Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection - PubMed (original) (raw)
Estimating biologically relevant parameters under uncertainty for experimental within-host murine West Nile virus infection
Soumya Banerjee et al. J R Soc Interface. 2016 Apr.
Abstract
West Nile virus (WNV) is an emerging pathogen that has decimated bird populations and caused severe outbreaks of viral encephalitis in humans. Currently, little is known about the within-host viral kinetics of WNV during infection. We developed mathematical models to describe viral replication, spread and host immune response in wild-type and immunocompromised mice. Our approach fits a target cell-limited model to viremia data from immunocompromised knockout mice and an adaptive immune response model to data from wild-type mice. Using this approach, we first estimate parameters governing viral production and viral spread in the host using simple models without immune responses. We then use these parameters in a more complex immune response model to characterize the dynamics of the humoral immune response. Despite substantial uncertainty in input parameters, our analysis generates relatively precise estimates of important viral characteristics that are composed of nonlinear combinations of model parameters: we estimate the mean within-host basic reproductive number,R0, to be 2.3 (95% of values in the range 1.7-2.9); the mean infectious virion burst size to be 2.9 plaque-forming units (95% of values in the range 1.7-4.7); and the average number of cells infected per infectious virion to be between 0.3 and 0.99. Our analysis gives mechanistic insights into the dynamics of WNV infection and produces estimates of viral characteristics that are difficult to measure experimentally. These models are a first step towards a quantitative understanding of the timing and effectiveness of the humoral immune response in reducing host viremia and consequently the epidemic spread of WNV.
Keywords: West Nile virus infection; basic reproductive number; biologically relevant parameters; ordinary differential equation models; parameter estimation; within-host viral dynamics.
© 2016 The Author(s).
Figures
Figure 1.
Outline of the computational approach. The model parameters are _T_0 (initial target cell density), k (rate of transition from latently infected to productively infected cells), γ (WNV clearance rate), _V_0 (inoculated virus density), β (rate constant of infection), δ (death rate of productively infected cells), p (infectious virus production rate), ρ (efficacy of antibody neutralization) and ti (time of initiation of the IgM response).
Figure 2.
Fit of the function A(t) given by equation (2.5) to the neutralizing antibody data (circles) from the antibody titre study [13]. (Online version in colour.)
Figure 3.
Equation (2.10) fitted to data from [35] (viral decay study) where viral titres in serum were measured within the first 90 min following intravenous inoculation of mice with WNV. Circles, experimental data points from [35]. Solid line, best fit to log-transformed data using linear least-squares regression. _r_2 = 0.85 and _p_-value = 2 × 10−5. (Online version in colour.)
Figure 4.
The numerical solutions of the models (virus titre) and variation in model fits. The variation (dotted lines) is from the points from step 1 of the computational approach (knockout mice: SSR less than 4 and wild-type mice: SSR less than 0.1). A visual representation of the model-predicted virus trajectory with SSR of 4 and 0.1 is also shown (solid lines).
Figure 5.
The numerical solutions of the models (virus titre) together with data from the wild-type and knockout study [12]. The solid black line is the numerical solution of the virus titre from the target cell-limited model (equations (2.1)–(2.4)) using one representative parameter set from our estimation algorithm and the black squares are the data from knockout mice. The black dashed line is the predicted corresponding target cell dynamics (fraction of target cells remaining). The red solid line is the numerical solution of the virus titre from the model including a humoral response (equations (2.6)–(2.9)) and the red circles are the data for wild-type mice. The red dashed line is the corresponding predicted target cell dynamics. The limit of detection (LOD) of the assay is indicated by the horizontal dashed line. The day 6 data point for wild-type mice was below the LOD and set to half the LOD [53]. The parameters used to generate the plot are: _T_0 = 2.3 × 105 ml−1, _V_0 = 4.3487 PFU ml−1, β = 4 × 10−4 ml day−1, δ = 23.0341 day−1, p = 57.88 PFU day−1, γ = 44.43 day−1, _V_0 for WT = 4 PFU ml−1, 
, ti = 3.5 days.
Figure 6.
Histograms of estimated model parameters (_V_0, β, p, δ, ρ, ti) from the target cell-limited model and model with humoral response. (Online version in colour.)
Figure 7.
Histograms of biologically relevant quantities estimated by our approach. (a) Infectious virion burst size (in PFU). (b) Average number of cells infected per infectious virion. (c) Basic reproductive number (_R_0). (Online version in colour.)
Figure 8.
Correlation between target cell-limited model parameters (_T_0, _V_0, β, p, δ).
References
- Ceausu E, et al. 1997. Clinical manifestations in the West Nile virus outbreak. Rom. J. Virol. 48, 3–11. - PubMed
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