02.01.2013: Second analysis of run 001¶
We study here how the model solution behaves for different values of β. In all cases, the populations are uniform (so advection and diffusion are inactive), and we start with Ps0 = 0.5, Pi0 = 0.0, Z0 = 0.0 and V0 = 0.25. See 11.02.2012: First analysis of run 001 for a study of the behavior of the solution for a fixed value of β but various initial conditions for Ps and V.
There are two regimes. For β smaller than 0.12, Ps will obtain its maximum and final value very rapidly (Figs. 1a and c and Figs. 4 and 5), although it takes him longer and longer to reach this value (Fig. 1b). In this regime, the maximum of Pi and V are their initial value and they decay rapidly to zero stays (Figs. 2a and 3a and Figs. 4 and 5).
For β larger than 0.12, the maximum value of Ps decays with β and it is reached at the first oscillation, right at the beginning of the run (Figs. 1a and b and Figs. 6 and 7). Its final value also decays with β. For Ps and V, their maximum values increase with β and these are reached also at the first oscillation at the beginning of the run. Interestingly, their final value peaks for β around 0.35. Finally, the larger β, the smaller the period of oscillations and the slower the solution asymptotes to equilibrium (Figs. 6 and 7).
These results are consistent with Fig. 4 of Rhodes et al. (2008).
Figs. 1a and 1c shows the ratio of the maximum value to the final value. In 11.02.2012: First analysis of run 001, where β = 0.35, it was noticed that the maximum value was about twice the final value. We see by looking at these two figures, that this was somewhat of a coincidence and the relationship between the two quantities are more complicated.
Figure 1: Maximum value of Ps and its timing, final value of Ps and a measure of the convergence of the run.
Figure 2: Maximum value of Pi and its timing, final value of Pi and a measure of the convergence of the run.
Figure 3: Maximum value of V and its timing, final value of V and a measure of the convergence of the run.
Figure 4: Time series of Ps, Pi and V for β = 0.05.
Figure 5: Time series of Ps, Pi and V for β = 0.10.
Figure 6: Time series of Ps, Pi and V for β = 0.25.
Figure 7: Time series of Ps, Pi and V for β = 0.70.
To produce the first three figures, manyruns_2.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001 has been used and it was plotted with plot_all_outputs.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001/analysis/manyruns_2. To produce Figs. 4 to 7, we use plot_timeseries_current_run.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001/analysis/.