Global travel decreases lethality and increases immunity.

3. DISCUSSION The large increase in international travel over the last century might be assumed to have resulted in a high chance of a devastating global pandemic (see e.g. [32]). Here we have used a general epidemiological model to demonstrate that an important, yet often overlooked, factor in the dynamics of a newly introduced high-virulence (HV) pathogen strain is partial immunity driven by exposures to related pathogen strains. When a HV pathogen strain arrives in a population following an epidemic of a related but low virulence (LV) strain, the probability of a major epidemic of the HV strain is decreased. High rates of travel between spatially distinct subpopulations can drive larger outbreaks of low virulence pathogens, in turn providing higher levels of immunity if/when a HV strain, which has the potential to cause a devastating epidemic, appears in the population (Fig 4a-c). Not only did we find that the probability of a major epidemic of the HV strain decreases when travel between subpopulations increases, but the expected final size of the HV strain outbreak can also be reduced. This was particularly pronounced when the level of cross-immunity between strains was high (Fig 4i), since lower cross-immunity levels combined with high travel rates can lead to large epidemics due to increased mixing between subpopulations (Fig 4g). When between-subpopulation travel was increased, the reduction in the probability of a major epidemic of the HV strain, and the expected size, was largely due to cross-immunity reducing the proportion of outbreaks that proceeded to become major epidemics. If/when major epidemics occurred, we found that they were typically larger when there was more travel between regions (Fig 4d-e), although this was not always the case, particularly when the level of cross-immunity was very high (Fig 4f). Partial cross-immunity against a highly virulent strain from prior exposure to a less virulent strain is characteristic of influenza outbreaks in different seasons. For example, it has been suggested that individuals born before 1890 were protected against the 1918 H1N1 pandemic due to the outbreak in 1889-90 [33] and that individuals infected with multiple historical seasonal H1N1 influenza strains were protected against the 2009 H1N1 influenza pandemic strain [34]. Our results suggest that cross-immunity might be a potential explanatory factor as to why there has not been a pandemic as devastating as the 1918 influenza epidemic in the century since, despite the emergence of a strain antigenically similar to the 1918 pandemic strain in 2009. Travel rates increased substantially during the 20th century. As a theoretical exercise, we obtained crude estimates of the travel rates from Europe to the USA, comparing rates during the early 20th century with current travel rates. For the early 20th century rates, we used registry statistics from USA ports from 1914 to 1924 (see Supplementary Material Section 5). Oceanic travel should approximate overall trans-Atlantic travel in this time period, as other modes of long-distance travel were extremely rare. This yielded the approximation λ≈ 3.6· 10-6 per day. Conversely, when estimating current rates of travel from European countries to the USA, approximated using data on air travel, we obtain much higher values of λ≈ 3.7· 10-4 per day. It might be expected that such a significant rise in travel in this time period might have reduced the risk of a global pandemic of a pathogen with circulating strains that induce cross-immunity. Cross-immunity is known to affect the dynamics of outbreaks of various pathogens. Vibrio cholera, for example, exhibits almost complete cross-immunity between strains (a study by Koelle et al. [35] used a cross-immunity level of α= 0.955). On the other hand, human Respiratory Syncytial Virus (hRSV) has been shown to provide incomplete cross-immunity against infections from the same virus group (α ≈ 0.6, [36]). It also provides low levels of cross-immunity again hRSV infections