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 ( σ inh ) and (ii) external infectivity ( ι ext ), 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 σ inh and ι ext are combined into a new parameter Ω, defined as Ω = σ inh × ι ext ; infection occurs only if the value of Ω is greater than a Pandemic Infection Parameter (PIP), Ω 0 . Not only does this parameter provide a microscopic viewpoint of the reproduction number R0 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. The figure represents the network model for spread of infectious diseases considered in this work. It also shows the resultant multiwave infection graph by inclusion of inherent susceptibility and external infectivity distributions and migration of infected individuals.