Analysis of Transmission of Infection in Epidemics: Confined Random Walkers in Dimensions Higher Than One

Home range variability, spatial aggregation, and excursions of Akodon azarae and Oligoryzomys flavescens in Pampean agroecosystems

“…On the other hand, theoretical studies of spatially explicit epidemiological models may provide invaluable perspectives. Sugaya and Kenkre (2018) showed that the frequency of contacts between two individuals depends non-monotonically on their home-range size-todistance ratio. Hence, virus transmission rates by direct contact do not necessarily increase with home range size, but population density and spatial aggregation need to be considered as well.…”

Spatio-temporal dynamics of random transmission events: from information sharing to epidemic spread

“…In panels (b)-(e) we have used, respectively, the values (ρ, q) = (1, 0.072), (0.8, 0.47), (0.8, 0.51), and (0.02, 1). The solid lines are the exact results from equation (17) with M = L 2 , while T R n 0 (triangles) and T M n 0 (circles) are, respectively, the first order capture and motion limited approximations, respectively in equations ( 18) and (19). Except when ρ is small, the corresponding MTT derived from equation ( 16) fails to capture any of the qualitative features present in these curves (see figure C1).…”

“…The technique was introduced to study exciton movement on lattices with traps [16], and was used for sensitized luminescence in molecular crystals [17] and molecular motion in cell membranes [40], and it is of relevance to the vast literature on first-passage processes [41][42][43][44]. More recently it has also been applied to study the transmission dynamics between two Brownian walkers bounded to move in a quadratic potential [18,19]. In these examples the νformalism is shown to be exact, but has also been shown to be a good approximation and to be related, when defects are randomly placed, to the defect-placement pair correlation function [17].…”

“…Irrespective of the type of information exchanged, transmission events represent a type of reaction diffusion process whereby moving entities may undergo a reaction at one or multiple spatial locations. While with large population density a vast body of literature has pushed forward the understanding of the spatial and temporal scales that affect reaction kinetics [7][8][9][10][11][12][13][14], in the low density or dilute regime, most findings relate to specific models or geometry [15][16][17][18][19][20], and a general methodology is still lacking. The difficulty stems from the need to quantify, in the presence of multiple reactive centres, the time-dependent probability for a random event to occur at one location and not others, the so-called time-dependent splitting probabilities.…”

“…Standard approaches to overcome this challenge and analyse transmission events employ stochastic simulations, but they are known [21] to generate large fluctuations in the output predictions, possess limited scalability, and fail to elucidate the impact of dimensionality and confinement on information transfer. Here we move past these limitations by predicting the splitting probability dynamics and developing a general theory of random transmission events by building on the pioneering results developed for spatially symmetric scenarios and unbounded domains, namely studies on discrete lattices in the '80s on exciton annihilation in molecular crystals [15,16] and sensitised luminescence [17], and more recent ones in continuous space on infection/reaction dynamics [18][19][20]. Pictorial representation of a stochastic transmission event between two randomly moving individuals: a red one that carries information, the emitter or 'infected', and a green one that initially does not, the receiver or 'susceptible'.…”