The relative contributions of infectious and mitotic spread to HTLV-1 persistence
Fig 2
Schematic of full simulation hybrid model.
A: Observed and estimated clone frequency distributions. From an observed sample of clones, the clone frequency distribution of the body in one host is estimated using DivE. B: Propagation of hybrid model: Estimated clone frequency distribution partitioned into deterministic and stochastic systems. Clones of frequency less than and greater than threshold F are respectively modelled stochastically and deterministically. F is chosen with respect to probability of clone extinction (S2 Text). The deterministic system is modelled using ordinary differential equations (Eq (1)). The stochastic system consists of multiple birth-death processes (one for each stochastically modelled clone) each with an absorbing state at zero (Fig 3A and 3B). The evolution of the clone probability distribution over time is governed by the chemical master equation (Eq (10), Fig 3C and 3D). New clones are created through infectious spread, i.e. the per-capita rate rI multiplied by the expected number of infected cells, in both deterministic and stochastic compartments (Eq (11)). Deterministic and stochastic systems are propagated concurrently with Strang splitting (S2 Text). C: Hybrid model diversity. The estimated number of clones S(t) (Eq (13)) at time t, given parameters θ = {π, δ, K, rI} is given by the number of clones created (Eq (11)), minus the number of clones that are expected to have died between 0 and t (Eq (12)), plus the number of clones S0 at t = 0. The number of clones is assumed to be at equilibrium in the chronic phase of infection. D: Model fitting schematic: Expected diversity at S(tDur) increases with per-capita infectious spread rate rI. Model fitted using non-linear least squares to DivE estimated diversity in the body, where the objective function is the square of the discrepancy between this value and the value of S(tDur) at equilibrium.