Normalized Fitness as measured by and for direct transmission and environmental transmission.

<p>The dashed vertical lines indicate the level of above which becomes so large that no infection takes place (c.f. horizontal line in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002989#pcbi-1002989-g007" target="_blank">figure 7</a>). Note that results for and are virtually indistinguishable and therefore the curves are on top of each other.</p

Flow diagram for the between-host model.

<p>, and are the variables describing susceptible hosts, infected hosts, and pathogen (i.e. virus) in the environment. Transmission can occur directly between uninfected and infected hosts at rate and through contact of uninfected hosts with virus in the environment at rate . Infected hosts shed virus into the environment at rate , and recover (and are assumed to become immune to re-infection) at rate . Virus in the environment decays at rate . Note that the parameters , and , i.e. the rate of transmission between hosts, the rate of shedding and the rate of recovery all depend on the time since infection. Solid lines indicate physical flows, dashed lines indicate interactions.</p

A Multi-scale Analysis of Influenza A Virus Fitness Trade-offs due to Temperature-dependent Virus Persistence

<div><p>Successful replication within an infected host and successful transmission between hosts are key to the continued spread of most pathogens. Competing selection pressures exerted at these different scales can lead to evolutionary trade-offs between the determinants of fitness within and between hosts. Here, we examine such a trade-off in the context of influenza A viruses and the differential pressures exerted by temperature-dependent virus persistence. For a panel of avian influenza A virus strains, we find evidence for a trade-off between the persistence at high versus low temperatures. Combining a within-host model of influenza infection dynamics with a between-host transmission model, we study how such a trade-off affects virus fitness on the host population level. We show that conclusions regarding overall fitness are affected by the type of link assumed between the within- and between-host levels and the main route of transmission (direct or environmental). The relative importance of virulence and immune response mediated virus clearance are also found to influence the fitness impacts of virus persistence at low versus high temperatures. Based on our results, we predict that if transmission occurs mainly directly and scales linearly with virus load, and virulence or immune responses are negligible, the evolutionary pressure for influenza viruses to evolve toward good persistence at high within-host temperatures dominates. For all other scenarios, influenza viruses with good environmental persistence at low temperatures seem to be favored.</p> </div

Parameters for the between-host model.

<p>Parameters for the between-host model. Parameters marked with ^* depend on time since start of infection. Specific choices for these parameters are described in the text. Note that we do not make use of specific numeric values for any of these parameters, therefore none are given.</p

Best fit of within-host model to fecal virus load from influenza infections of mallards (Anas Platyrhynchos).

<p>The limit of detection for the virus load was ( = 50% Egg Infectious Doses) and is indicated by the dashed horizontal line. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002989#pcbi.1002989-Brown3" target="_blank">[69]</a> for more details on the experiments and data. Fitting was done using a least squares approach for the logarithm of the virus load, corresponding to the assumption of log-normally distributed errors <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002989#pcbi.1002989-Bolker1" target="_blank">[89]</a>. For data at the limit of detection (i.e. left-censored data), differences between model and data were accounted for if the model was above the data point, but not if the model took on any value below the limit of detection <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002989#pcbi.1002989-Handel3" target="_blank">[75]</a>.</p

Initial conditions and parameter values for the within-host model.

<p>Initial conditions and parameter values for the within-host model.  = 50% Egg Infectious Dose.</p

Decay rate for 12 different influenza strains as function of temperature.

<p>Symbols show data, lines show best fit of an exponential function. Virus decay for all strains was measured at the indicated temperature, a pH of 7.2, and salinity of 0. Decay for each strain was measured once for these specific conditions. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002989#pcbi.1002989-Brown2" target="_blank">[33]</a> for more experimental details.</p

Best fit values for the different influenza strains.

<p>Best fit values for the different strains fitted to the function . Parameter is in units of 1/degree Celsius, is in units of 1/day. Also shown are decay rates (units of 1/day) for each strain at 5 () and 40 () degrees Celsius. Numbers in parentheses following each strain indicate the genotype group (see main text). Numbers in parentheses following the other values indicate the rank of this value for each strain (with rank 1 given to the strain with the lowest value, corresponding to better persistence.)</p

Summary of quantities linking the within-host and between-host scales.

<p>Summary of quantities linking the within-host and between-host scales.</p

Temperature trade-off between strains.

<p>A) Decay rates for H8N4, H9N2 and H10N7, plotted on a log scale to illustrate the cross-over of decay rates. B) absolute values of and for all strains, (note the log scale). C) Ranks of these parameters. Also plotted in each figure are regression lines.</p