Stochastic formulation of multiwave pandemic: decomposition of growth into inherent susceptibility and external infectivity distributions

Many known and unknown factors play significant roles in the persistence of an infectious disease, but two that are often ignored in theoretical modelling are the distributions of (i) inherent susceptibility ([Formula: see text] ) and (ii) external infectivity ([Formula: see text] ), in a population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the exposure of a susceptible person to the infection. We model the spatio-temporal propagation of a pandemic as a chemical reaction kinetics on a network using a modified SAIR (Susceptible-Asymptomatic-Infected-Removed) model to include these two distributions. The resulting integro-differential equations are solved using Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Coupling between [Formula: see text] and [Formula: see text] are combined into a new parameter Ω, defined as [Formula: see text] ; infection occurs only if the value of Ω is greater than a Pandemic Infection Parameter (PIP), [Formula: see text] . Not only does this parameter provide a microscopic viewpoint of the reproduction number R(0) advocated by the conventional SIR model, but it also takes into consideration the viral load experienced by a susceptible person. We find that the neglect of this coupling could compromise quantitative predictions and lead to incorrect estimates of the infections required to achieve the herd immunity threshold. [Figure: see text]