Figure 3.

(A) Dynamics predicted by the stochastic, Gillespie simulation of ODE system (1), depending on the virophage pathogenicity, f. The host population is shown in black, cells infected with the primary virus in blue, and cells infected with the virophage in red. Figure 2 showed that dynamics become more unstable for lower f. Here, simulations were started at the equilibrium levels predicted by the ODEs (the nearest integer number) and typical outcomes were plotted. Starting around the equilibrium minimizes the chances of extinction due to oscillatory dynamics. For f = 0, the dynamics are the most unstable and the system crashes to extinction. Higher values of f stabilize the dynamics, resulting in long-term persistence. Parameters were chosen as follows: r = 0.01; β₁ = 2.5 × 10⁻⁷; a₁ = 0.01; β₂ = 2 × 10⁻⁵; a_ph = 0.05; k = 5 × 10⁵. (B) Gillespie simulation of the ODE system (1a), which takes free virus populations into account explicitly. All simulations assume maximal virophage pathogenicity, f = 0. The turnover of the free virus populations is varied, while keeping their basic reproductive ratios identical. (i) Baseline scenario, where η₁ = 10; u₁ = 10; η₂ = 10; u₂ = 10. Extinction occurs relatively quickly, similar to model (1) which assumed free virus to be in a quasi steady state. (ii) The turnover of the primary virus was reduced such that the death rate of free viruses is on the same order of magnitude as that of infected cells, that is, η₁ = 0.01; u₁ = 0.01; η₂ = 10; u₂ = 10. More stable dynamics and long-term persistence are observed. (ii) The turnover of the virophage population is reduced such that the death rate of virophages is of the same order of magnitude as that of infected cells, that is, η₁ = 10; u₁ = 10; η₂ = 0.01; u₂ = 0.01. This destabilizes the dynamics, accelerating extinction.