A Case for the Age-Structured SIR Dynamics for Modelling COVID-19

Accuracy Criterion for Mean Field Approximations of Markov Processes on Hypergraphs

“…In this section we compare our results to the recent independent work of Sridhar and Kar [12,13] and Parasnis et al [14]. In [12] the authors describe how the state densities of certain related stochastic processes on weighted graphs with doubly symmetric matrix W can be approximated by a set of O(N) ODEs analogous to NIMFA given that the normalized Frobenius norm 1…”

“…In [14] the authors study the SIR process in age-structured populations on time-varying networks. They show that when N and the rewiring rate is high the prevalence of the age groups can be described via an ODE system analogous to the metapopulation NIMFA model (34) in Section 4.2.…”

“…Section 2 introduces basic notation and setup for density-dependent Markov population processes along with examples of models used in the literature to illustrate these concepts and their applicability. Section 3 states the main results and also relates them to the recent work of Sridhar and Kar [12,13] and Parasnis et al [14]. Section 4 discusses further reductions of NIMFA to more simple approximations used throughout the literature.…”

“…On the flip side, the computational complexity is considerably increased compared to the homogeneous mean-field approximation; nevertheless, it remains tractable for population sizes large enough to make it relevant for practical applications. Unfortunately, unlike for homogeneous systems, the justification for using NIMFA is poorly understood, mostly relying on numerical evidence [9,10] along with a few theoretical results [11][12][13][14].…”

Usefulness of the Age-Structured SIR Dynamics in Modelling COVID-19

“…1. Modeling: We extend our previously proposed stochastic epidemic model [22] to a more general model that incorporates (a) a random and time-varying network of physical contacts (in-person interactions between pairs of individuals) that are updated asynchronously and at random times, (b) random transmissions of disease-causing pathogens from infected individuals to their susceptible neighbors, and (c) recoveries of infected individuals that occur at random times. We analyze the resulting dynamics and show that under certain independence assumptions, the expected trajectories of the fractions of susceptible/infected/recovered individuals in any age group converge in mean-square to the solutions of the age-structured SIR ODEs as the population size goes to ∞.…”