Spatial SIR epidemic model with varying infectivity in an unbounded domain: Law of Large Numbers

2025/11/15 by Armand Kanga, Kanga, Armand, Étienne Pardoux +1
Mathematics · Medicine · Environmental Science · #COVID-19 epidemiological studies #Mathematical and Theoretical Epidemiology and Ecology Models #Bacteriophages and microbial interactions

paper · pdf · doi:10.48550/arxiv.2511.12350

Abstract

We consider a spatial SIR epidemic model where the infectivity of infected individuals depends upon their age of infection, and infections are non local. The domain is an unbounded subset of \R^d,and the individuals do not move. We extend our earlier result in \citeAK-EP, where the domain was bounded, and prove a law of large numbers as the size of the population tends to ∞.

Citations

• Spatially dense stochastic epidemic models with infection-age dependent infectivity
• Conditional propagation of chaos in a spatial stochastic epidemic model with common noise
• A Spatial Stochastic Epidemic Model: Law of Large Numbers and Central Limit Theorem
• Epidemic models with varying infectivity

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• A SIR Stochastic Epidemic Model in Continuous Space: Law of Large Numbers and Central Limit Theorem
• Spatial Epidemics: Critical Behavior in One Dimension