Fig. 4

Consequences of seasonal travel in a spatial diffusion model. We simulated spatial spread of a pathogen (Methods) starting in the most populated district (Windhoek East in Namibia). Pathogen transmissibility, proportion of the population susceptible, and monthly connectivity value between districts defined a time varying hazard of introduction into each district. We compared the time (y-axis in days) each location became infected vs. Euclidean distance from Windhoek (x-axis). Each district is colored by the slowest month (i.e., when the pathogen on average took the longest to reach a particular district). To explore the impact of different pathogen life histories, we compared varying magnitudes of transmission (β) ranging from low (a, d) (\(\beta = 2\)) to intermediate (b, e) (\(\beta = 10\)) to high (c, f) (\(\beta = 15\)). We compared across two proportion of the population susceptible reflecting a–c low (10%) and d–f high (90%) values. The bars show the range in timings across the different months. We performed each hazard simulation 100 times per month and then average across simulations and months. When a small percentage of the population is susceptible and transmission is low (a), many locations will not become infected. Those that are infected are infected early, likely related to stochastic nature of the simulations. In medium–high proportion of the population susceptible simulations, for places nearby Windhoek, the time they become infected is consistent with physical distance, i.e., those closest to Windhoek become infected earlier. The only exception is the influenza-like simulation (e.g., corresponding to low magnitude of transmission), where many locations do not become infected; and this pattern is intensified where susceptibility is low. As the transmission parameter increases, the pathogen spreads faster throughout the population, often reaching all districts within a few generation times (i.e., e, f). The timing at which a district becomes infected will also depend on when during the year the pathogen was introduced, given seasonal fluctuations in mobility. For locations nearby Windhoek, the pathogen reaches these locations the latest in December, reflective of the decrease in travel from Windhoek East to nearby locations in this month