The spread of awareness and its impact on epidemic outbreaks

Abstract

When a disease breaks out in a human population, changes in behavior in response to the outbreak can alter the progression of the infectious agent. In particular, people aware of a disease in their proximity can take measures to reduce their susceptibility. Even if no centralized information is provided about the presence of a disease, such awareness can arise through first-hand observation and word of mouth. To understand the effects this can have on the spread of a disease, we formulate and analyze a mathematical model for the spread of awareness in a host population, and then link this to an epidemiological model by having more informed hosts reduce their susceptibility. We find that, in a well-mixed population, this can result in a lower size of the outbreak, but does not affect the epidemic threshold. If, however, the behavioral response is treated as a local effect arising in the proximity of an outbreak, it can completely stop a disease from spreading, although only if the infection rate is below a threshold. We show that the impact of locally spreading awareness is amplified if the social network of potential infection events and the network over which individuals communicate overlap, especially so if the networks have a high level of clustering. These findings suggest that care needs to be taken both in the interpretation of disease parameters, as well as in the prediction of the fate of future outbreaks.

Fig. 1.

Awareness g(ρ,t) in the well-mixed population as a function of time for a given ρ < 1 if information is not replenished by the presence of the disease.

Fig. 2.

Per contact information transmission rate $\widehat{\alpha }$ needed to push the outbreak below the epidemic threshold for a given basic reproductive number of the disease $\widehat{R}$₀. Shown is the theoretical prediction (line) and simulation results for different values of s, the number of steps information is allowed to travel from the source. The nodes were connected as a random regular graph, i.e., randomly with uniform degree k = 6, and the data points closely follow the predicted line. The critical $\widehat{R}$₀^crit for the parameters used here (ρ = 0.9) is indicated by a vertical line.

Fig. 3.

Average awareness in the susceptible members of SI pairs in terms of the average awareness in all susceptibles, measured in stochastic simulations on the following scenarios of disease and information network structure: completely overlapping (filled squares) and completely disjointed (open squares) regular random graphs, completely overlapping lattices (filled circles) and the disease network as a lattice with the information network as a regular random graph (open circles). The line corresponds to the case p_i^SI = p_i^S.

Fig. 4.

Snapshot of a simulated disease outbreak on a triangular lattice. Red represents nodes that have been infected during the outbreak, with light red indicates nodes that are still spreading the disease. Darker shades of gray correspond to higher levels of awareness in susceptibles. Animated versions are available as supporting video. (See SI Appendix, Movies S1 and S2).