Work

Epidemic Models with Varying Infectivity on a Refining Spatial Grid—I—The SI Model

Year: 2024

Type: article

Abstract: We consider a space–time SI epidemic model with infection age dependent infectivity and non-local infections constructed on a grid of the torus Td=[0,1)d, where the individuals may migrate from node to node. The migration processes in either of the two states are assumed to be Markovian. We establish a functional law of large numbers by letting the initial approximate number of individuals on each node, N, to go to infinity and the mesh size of the grid, ε, to go to zero jointly. The limit is a system of parabolic PDE/integral equations. The constraint on the speed of convergence of the parameters N and ε is that Nεd→∞ as (N,ε)→(+∞,0).

Source: Mathematics

DOI: 10.3390/math12182826

Authors: Anicet Mougabe-Peurkor, Étienne Pardoux, Ténan Yeo

Institutions: Université Félix Houphouët-Boigny, Centre National de la Recherche Scientifique, Aix-Marseille Université, Institut de Mathématiques de Marseille

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Centre National de la Recherche Scientifique, Université Félix Houphouët-Boigny