Ding (equation 15) link-function to connect virus load with transmission, assuming logarithmic relation (equation 16)doi:10.1371/journal.pcbi.1002989.tthe intercept with the decay price curve, a, (quantifying virus persistence at low temperature, particularly at 00 C) against the worth for the temperature-dependence in the decay rate, c, (quantifying virus persistence at higher temperature). In figure 4C, we provide exactly the same information and facts, but for the rank of those parameters. These plots demonstrate a adverse correlation in between persistence at low and higher temperatures. Because the center panel indicates a linear relation for the logarithm of a and c, we fitted a regression line log(c) gzk log(a) towards the information. We locate for the regression match g {3:28, k {0:26 (R2 0:70, p 0:00068). Similarly, computing a correlation coefficient for the rank-transformed data, we find a negative correlation of {0:72 (p 0:011). The analysis of this dataset can be taken as suggestion for the presence of a trade-off between stability at low and high temperatures at least for the panel of strains we investigated here. Since this is a small sample of strains, we do not want to over-emphasize the PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20160000 finding. However it seemed real and interesting enough to ask the questio: “How would such a potential trade-off lead to interactions on the within-host and between-host levels and affect overall virus fitness”. We address this question in the remainder of the paper. As a potentially interesting side question not further considered in the remainder of this paper we wondered whether there are systematic differences between strains belonging to different groups. Based on amino acid differences, strains with different HA types can be clustered into two groups, as indicated in Table 4 (see e.g. [668]). We were curious to see if systematic differences in the decay behavior between the two groups could be observed. However, statistical tests applied to both the absolute and rank-transformed values of a and c did not identify significant differences between groups, suggesting that based on the available data differences in HA sequences between the two groups do not express themselves phenotypically as differences in temperature-dependent decay characteristics.both cw and death rate of infected cells, d, from virus titer data alone [42,70]. Because of this, we instead set cw 2:78 per day, which is the mean value of cw for the 12 strains reported in table 4. We also tried to fit cw , and as expected, the fit did not improve and cw could not be properly estimated. To perform the fit, we assume that the infection was started by a 1 EID50 =mL (EID50 is the viral dose that results in a 50 chance of infecting an embryonated egg, assumed to correspond to 1 infectious virion) and that the initial number of uninfected target cells is 2:5|107 [71] (while this estimate is for chickens rather than ducks, the exact value is not qualitatively important: changes in the target cell numbers only rescale the model parameter p and otherwise produce the same dynamics). In figure 5, we show the best fit to the data, with parameter values presented in Table 1. We want to point out that while these parameter estimates are useful and accurate enough for the purpose of our study, they come with caveats. Most importantly, estimates are based on the validity of the model used. A model that does not include an immune response is likely an over-simplification, albeit a necessary one since BQ-123 web adding additional immu.