A Biological Model for Influenza Transmission: Pandemic Planning Implications of Asymptomatic Infection and Immunity

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 R0 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 R0. \ud \ud 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. \ud \ud 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 R0 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. R0 in this population was also lower [2.9 (2.3–4.3)], suggesting reduced viral transmission in a partially immune population. \ud \ud 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

Population and health care system diversity in Southeast Asia and the Western Pacific.

<p><b>(A)</b> Population density ranges from less than 1 person per square kilometre in parts of Papua New Guinea and Indonesia to over 6,800 people per square kilometre in Singapore. Data obtained from Center for International Earth Science Information Network (CIESIN), Columbia University (<a href="http://sedac.ciesin.columbia.edu/gpw" target="_blank">http://sedac.ciesin.columbia.edu/gpw</a>). <b>(B)</b> Number of health care workers per thousand population ranges from 1.2 in Cambodia to 11.5 in Brunei Darussalam. Data obtained from Global Health Observatory data repository (<a href="http://apps.who.int/gho/data/" target="_blank">http://apps.who.int/gho/data/</a>).</p

The Ebola model.

<p>The natural history of infection comprises susceptibility (S), exposure (E) at a rate determined by the force of infection β and the current prevalence of infectious individuals and unburied dead bodies. Exposed individuals progress to mild infectiousness prior to developing symptoms (I0) at rate σ, and symptomatic infection (I) at rate γ₀, followed by either death (D) or recovery (R) at rate γ₁. The proportion of infections leading to death or recovery is informed by estimates of the case fatality ratio (CFR). Dead bodies remain infectious prior to burial (B) at rate τ. Ascertainment of cases (with probability p_asc) allows symptomatic individuals to be hospitalised in isolation wards (H), which reduces their contribution to transmission and increases their probability of recovery. Full equations describing the model are provided in Model description in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0005018#pntd.0005018.s001" target="_blank">S1 Methods</a>.</p

Effect of increased case ascertainment.

<p>Starting with a baseline case ascertainment of 20%, this figure shows the effect of boosting ascertainment to 100% (i.e., perfect detection) at different times after the first detected case. This clearly shows the simultaneous importance of early detection and high ascertainment; provision of one is not a substitute for lack of the other.</p

Effect of behavioural interventions in Southern region.

<p>The effect of reducing the force of infection in the community and/or from dead bodies by 25%, in the rural population of the Southern region where community transmission is low. When transmission is reduced in both settings, the overall force of infection is sufficiently low that uncontrolled outbreaks never occur.</p

Effect of behavioural interventions in Port Moresby region.

<p>The effect of reducing the force of infection in the community and/or from dead bodies by 25%, in the urban population of Port Moresby where community transmission is high. When case ascertainment is 40% or higher, reducing transmission in both settings has a synergistic effect on outbreak control.</p

Effect of improved health care system capacity.

<p>Starting with a baseline case ascertainment of 80% and a small health care system (0.1% of population are HCWs, 1:15 and 1:50 ratio of bed and contact-tracing capacities to HCWs, as above), this figure shows the effect of doubling both the health care capacity and the health care workforce at different times after the first detected case. This increase in capacity represents the transition from a small health care system to a medium health care system, as defined in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0005018#pntd.0005018.g005" target="_blank">Fig 5</a>. This clearly shows the importance of early detection; the time delay in delivering the additional capacity is less important over this timescale of 0–8 weeks, because the existing health care system is capable of accommodating patients in the early stage of the outbreak.</p

The classification of epidemic outcomes.

<p>In the absence of a health care response, EVD importation may result in zero or very few secondary cases (green, left panel) or may result in a large, uncontrolled epidemic (red, left panel). A health care response may mitigate some of these uncontrolled epidemics by greatly reducing their final size (yellow, right panel).</p

The administrative regions of Papua New Guinea.

<p>We separate Port Moresby (the largest city and national capital) from the rest of the Southern (“Papua”) region on the grounds that Port Moresby comprises a much more urbanised population than the rest of the region.</p

Effect of reducing force of infection from community transmission.

<p>Starting with a baseline case ascertainment of 70% and a small health care system (0.1% of population are HCWs, 1:15 and 1:50 ratio of bed and contact-tracing capacities to HCWs, as above), this figure shows the effect of reducing the force of infection from dead bodies (β_D) and in the community (β_I) by 25%. This represents a sociocultural intervention that changes both burial practices and social mixing in the community. Similar to <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0005018#pntd.0005018.g007" target="_blank">Fig 7</a>, success of such an intervention relies upon early detection and a rapid response from the community.</p