In early 2009 a novel influenza A (H1N1) variant emerged which spread globally causing the first influenza pandemic in over 40 years. The dynamics and impact of this pandemic are difficult to predict, especially since the world has changed significantly in 40 years - the global population has almost doubled, more people live in cities, people travel more frequently and over longer distances. These facts will undoubtedly influence the global pattern of this pandemic, just as geographical heterogeneities will result in different local patterns [1]. More than 60% of the world's population live in low-income and lower-middle income countries, and yet, at the time of writing only, about 10% of confirmed cases have occurred in these areas [2, 3]. In densely populated low-income countries, where public health systems, health care services and drug availability are all stretched, influenza H1N1 is likely to be almost impossible to contain resulting in a greater number of cases occurring in more vulnerable populations resulting in a less benign epidemic.

Even more worrying, almost 60% of the world's human population and over 50% of the world's poultry population live in Asia, where highly pathogenic avian influenza (HPAI) maintains a foothold and seasonal influenza transmission is complex [4]. Previous pandemics have demonstrated the potential consequences of reassortment between human and animal influenza viruses. It is possible, therefore, that the new H1N1 - itself a reassortant of swine viruses that had previously reassorted with human and avian influenza - may follow a similar pattern [5, 6]. The new H1N1 variant has already shown that it can be transmitted from humans to pigs, and we know that the H5N1 subtype is capable of infecting humans and of successfully reassorting with human seasonal influenza viruses under in vitro and in vivo experimental conditions [7, 8]. As the population is increasing and standards of living are improving there has been an increase in livestock production and thus there is probably more contact between animals and humans than before. These contacts offer opportunities for reassortment, and, if a novel virus with the transmissibility of H1N1 and even a fraction of the virulence of H5N1 were to emerge, the consequences would be devastating.

In order to explore the potential impact of influenza A (H1N1) on a densely populated low-income country, we developed a mathematical model showing how an influenza A (H1N1) epidemic might progress in Vietnam. We used this model to estimate the frequency of contact between H1N1 infected humans and domestic animals in an attempt to quantify the opportunities for reassortment between H1N1 and animal influenza viruses.

The first cases of H1N1 were detected in Vietnam on 31 May 2009 and by mid-July there were more than 100 confirmed cases with probable community transmission that was most likely the initial budding of the coming nationwide epidemic. We have used a mathematical model to explore how the epidemic might progress in the absence of interventions and have estimated the number of pigs, ducks and chickens that might be exposed to infected humans during the epidemic. Employing mathematical modelling for such a forecasting exercise comes with many caveats. Of these, the most important are that real individuals are heterogeneous in behaviour and transmission, that human behaviour can change as a result of the severity of the epidemic and that the spatial dimensions of transmission have many nested levels that may or may not alter the progression of the epidemic on a larger scale [23, 24]. We used a 'patch model' with coarse province-level spatial resolution for simplicity of model development and rapid computation; the model results should, therefore, be viewed as rough estimates of the epidemic's impact in Vietnam on a year-long time scale.

The most important caveat in our analysis is that the true basic reproductive number is not known; we used a conservative estimate, between 1.2 and 3.1, based on early measurements taken in Mexico, USA and Japan, and we stress that the R ₀ for Vietnam may be higher than these estimates. For an R ₀ value of 4.0, our model predicted a total of 13.3 million cases among humans; for an R ₀ value of 5.0, 16.6 million cases were predicted. Unfortunately, the uncertainty in Vietnam's R ₀ will not be resolved until we analyse the progression of cases from the first wave of this pandemic.

Although the model predicts substantially more cases than have so far been reported from other H1N1 affected countries, the clinical illness is predominantly mild and, therefore, reported H1N1 cases to date reflect only a small proportion of the total number of cases. Our modelled epidemic affects a median of 7.4% of the population (IQR: 5.2-9.3%). This rate is below the figures for previous pandemics and might be considered too low given the high transmissibility of this virus in some settings and the expectation that most of the population would have no immunity [12]. Due to the low probability of hospitalization, it is unlikely that the health sector as a whole will be over-whelmed in the scenario outlined in this model. However, there is considerable variation in reported hospitalization rates for H1N1 and the estimate of 1% that we have used is considerably lower than the maximum of 6% [25]. As elsewhere, the number of intensive care beds is limited in Vietnam and occupancy is routinely at maximum; therefore intensive care capacity is likely to be easily overwhelmed. Also, although Vietnam has impressive health indicators for its economic status - the population may have vulnerabilities, such as under-nutrition in children, which might result in a greater number of severe cases than observed elsewhere.

Containment does appear to have been temporarily successful in some countries (Mexico and Japan) but not in others (Australia and the USA). The reasons for these differences are undoubtedly complex, but successful case detection, isolation and treatment, quarantine and chemoprophylaxis of contacts, and social distancing measures, may all have an effect on the results. In our model, school closures did not make a substantial difference to the epidemic progression, although substantial decreases in contact frequency across all age groups would delay the time course of the epidemic. School outbreaks have been a major feature in the early stages of this pandemic, and it is possible that our model underestimates the role of the range of contacts and susceptibility of school-age children on the epidemic dynamics. School closures did seem to be effective in Kobe, Japan, during 11-24 May 2009, but this may have reflected the low number of overall infections in Japan at that time (between four and 345 confirmed cases) [26]. In the UK, a plateau in consultation rates appears to have coincided with the closure of schools for the annual summer holidays [27]. Previous work suggests that school closure can modify peak attack rates and may result in a modest reduction of the final number of cases, but empiric data is still required on the effectiveness of school closure on reducing the number of transmissions [28–31]. Climate and other seasonally variable factors may also have acted to limit transmission in temperate regions [32, 33]. Seasonal factors are likely to have less influence in tropical regions where the seasonality of influenza transmission is much less marked [4].

In the absence of effective interventions, we predict a large amount of contact between infected humans and animals that might harbour other influenza viruses, including HPAI. In fact, we believe our model probably underestimates the amount of contact between infected human and animals for three reasons. First, we divided the total number of human cases by the number of people per household in order to derive an estimate of the number of households with an infectious case. We did this to avoid over counting animals that were exposed to multiple infected individuals in the same household, but this is a very conservative correction. Second, domestic animal production is concentrated close to urban centres, where population densities are higher than average. Third, we did not model contacts which occurring in live poultry markets or commercial farms.

The danger of human-animal contact lies in the opportunity for reassortment among different influenza subtypes. It is well known that influenza reassorts in humans [34], that pigs play an important role in reassortment of human/avian/swine influenza viruses [35–37] and that the history of avian influenza viruses includes multiple reassortment events [38, 39]. However, very little is known about the potential of human influenza viruses to jump to animals, since most studies to date have focused on animal influenza activity and the risk it poses to humans [40–42]. Pandemic H1N1 has already been detected in swine and, since poultry and swine populations in Asia may harbour many different subtypes of influenza (at least H4, H5, H6, H7, H9, H11, H12), the generation of a new subtype through a reassortment event is a real possibility [43, 44] [personal communication, Ken Inui].

Although these opportunities for genetic reassortment are not unique, the current influenza landscape contains worrying features. Widespread epidemics of novel H1N1 are likely in tropical countries where HPAI is endemic and seasonal influenza transmission is complex and sustained, without the seasonal bottlenecks that characterize transmission in temperate regions [4, 33]. The overall diversity of influenza viruses in southeastern Asia ensures that an epidemic of the novel H1N1 will create many opportunities for co-infection with other subtypes circulating in the region. Genetic and antigenic data suggest that Asia is a key source of influenza viruses that cause seasonal outbreaks in the northern and southern hemispheres [45]. This region, therefore, possesses the conditions necessary for the genesis and dissemination of new influenza variants [33, 45]. Finally, the introduction of H1N1 into southeastern Asia creates an optimal evolutionarily environment for the virus, where re-assortment is neither too frequent nor too rare [46]. This means the virus receives the benefits of limited reassortment (a genetic novelty) but not the penalty of high levels of reassortment (the breaking apart of beneficial gene combinations).

Our model provides a rough picture of what might happen in Vietnam, but it includes many assumptions, uncertainties and un-modelled heterogeneities which require that the results be interpreted with caution. Although changes in human demography and migration over the past 40 years may make a pandemic more difficult to control, the same period has seen massive advances in technology and communication that allow us to monitor and predict this pandemic as never before. Mathematical models are one tool, but a criticism of these models is that the predictions are not subsequently tested against real outbreak data [47]. Our model development has coincided with the arrival of H1N1 in Vietnam and we are planning to track the progression of the outbreak in Vietnam in an attempt at real-time model validation and diagnostics.