Key transmission parameters of an institutional outbreak during the 1918 influenza pandemic estimated by mathematical modelling

AIM: To estimate the key transmission parameters associated with an outbreak of pandemic influenza in an institutional setting (New Zealand 1918). METHODS: Historical morbidity and mortality data were obtained from the report of the medical officer for a large military camp. A susceptible-exposed-infectious-recovered epidemiological model was solved numerically to find a range of best-fit estimates for key epidemic parameters and an incidence curve. Mortality data were subsequently modelled by performing a convolution of incidence distribution with a best-fit incidence-mortality lag distribution. RESULTS: Basic reproduction number (R(0)) values for three possible scenarios ranged between 1.3, and 3.1, and corresponding average latent period and infectious period estimates ranged between 0.7 and 1.3 days, and 0.2 and 0.3 days respectively. The mean and median best-estimate incidence-mortality lag periods were 6.9 and 6.6 days respectively. This delay is consistent with secondary bacterial pneumonia being a relatively important cause of death in this predominantly young male population. CONCLUSION: These R(0 )estimates are broadly consistent with others made for the 1918 influenza pandemic and are not particularly large relative to some other infectious diseases. This finding suggests that if a novel influenza strain of similar virulence emerged then it could potentially be controlled through the prompt use of major public health measures

Deaths from Bacterial Pneumonia during 1918–19 Influenza Pandemic

A sequential-infection hypothesis is consistent with characteristics of this pandemic

Modelling and analysis of influenza A (H1N1) on networks

Network modelling is a useful tool for studying the transmission of H1N1 in China, capturing the main features of the spread of H1N1. The paper calculates the basic reproduction number and studies the effects of various immunization schemes. The final size relation is derived for the network epidemic model. While a uniform, mass-immunization strategy helps control the prevalence, a targeted immunization strategy focusing on specific groups with given connectivity may better control an epidemic

Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918–19

<p>Abstract</p> <p>Background</p> <p>Time variations in transmission potential have rarely been examined with regard to pandemic influenza. This paper reanalyzes the temporal distribution of pandemic influenza in Prussia, Germany, from 1918–19 using the daily numbers of deaths, which totaled 8911 from 29 September 1918 to 1 February 1919, and the distribution of the time delay from onset to death in order to estimate the effective reproduction number, Rt, defined as the actual average number of secondary cases per primary case at a given time.</p> <p>Results</p> <p>A discrete-time branching process was applied to back-calculated incidence data, assuming three different serial intervals (i.e. 1, 3 and 5 days). The estimated reproduction numbers exhibited a clear association between the estimates and choice of serial interval; i.e. the longer the assumed serial interval, the higher the reproduction number. Moreover, the estimated reproduction numbers did not decline monotonically with time, indicating that the patterns of secondary transmission varied with time. These tendencies are consistent with the differences in estimates of the reproduction number of pandemic influenza in recent studies; high estimates probably originate from a long serial interval and a model assumption about transmission rate that takes no account of time variation and is applied to the entire epidemic curve.</p> <p>Conclusion</p> <p>The present findings suggest that in order to offer robust assessments it is critically important to clarify in detail the natural history of a disease (e.g. including the serial interval) as well as heterogeneous patterns of transmission. In addition, given that human contact behavior probably influences transmissibility, individual countermeasures (e.g. household quarantine and mask-wearing) need to be explored to construct effective non-pharmaceutical interventions.</p

A mechanistic model of infection: why duration and intensity of contacts should be included in models of disease spread

<p>Abstract</p> <p>Background</p> <p>Mathematical models and simulations of disease spread often assume a constant per-contact transmission probability. This assumption ignores the heterogeneity in transmission probabilities, e.g. due to the varying intensity and duration of potentially contagious contacts. Ignoring such heterogeneities might lead to erroneous conclusions from simulation results. In this paper, we show how a mechanistic model of disease transmission differs from this commonly used assumption of a constant per-contact transmission probability.</p> <p>Methods</p> <p>We present an exposure-based, mechanistic model of disease transmission that reflects heterogeneities in contact duration and intensity. Based on empirical contact data, we calculate the expected number of secondary cases induced by an infector (i) for the mechanistic model and (ii) under the classical assumption of a constant per-contact transmission probability. The results of both approaches are compared for different basic reproduction numbers <it>R</it>₀.</p> <p>Results</p> <p>The outcomes of the mechanistic model differ significantly from those of the assumption of a constant per-contact transmission probability. In particular, cases with many different contacts have much lower expected numbers of secondary cases when using the mechanistic model instead of the common assumption. This is due to the fact that the proportion of long, intensive contacts decreases in the contact dataset with an increasing total number of contacts.</p> <p>Conclusion</p> <p>The importance of highly connected individuals, so-called super-spreaders, for disease spread seems to be overestimated when a constant per-contact transmission probability is assumed. This holds particularly for diseases with low basic reproduction numbers. Simulations of disease spread should weight contacts by duration and intensity.</p

Can Interactions between Timing of Vaccine-Altered Influenza Pandemic Waves and Seasonality in Influenza Complications Lead to More Severe Outcomes?

Vaccination can delay the peak of a pandemic influenza wave by reducing the number of individuals initially susceptible to influenza infection. Emerging evidence indicates that susceptibility to severe secondary bacterial infections following a primary influenza infection may vary seasonally, with peak susceptibility occurring in winter. Taken together, these two observations suggest that vaccinating to prevent a fall pandemic wave might delay it long enough to inadvertently increase influenza infections in winter, when primary influenza infection is more likely to cause severe outcomes. This could potentially cause a net increase in severe outcomes. Most pandemic models implicitly assume that the probability of severe outcomes does not vary seasonally and hence cannot capture this effect. Here we show that the probability of intensive care unit (ICU) admission per influenza infection in the 2009 H1N1 pandemic followed a seasonal pattern. We combine this with an influenza transmission model to investigate conditions under which a vaccination program could inadvertently shift influenza susceptibility to months where the risk of ICU admission due to influenza is higher. We find that vaccination in advance of a fall pandemic wave can actually increase the number of ICU admissions in situations where antigenic drift is sufficiently rapid or where importation of a cross-reactive strain is possible. Moreover, this effect is stronger for vaccination programs that prevent more primary influenza infections. Sensitivity analysis indicates several mechanisms that may cause this effect. We also find that the predicted number of ICU admissions changes dramatically depending on whether the probability of ICU admission varies seasonally, or whether it is held constant. These results suggest that pandemic planning should explore the potential interactions between seasonally varying susceptibility to severe influenza outcomes and the timing of vaccine-altered pandemic influenza waves

Transmission Characteristics of the 2009 H1N1 Influenza Pandemic: Comparison of 8 Southern Hemisphere Countries

While in Northern hemisphere countries, the pandemic H1N1 virus (H1N1pdm) was introduced outside of the typical influenza season, Southern hemisphere countries experienced a single wave of transmission during their 2009 winter season. This provides a unique opportunity to compare the spread of a single virus in different countries and study the factors influencing its transmission. Here, we estimate and compare transmission characteristics of H1N1pdm for eight Southern hemisphere countries/states: Argentina, Australia, Bolivia, Brazil, Chile, New Zealand, South Africa and Victoria (Australia). Weekly incidence of cases and age-distribution of cumulative cases were extracted from public reports of countries' surveillance systems. Estimates of the reproduction numbers, R0, empirically derived from the country-epidemics' early exponential phase, were positively associated with the proportion of children in the populations (p = 0.004). To explore the role of demography in explaining differences in transmission intensity, we then fitted a dynamic age-structured model of influenza transmission to available incidence data for each country independently, and for all the countries simultaneously. Posterior median estimates of R0 ranged 1.2–1.8 for the country-specific fits, and 1.29–1.47 for the global fits. Corresponding estimates for overall attack-rate were in the range 20–50%. All model fits indicated a significant decrease in susceptibility to infection with age. These results confirm the transmissibility of the 2009 H1N1 pandemic virus was relatively low compared with past pandemics. The pattern of age-dependent susceptibility found confirms that older populations had substantial – though partial - pre-existing immunity, presumably due to exposure to heterologous influenza strains. Our analysis indicates that between-country-differences in transmission were at least partly due to differences in population demography

Models of epidemics: when contact repetition and clustering should be included

Background The spread of infectious disease is determined by biological factors, e.g. the duration of the infectious period, and social factors, e.g. the arrangement of potentially contagious contacts. Repetitiveness and clustering of contacts are known to be relevant factors influencing the transmission of droplet or contact transmitted diseases. However, we do not yet completely know under what conditions repetitiveness and clustering should be included for realistically modelling disease spread. Methods We compare two different types of individual-based models: One assumes random mixing without repetition of contacts, whereas the other assumes that the same contacts repeat day-by-day. The latter exists in two variants, with and without clustering. We systematically test and compare how the total size of an outbreak differs between these model types depending on the key parameters transmission probability, number of contacts per day, duration of the infectious period, different levels of clustering and varying proportions of repetitive contacts. Results The simulation runs under different parameter constellations provide the following results: The difference between both model types is highest for low numbers of contacts per day and low transmission probabilities. The number of contacts and the transmission probability have a higher influence on this difference than the duration of the infectious period. Even when only minor parts of the daily contacts are repetitive and clustered can there be relevant differences compared to a purely random mixing model. Conclusion We show that random mixing models provide acceptable estimates of the total outbreak size if the number of contacts per day is high or if the per-contact transmission probability is high, as seen in typical childhood diseases such as measles. In the case of very short infectious periods, for instance, as in Norovirus, models assuming repeating contacts will also behave similarly as random mixing models. If the number of daily contacts or the transmission probability is low, as assumed for MRSA or Ebola, particular consideration should be given to the actual structure of potentially contagious contacts when designing the model.ISSN:1742-468

A model for the spread and control of pandemic influenza in an isolated geographical region

In the event of an influenza pandemic, the most probable way in which the virus would be introduced to an isolated geographical area is by an infected traveller. We use a mathematical model, structured on the location at which infection occurs and based on published parameters for influenza, to describe an epidemic in a community of one million people. The model is then modified to reflect a variety of control strategies based on social distancing measures, targeted antiviral treatment and antiviral prophylaxis and home quarantine, and the effectiveness of the strategies is compared. The results suggest that the only single strategy that would be successful in preventing an epidemic (with R0=2.0) is targeted antiviral treatment and prophylaxis, and that closing schools combined with either closing work places or home quarantine would only prevent such an epidemic if these strategies were combined with a modest level of antiviral coverage