Modeling rapidly disseminating infectious disease during mass gatherings

Abstract

We discuss models for rapidly disseminating infectious diseases during mass gatherings (MGs), using influenza as a case study. Recent innovations in modeling and forecasting influenza transmission dynamics at local, regional, and global scales have made influenza a particularly attractive model scenario for MG. We discuss the behavioral, medical, and population factors for modeling MG disease transmission, review existing model formulations, and highlight key data and modeling gaps related to modeling MG disease transmission. We argue that the proposed improvements will help integrate infectious-disease models in MG health contingency plans in the near future, echoing modeling efforts that have helped shape influenza pandemic preparedness plans in recent years.

Figure 1

Effect of demographic stochasticity on influenza epidemics. The classic stochastic SEIR (susceptible, exposed, infectious, recovered) model tailored to the epidemiology of influenza, based on a latent period of 1.5 days, an infectious period of 3 days, basic reproduction number (R₀) of 1.5, and an assumption of homogenous mixing of the population, was used to generate 100 stochastic simulations in two population sizes of n = 1,000 (left panels) and 11,000 individuals (right panels). Simulations were initialized with five infectious individuals. Histograms show a higher probability of epidemic extinction in the lower population setting. Stochastic epidemic realizations are shown in light blue, while the red solid line curve corresponds to the average of the stochastic realizations that resulted in epidemics.

Figure 2

Effect of contact-network structure on influenza epidemics. The classic stochastic SEIR (susceptible, exposed, infectious, recovered) model was tailored to the epidemiology of influenza, based on a latent period of 1.5 days, an infectious period of 3 days, and fixed transmission probability per contact, simulated using two different contact networks: 1) a small-world contact network based on the model of Watts and Strogatz [74], with an average degree of 4 and disorder parameter (p) of 0.1 in a population of 1,000 individuals (left panels) and 2) in a random network model with an average degree of 4 (right panels) with the same population size. Histograms show the distribution of outbreak sizes for both network topologies when everything else is kept fixed. Epidemic realizations are shown in blue, while the red solid line curve corresponds to the average of the stochastic realizations that resulted in epidemics.

Figure 3

Effect of the initial number of infectious individuals. The classic stochastic SEIR (susceptible, exposed, infectious, recovered) model tailored to the epidemiology of influenza, based on a latent period of 1.5 days, an infectious period of 3 days, and fixed probability of transmission per contact, was simulated on small-world contact networks based on the Watts and Strogatz network model [74] with an average degree of 4 and disorder parameter (p) of 0.1 in a populations of 1,000 individuals. Initially infectious individuals were selected uniformly at random from the population. Histograms show how the distribution of outbreak sizes shifts to larger epidemics as the initial number of infectious individuals increases.