A biological model for influenza transmission: pandemic planning implications of asymptomatic infection and immunity

Abstract

Background: The clinical attack rate of influenza is influenced by prior immunity and mixing patterns in the host population, and also by the proportion of infections that are asymptomatic. This complexity makes it difficult to directly estimate R(0) from the attack rate, contributing to uncertainty in epidemiological models to guide pandemic planning. We have modelled multiple wave outbreaks of influenza from different populations to allow for changing immunity and asymptomatic infection and to make inferences about R(0).

Data and methods: On the island of Tristan da Cunha (TdC), 96% of residents reported illness during an H3N2 outbreak in 1971, compared with only 25% of RAF personnel in military camps during the 1918 H1N1 pandemic. Monte Carlo Markov Chain (MCMC) methods were used to estimate model parameter distributions.

Findings: We estimated that most islanders on TdC were non-immune (susceptible) before the first wave, and that almost all exposures of susceptible persons caused symptoms. The median R(0) of 6.4 (95% credibility interval 3.7-10.7) implied that most islanders were exposed twice, although only a minority became ill in the second wave because of temporary protection following the first wave. In contrast, only 51% of RAF personnel were susceptible before the first wave, and only 38% of exposed susceptibles reported symptoms. R(0) in this population was also lower [2.9 (2.3-4.3)], suggesting reduced viral transmission in a partially immune population.

Interpretation: Our model implies that the RAF population was partially protected before the summer pandemic wave of 1918, arguably because of prior exposure to interpandemic influenza. Without such protection, each symptomatic case of influenza would transmit to between 2 and 10 new cases, with incidence initially doubling every 1-2 days. Containment of a novel virus could be more difficult than hitherto supposed.

Figure 1. Flexible Influenza Model.

Each compartment corresponds to a class of individuals in the population, and the arrows indicate the flows of individuals from class to class over time. As a result of exposure to the force of infection (λ), susceptible individuals (S) flow through two exposed classes of latent infection (E1 and E2). A proportion (α) then become infective and symptomatic (I), and a proportion 1-α become asymptomatic (A). Both I and A pass to the recovered class (R) from which a proportion ρ develop longer-lasting protection (L), while the remainder eventually return to the susceptible class after passing through a temporary state (T).

Figure 2. Incidence data and fitted model for Tristan da Cunha.

Observed and fitted (median parameters) incidences for the H3N2 outbreak on the island of Tristan da Cunha in 1971 (cases per day, starting from 15^th August). Error bars (+/− one SD) are calculated using the negative binomial variance (See Appendix S1).

Figure 3. Incidence data and fitted model for RAF.

Observed and fitted (median parameters) incidences of influenza reported from RAF camps in UK during the 1918 pandemic of H1N1 (cases per week, starting from week of June 8). Error bars (+/− one SD) are calculated using the negative binomial variance.