Most critical is capturing the movement of people. To do so, we use data from the Thai national migration survey, which asked a sample of people the distance they travel to work. The cumulative probability distribution function for those data is typical of many countries: most people travel a very short distance to work, but the distribution includes a fat tail—some people travel tens of kilometers or even 100 kilometers. The distribution of individuals going to school includes a distance cutoff, as students clearly do not travel quite so far to school as adults do to work. Although sample size is limited, the curve is similar to that seen in other countries, so we have some confidence in it. The model also captures the proportion of the population that is working.
The transmissibility of the pathogen will determine the outcome or feasibility of containment policies for pandemic influenza. To investigate this, we are aided by work done by Dr. Mark Lipsitch's group led by Dr. C.E. Mills in 2004, which tried to quantify the transmissibility of pandemic influenza in 1918 and came up with a range of 2 to 3 for R0. Our later work noted that this assumes a serial interval for influenza—the delay between one generation of infections and the next – of about 3.5 days. This value was also assumed by many other past publications, but relatively few data exist with which to back up the figure.
Reanalyzing the available data on the incubation period of influenza and the duration of infectiousness reduces that figure to perhaps 2.5 days, which paradoxically drops estimates of R0. Our revised estimates of R0 for the pandemic waves in the United Kingdom in 1918 and 1919 peak at 1.8, and are considerably less most of the time. However, those adjustments do not mean that pandemic influenza will spread more slowly, because the doubling time of these epidemics remains the same. That is, if we reduce the serial interval and the reproduction number, then the overall rate of spread can remain constant.
The model tries to capture the natural history of influenza as realistically as possible. We are using current H3 and H1 influenza as our principal model. We are well aware that the H5-based pandemic may not show the same natural history parameters, and so are undertaking sensitivity analyses, but we felt it was best to root the model in what we know about human influenza. We are use data published by Moser et al. on the distribution of latent periods of the disease, which average about 1.5 days. The model also incorporates data on the distribution of infectiousness, and we tried to match the model to previous age-dependent attack rates of pandemics.
We base our assumptions on the effect of antiviral drugs on parameters estimated by Dr. Fred Hayden and by Dr. Ira Longini. Our baseline assumptions are that prophylaxis of uninfected individuals reduces their susceptibility by about 30 percent, and the infectiousness of infected people by 60 percent for as long as they are on therapy. A treated person also sees a 65 percent drop in the chance of becoming a clinically diagnosable case.
We assume that only about half of infections result in clinically identifiable disease. That means that should a pandemic strain of H5 emerge through reassortment, its virulence will be less than what we are now seeing. However, if the current human virulence of the avian H5N1 virus remained unchanged for an emergent pandemic H5 strain, severe clinical disease would actually occur in a much higher proportion of cases. Our assumption of the 50 percent clinical case rate is thus quite pessimistic from the perspective of case ascertainment. Our assumption that treatment reduces someone’s chance of becoming a case by 65 percent reduces the average infectiousness of infected individuals still further.