The role of geographical spreaders in infectious pattern formation and front propagation speeds

The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible–Infectious–Recovered (SIR) model applicable across a wide range of basic reproduction numbers Ro. The goal is to examine the role of geographical spreaders on transient spatial pattern formation of infectious populations and the associated maximum invasive front speeds cmax. In the simulations conducted here, geographical spreaders are defined as a portion of the infected population ϕ experiencing high mobility between identical communities. The spatial organization of the infected population and cmax are determined when the infections are randomly initiated in space within multiple communities. For small but finite ϕ, scaling analysis and numerical simulations in 1-dimension suggest that cmax∼γ(Ro−1) when the spreading kernel is Gaussian-shaped, where γ is the inverse of the infectious duration. This finding for cmax agrees with a diffusion-based representation of mobility in 1-D. Numerical simulations in 2-D across wide-ranging Ro suggest that σ, the variance of the spatial kernel describing mobility of long-distance geographical spreaders across communities, determines the spatial organization of infections across communities. When σ/Lr>5 (long-distance mobility, where Lr is the minimum spatial extent defining adjacent communities), the infectious population will experience a transient but spatially coherent pattern with a wavelength that can be derived from the spreading kernel properties. Moreover, the 2-D simulations for the bounded kernel suggest that attainment of cmax is also dictated by ϕ but the magnitude is not sensitive to ϕ unlike diffusion-based models.