Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866907978838310912 |
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| author | Carvalho, V. R. Alves, T. F. A. Alves, G. A. Alencar, D. S. M. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. |
| author_facet | Carvalho, V. R. Alves, T. F. A. Alves, G. A. Alencar, D. S. M. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. |
| contents | 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 $μ_c$ if they share the same lattice node with an infected individual and recover with rate $μ_r$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions Carvalho, V. R. Alves, T. F. A. Alves, G. A. Alencar, D. S. M. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. Statistical Mechanics Physics and Society 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 $μ_c$ if they share the same lattice node with an infected individual and recover with rate $μ_r$, 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. |
| title | Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions |
| topic | Statistical Mechanics Physics and Society |
| url | https://arxiv.org/abs/2407.08175 |