of viremia rebound. Analysis of the neutralizing antibody(nAb) data indicated that there was a ubiquitous strong response to the homologous PRRSV challenge, but high variability in the range of cross-protection of the nAbs. Persistent pigs were found to have a significantly higher nAb cross-protectivity than pigs that either cleared viremia or experienced rebound within 42 dpi.

Our study provides novel insights into the nature and degree of variation of hosts’ responses to infection as well as new informative traits for subsequent genomic and dynamic modelling studies. The development of a within-host dynamic model, parameterised by the statistical model outputs, extends the existing model of PRRSV infection dynamics to allow for testing hypothesis surrounding: quasi-species dynamics, virus mutation mechanisms and the latest host genetic insights into the immune response. We aim to combine the insights gained from the statistical model with the results of immunological and genomic studies to develop a dynamic framework that describes how individual components interact. The model’s dynamic nature allows for predictions of virus load, the host’s infection status and immune response over the time-course of infection. Both the statistical and the dynamic mathematical modelling of the within-host dynamics of PRRS virus infections provides insights into the consequences of treatment and control of infection in individual hosts, and allow us to identify important knowledge gaps to be addressed in future studies.


within host; virus; viremia; statistical modelling; dynamic modelling