Cross-scale dynamics and the evolutionary emergence of infectious diseases

Sebastian J. Schreiber; Ruian Ke; Claude Loverdo; Miran Park; Priyanna Ahsan; James O. Lloyd-Smith

Derivation of the Mean Field Frequency Dynamics. To understand how the viral composition of infected individuals change across generations, we derive a mean field approximation for the dynamics of the mean mutant viral load at the beginning of each generation of disease spread. To this end, we define a map from h : [0, 1] → [0, 1] where x ∈ [0, 1] represents the current mean mutant viral load in the population at the beginning of the infectious period and h(x) is the mean at the beginning of infectious period in the next generation. Our derivation of this mean field dynamic is done in the limit of large N ↑ ∞ and µ ↓ 0. None-the-less, as shown by the dashed red line in Fig 2D, this approximation works quite well away from this limit.