Figure 2
A synthetic immune response. The upper left plot shows the latent variables in terms of the different types of antibody. This distinguishes between the faster IgM response, and the more prolonged IgG response, and between the neutralising and non-neutralising variants of each. The upper right plot shows the cellular latent variables, with an initial increase in the activated T-cell proportions that leads to a later increase in plasma and memory cells, with a persistent memory response developing. The middle left plot shows the viral states, subdivided into intracellular and extracellular components. The middle right plot shows the total antibody level, including both neutralising and non-neutralising. The lower left plot shows the viral load in terms of the ‘threshold cycle’ (Ct) which indicates the number of cycles of polymerase chain reaction (PCR) required before the viral nucleic acids are detectable. A greater number of cycles indicates a greater dilution (i.e., a smaller concentration). To generate these data, we took the negative log39,40 of y(τ)VL, scaled it by a factor of 4, and added a constant 50—under the assumption that more than 40 cycles implies a negligible viral concentration, based on fluorescence amplification results for a typical qPCR run41. These scale factors and constants could in principle be fit to empirical data. Here they are used only for the plotting and have no influence on model inversion. Finally, the lower right plot shows the proportion of CD4+ and CD8+ cells releasing IFN-γ. In this and subsequent figures, the intervals are 90% credible intervals for the predictive distribution. These are calculated as in1, using a first order approximation to the variance based upon the chain rule. The uncertainty in the predicted data inherits from uncertainty about the parameters generating those data. Here, the uncertainty about the parameters under prior beliefs is used. However, these could be replaced by posterior beliefs when fitting to empirical data. One thing that is important to note is that day 1 is not the first day of symptoms. It represents the day of initial exposure to the virus.
