General epidemiological models: law of large numbers and contact tracing

We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement control measures. show that the large-population dynamics are deterministic and relate to Kermack–McKendrick PDE. Our assumptions minimalistic sense only important requirement is basic reproduction number R0 be finite, allow us tackle both Markovian non-Markovian dynamics. The novelty our approach “infection graph” population. local convergence this random graph Poisson (Galton–Watson) marked tree, recovering backward-in-time limit as we trace back transmission chain leading focal infection. This effectively process tracing large It expressed terms Doob h-transform certain renewal encoding time infection along chain. results provide mathematical formulation relating fundamental epidemiological quantity, generation distribution, successive infections