Time-Delayed Spread of Viruses in Growing Plaques

Abstract

The spread of viruses in growing plaques predicted by classical models is greater than that measured experimentally. There is a widespread belief that this discrepancy is due to biological factors. Here we show that the observed speeds can be satisfactorily predicted by a purely physical model that takes into account the delay time due to virus reproduction inside infected cells. No free or adjustable parameters are used.

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

“…[30], Sec. 4.2), language competition [63], the spread of diseases [64] and epidemics [17], and virus infection fronts [4].…”

“…In Eq. (1), which is useful in several anthropological [6,13,14] and biophysical systems [4], the generation time T plays a role analogous to that of a delay time in many physical systems [16]. The dispersal kernel φ( x , y ) appearing in Eq.…”

“…Front propagation models have been applied to many physical, biological, and cross-disciplinary systems, including combustion flames [1], Taylor-Couette and Rayleigh-Bénard experiments [2], superconductors [3], viral infections [4], tumor growth [5], and human invasions [6][7][8][9][10][11][12]. The latter application is considered in this paper, going beyond previous models by taking the role of cultural diffusion into account.…”

Fronts from complex two-dimensional dispersal kernels: Theory and application to Reid’s paradox

“…5,6 Indeed, classical diffusion ͑Fick's law͒ is well known to break down in some relevant phenomena. One example is time-delayed diffusion due to the rest time of particles ͑or individuals͒ between successive jumps 8,9 ͑this delay can be the same for all jumps [10][11][12] or there may be several possible delays [13][14][15] ͒. A second case is sometimes called reaction dispersal.…”

Propagating fronts in reaction–transport systems with memory

“…To remedy the unphysical nature of Fickian diffusion, namely transport with infinite speed, hyperbolic evolution equations, such as reaction random walks [5], time-delayed hyperbolic reactiondiffusion equations [6][7][8], and reaction-telegraph equations [9,10], have been introduced and analyzed in the context of (…”