The use of mathematical models to inform influenza pandemic preparedness and response

Abstract

Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a realtime tool for pandemic control is currently limited by the lack of essential surveillance information such as serological data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases.

Figure 1

Schematic of the Susceptible-Infectious-Recovered model (left) and the typical epidemic curve that it generates (right).

Figure 2. The nonlinear dependence of the final attack rate and critical coverage on R₀

Knowing R₀, we can use the Susceptible-Infectious-Recovered model to estimate the final attack rate as well as the level of vaccination coverage required to prevent an epidemic (left). Similarly, the model can be used to estimate the potential reduction in attack rate provided by different levels of vaccination coverage (right).

Figure 3. A schematic of transmission network for agent-based simulations

In general, a network is consisted of nodes (the circles) and edges (the links between circles). In agent-based simulations, each node represents a single person (“an agent”) and each edge represents a possible route of disease transmission between two persons. As such, there can be multiple types of edges and edges can form and disappear over time. In this example, solid edges represent family membership while dashed edges represent peer-group membership. In this hypothetical population of 12 individuals, there are 4 families (A-B-C-D, E-F-G, H-I, and K-L-J) and 2 peer-groups (B-G-H and K-E). The transmission network for homogeneous mixing models (e.g. the basic SIR model) would correspond to a network with one edge between every pair or nodes.