Evolutionary entropy determines invasion success in emergent epidemics

Abstract

Background: Standard epidemiological theory claims that in structured populations competition between multiple pathogen strains is a deterministic process which is mediated by the basic reproduction number (R0) of the individual strains. A new theory based on analysis, simulation and empirical study challenges this predictor of success.

Principal findings: We show that the quantity R0 is a valid predictor in structured populations only when size is infinite. In this article we show that when population size is finite the dynamics of infection by multi-strain pathogens is a stochastic process whose outcome can be predicted by evolutionary entropy, S, an information theoretic measure which describes the uncertainty in the infectious age of an infected parent of a randomly chosen new infective. Evolutionary entropy characterises the demographic stability or robustness of the population of infectives. This statistical parameter determines the duration of infection and thus provides a quantitative index of the pathogenicity of a strain. Standard epidemiological theory based on R0 as a measure of selective advantage is the limit as the population size tends to infinity of the entropic selection theory. The standard model is an approximation to the entropic selection theory whose validity increases with population size.

Conclusion: An epidemiological analysis based on entropy is shown to explain empirical observations regarding the emergence of less pathogenic strains of human influenza during the antigenic drift phase. Furthermore, we exploit the entropy perspective to discuss certain epidemiological patterns of the current H1N1 swine flu outbreak.

Figure 1. Simulation showing evolutionary entropy of dominant variant decreasing over time for three realisations of the simulation (arbitrary units).

This corresponds to the scenario of , i.e. variants are competing against incumbents with positive growth rates in the host population. Because , a plot of H versus time would yield the same pattern.

Figure 2. Influenza A (H1N1) weekly mortality rates in large cities in England and Wales for the major influenza outbreaks 1918 to 1951.

Note the log scale on the mortality rates. The thick bars on each of the outbreaks proportional to the basic reproduction number of the epidemic.

Figure 3. Simulations showing evolutionary entropy increasing over time for three realisations of the simulation (arbitrary units).

This corresponds to the scenario of , i.e. variants are competing against incumbents at equilibrium in the host population. Because , a plot of H versus time would yield the same pattern.