Modelling seasonality and viral mutation to predict the course of an influenza pandemic

Abstract

As the 2009 H1N1 influenza pandemic (H1N1) has shown, public health decision-makers may have to predict the subsequent course and severity of a pandemic. We developed an agent-based simulation model and used data from the state of Georgia to explore the influence of viral mutation and seasonal effects on the course of an influenza pandemic. We showed that when a pandemic begins in April certain conditions can lead to a second wave in autumn (e.g. the degree of seasonality exceeding 0.30, or the daily rate of immunity loss exceeding 1% per day). Moreover, certain combinations of seasonality and mutation variables reproduced three-wave epidemic curves. Our results may offer insights to public health officials on how to predict the subsequent course of an epidemic or pandemic based on early and emerging viral and epidemic characteristics and what data may be important to gather.

Fig. 1

Plot of R₀ value as function of time. The figure shows the baseline reproductive rate $R_0^{\ast }=1·5$, degree of seasonality ε=0·07, 0·18, and 0·30. The four intervals represent four different times (January, April, July, October) when the initial seed case appears. Within different intervals, the variation patterns of R₀ are different (e.g. in the first interval, the value of R₀ first decreases then increases; in the third interval, the value of R₀ first increases then decreases).

Fig. 2

Epidemic curves (daily prevalence of infection) for seasonality scenarios. Nine curves in each panel correspond to nine pairs of ( $R_0^{\ast }$, ε) values. The x axis (northeast horizontal) represents the simulation day, the y axis (southeast horizontal) represents the degree of seasonality (ε), and the z axis (vertical) represents the daily prevalence of infectious cases (the number of symptomatic and asymptomatic persons over the total population). The epidemic starts in four different months: (a) January, (b) April, (c) July, (d) October.

Fig. 3

Epidemic curves (daily prevalence of infection) for mutation scenarios. Each panel contains six curves corresponding to six pairs of (δ, t*) values (δ=0·05 and 0·10, t*=60, 90, and 180). The x axis represents the simulation day, and the y axis represents the daily prevalence of infectious cases (the number of symptomatic and asymptomatic persons over the total population). The subfigures show different reproductive rates (a) R₀=1·5, (b) R₀=1·8, (c) R₀=2·1.

Fig. 4

Percentage of susceptible population (number of the daily susceptible persons over the total population) and the daily prevalence of infection. R₀=1·5 and the loss immunity rate δ=0·05 and 0·10. The curves are plotted with different scaling. The upper curves, which correspond to the susceptible population, use the scale on the left y axis; the lower curves, which correspond to the prevalence of infection, use the scale on the right y axis.

Fig. 5

Plot of the peak prevalence value as a function of t*. The value of the peak prevalence (maximum number of daily symptomatic and asymptomatic persons over the total population) in the second wave is plotted as a function of t*, the day when the mutant strain emerges. The subfigures show different reproductive rates (a) R₀=1·5, (b) R₀=2·1, and each panel contains two curves corresponding to two values of the loss immunity rate δ (δ=0·05 and 0·10).

Fig. 6

Reproduced epidemic curves for the 1918, 1957 and 1968 pandemics. The x axis represents the simulation day, and the y axis represents the daily prevalence of infectious cases (the number of symptomatic and asymptomatic persons over the total population). (a) Three prevalence peaks can occur with a baseline reproductive rate $R_0^{\ast }=1·5$, degree of seasonality ε=0·30, loss of immunity rate δ=0·015. The epidemic starts in April and the mutant strain emerges at day 275. (b) Simulating a mutation scenario with R₀=1·5 and loss of immunity rate δ=0·05. The epidemic starts in August and the mutant strain emerges at day 90 (November). (c) Simulating with R₀=1·5 (without mutation or seasonality). The epidemic starts in October.