Spatial spread of epidemic in a system of weakly connected networks

Evgeniy Khain

Oakland University

"Spatial spread of epidemic in a system of weakly connected networks"

A metapopulation consists of a group of spatially distanced subpopulations, each occupying a separate patch. It is usually assumed that each localized patch is well-mixed. In this talk, we will discuss the spread of an epidemic in a system of weakly connected patches, where the disease dynamics of each patch occurs on a network. The SIR dynamics in a single patch is governed by the rate of disease transmission, the disease duration, and the node degree distribution of a network. Monte-Carlo simulations of the model reveal the phenomenon of spatial disease propagation. The speed of front propagation and its dependence on the single patch parameters and on the strength of interaction between the patches was determined analytically, and a good agreement with simulation results was observed [1]. Next, we will discuss front propagation in case of an Allee effect, where the effective transmission rate depends on the fraction of infected, and the state of no epidemic is linearly stable. We discovered [2] a novel phenomenon of front stoppage: in some regime of parameters, the front solution ceases to exist, and the propagating pulse of infection decays despite the initial outbreak. [1]. E. Khain and M. Iyengar, Phys. Rev. E 107, 034309 (2023). [2]. E. Khain, Phys. Rev. E 107, 064303 (2023).

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