Research Article
Assessing Uncertainty in A2 Respiratory Syncytial
Virus Viral Dynamics
Gilberto González-Parra
1,2
and Hana M. Dobrovolny
1
1
Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76132, USA
2
Grupo de Matem´ atica Multidisciplinar (GMM), Universidad de Los Andes, M´ erida 5101, Venezuela
Correspondence should be addressed to Gilberto Gonz´ alez-Parra; gcarlos999@gmail.com
Received 15 March 2015; Accepted 30 August 2015
Academic Editor: Fabien Crauste
Copyright © 2015 G. Gonz´ alez-Parra and H. M. Dobrovolny. Tis is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
Respiratory syncytial virus (RSV) is the most common cause of bronchiolitis and pneumonia in children younger than 1 year of
age in the United States. Moreover, RSV is being recognized more ofen as a signifcant cause of respiratory illness in older adults.
Although RSV has been studied both clinically and in vitro, a quantitative understanding of the infection dynamics is still lacking.
In this paper, we study the efect of uncertainty in the main parameters of a viral kinetics model of RSV. We frst characterize the
RSV replication cycle and extract parameter values by ftting the mathematical model to in vivo data from eight human subjects. We
then use Monte Carlo numerical simulations to determine how uncertainty in the parameter values will afect model predictions.
We fnd that uncertainty in the infection rate, eclipse phase duration, and infectious lifespan most afect the predicted dynamics of
RSV. Tis study provides the frst estimate of in vivo RSV infection parameters, helping to quantify RSV dynamics. Our assessment
of the efect of uncertainty will help guide future experimental design to obtain more precise parameter values.
1. Introduction
Respiratory syncytial virus (RSV) is a major cause of lower
respiratory tract disease among infants, a frequent pathogen
in elderly and immunosuppressed patients, and a major
public health concern worldwide [1–5]. Healthy adults who
contract RSV experience mild or asymptomatic infections,
but it is the cause of 18% of hospitalizations due to pneumonia
in adults older than 65 [6]. Tere is currently no vaccine for
RSV and drug treatment is largely limited to treatment of
symptoms and supportive care [7]. Tus it is crucial that we
develop a detailed understanding of the viral kinetics of this
disease.
Historically, mathematical and computational methods
have not played a large role in immunology and virology.
Tis is now changing, and impressive advances have come
from the use of simple models applied to the interpretation of
quantitative data [8]. Mathematical models of viral infections
help us quantify key parameters of the infection process [9–
12], optimize drug treatment regimens [13–16], and under-
stand complex host-virus interactions [17–19]. Mathematical
modeling is now commonly used to study HIV [20] and is
becoming more common in other serious viral infections
such as infuenza [21] and HCV [22]; it has not yet been used
to investigate respiratory syncytial virus (RSV).
Initial modeling studies for any virus ofen use a system
of nonlinear diferential equations and the models are typ-
ically ft to viral time course data to generate estimates of
viral kinetic parameters. However, given the large amount
of experimental error in viral titer measurements [23],
parameter estimates vary widely and contain some degree
of uncertainty. Uncertainty in model parameters can limit
the predictive ability of the model, so it is important to
understand how parameter uncertainty alters the predicted
time course of the model.
Uncertainty in diferential equations has been considered
in recent decades in a wide variety of applied areas, such
as physics, chemistry, biology, economics, sociology, and
medicine [24–26]. Uncertainty in a diferential equation
model can arise either through uncertainty in the initial
conditions or through uncertainty in equation coefcients.
In this paper uncertainty of both types is considered in
Hindawi Publishing Corporation
Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 567589, 9 pages
http://dx.doi.org/10.1155/2015/567589