Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions

V. R. Carvalho; T. F. A. Alves; G. A. Alves; D. S. M. Alencar; F. W. S. Lima; A. Macedo-Filho; R. S. Ferreira

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arXiv · 2407.08175

Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions

V. R. Carvalho·T. F. A. Alves·G. A. Alves·D. S. M. Alencar·F. W. S. Lima·A. Macedo-Filho·R. S. Ferreira

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Abstract

We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are susceptible or infected, respectively, and recovered individuals possess permanent immunity. Individuals can be contaminated with rate $\mu_c$ if they share the same lattice node with an infected individual and recover with rate $\mu_r$, being removed from the dynamics. Therefore, the model does not have the conservation of the active particles composed of susceptible and infected individuals. The reaction-diffusion dynamics are separated into two stages: (i) Brownian diffusion, where the particles can jump to neighboring nodes, and (ii) contamination and recovery reactions. The dynamics are mapped into a growing process by activating lattice nodes with successful contaminations where activated nodes are interpreted as infection sources. In all simulations, the epidemic starts with one infected individual in a lattice filled with susceptibles. Our results indicate a phase transition in the dynamic percolation universality class controlled by the population size, irrespective of diffusion rates $D_S$ and $D_I$ and a subexponential growth of the epidemics in the percolation threshold.

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V. R. Carvalho, T. F. A. Alves, G. A. Alves, D. S. M. Alencar, F. W. S. Lima, A. Macedo-Filho, R. S. Ferreira. 2024-07-11. Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions. https://arxiv.org/abs/2407.08175

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