Simple models for containment of a pandemic

Abstract

Stochastic simulations of network models have become the standard approach to studying epidemics. We show that many of the predictions of these models can also be obtained from simple classical deterministic compartmental models. We suggest that simple models may be a better way to plan for a threatening pandemic with location and parameters as yet unknown, reserving more detailed network models for disease outbreaks already underway in localities where the social networks are well identified.We formulate compartmental models to describe outbreaks of influenza and attempt to manage a disease outbreak by vaccination or antiviral treatment. The models give an important prediction that may not have been noticed in other models, namely that the number of doses of antiviral treatment required is extremely sensitive to the number of initial infectives. This suggests that the actual number of doses needed cannot be estimated with any degree of reliability. The model is applicable to pre-epidemic vaccination, such as annual vaccination programs in anticipation of an 'ordinary' influenza outbreak with limited drift, and as a combination of treatment both before and during an epidemic.

Figure 1

SLIAR epidemic model.

Figure 2

Epidemic treatment model.

Figure 3

Total number of doses used in a population of 1000 individuals over the course of the outbreak as a function of the mean times to treatment and prophylaxis (in days), for $\mathcal{R}$₀=1.5, with S₀=999 and I₀=1.

Figure 4

Total cases as a function of the treatment rates, for $\mathcal{R}$₀=1.5, with S₀=999 and I₀=1.