Epidemic enhancement in partially immune populations

Abstract

We observe that a pathogen introduced into a population containing individuals with acquired immunity can result in an epidemic longer in duration and/or larger in size than if the pathogen were introduced into a naive population. We call this phenomenon "epidemic enhancement," and use simple dynamical models to show that it is a realistic scenario within the parameter ranges of many common infectious diseases. This finding implies that repeated pathogen introduction or intermediate levels of vaccine coverage can lead to pathogen persistence in populations where extinction would otherwise be expected.

Figure 1. Deterministic prediction of the parameter ranges where epidemic enhancement may be observed.

The range of parameter values (grey) for a population size of N = 50,000 and the initial condition (S₀,I₀ ) = (N−1, 1) which demonstrate the behavior of an initial epidemic which dies out (there exists t>0 such that I_t<1) followed by persistence upon reintroduction (I*>1), depending on the level of population turnover between pathogen extinction and reintroduction. R₀ is the basic reproductive number of the pathogen in a naïve host population; ρ is the duration of infectiousness relative to the average duration of immunity. Stars represent parameter values taken from the literature for a variety of common and emerging infectious diseases. Note that the x-axis is shown on a log scale. Parameter values used, estimated ranges of parameter values, and references are given in Table S1.

Figure 2. Stochastic demonstration of epidemic enhancement in partially immune populations.

Each plot is a comparison of the outcome of the runs starting with a particular immunity level to the 90^th percentile of runs in a naïve population. Black spaces show where enhancement occurs; that is, >15% of epidemics in partially immune population are longer (top row) or larger (bottom row) than the 90^th percentile of epidemics in a naïve population. Grey spaces show the area where 5–15% of the epidemics in the partially immune population are longer or larger than the 90^th percentile of epidemics in a naive population (so vaccination has little or no effect in either direction). The simulation was run 500 times for introduction into a naïve population for each set of parameter values, and these runs were used to determine the 90^th percentile for epidemic duration and size; the pathogen was considered to persist if it remained in the population for ≥300 disease generations. The simulation was then run 500 times for each of the levels of initial population immunity (25%, 50%, 75%, 90%) in the portion of parameter space for which the pathogen did not persist in the naïve population. The total population size is N = 50,000.

Figure 3. Enhancement of epidemic duration for diseases in human populations.

Epidemic duration in a population of N = 50,000 individuals for a variety of human pathogens as a function of population immunity at introduction. Solid lines show the median duration in disease generations for 1,000 simulation runs at each level of initial population immunity; dashed lines show quartiles. Each pathogen shows some level of enhancement of epidemic duration with increased immunity except pertussis. Enhancement of epidemic size is not observed for these pathogens for N = 50,000.