Stochastic Heterogeneous SIR Model with Infection-Age Dependent Infectivity on Large Random Graphs
Abstract
We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular characteristics (for example, spatial location and age structure), which may not be i.i.d., and is represented by a particular node. The connectivities among the individuals are given by a non-homogeneous random graph, whose connecting probabilities may depend on the individual characteristics of the edge. To each individual is associated a random infectivity function of its infection age, which is allowed to depend upon the individual characteristics. We use measure-valued processes to describe the epidemic evolution dynamics, tracking the infection age of all individuals, and their associated characteristics. We consider the epidemic dynamics as the population size grows to infinity under a specific scaling of the connectivity graph related to the convergence to a graphon. In the limit, we obtain a system of measure-valued equations, which can be also represented as a PDE model on graphon, and reflects the heterogeneities in individual characteristics and social connectivity.
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BibTeX
@article{pang2026stochastic,
title = {{Stochastic Heterogeneous SIR Model with Infection-Age Dependent Infectivity on Large Random Graphs}},
author = {Guodong Pang and Étienne Pardoux and Aurélien Velleret},
journal = {Mathematical Physics, Analysis and Geometry},
year = {2026},
month = aug,
doi = {10.1007/s11040-026-09582-y},
eprint = {2502.04225},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05738664v1},
note = {CC BY-ND 4.0},
}
RIS
TY - JOUR
TI - Stochastic Heterogeneous SIR Model with Infection-Age Dependent Infectivity on Large Random Graphs
AU - Guodong Pang
AU - Étienne Pardoux
AU - Aurélien Velleret
PY - 2026
DA - 2026/08/21
JO - Mathematical Physics, Analysis and Geometry
DO - 10.1007/s11040-026-09582-y
UR - https://hal.science/hal-05738664v1
AB - We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular characteristics (for example, spatial location and age structure), which may not be i.i.d., and is represented by a particular node. The connectivities among the individuals are given by a non-homogeneous random graph, whose connecting probabilities may depend on the individual characteristics of the edge. To each individual is associated a random infectivity function of its infection age, which is allowed to depend upon the individual characteristics. We use measure-valued processes to describe the epidemic evolution dynamics, tracking the infection age of all individuals, and their associated characteristics. We consider the epidemic dynamics as the population size grows to infinity under a specific scaling of the connectivity graph related to the convergence to a graphon. In the limit, we obtain a system of measure-valued equations, which can be also represented as a PDE model on graphon, and reflects the heterogeneities in individual characteristics and social connectivity.
SN - 1385-0172
SN - 1572-9656
ER -