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The European Centre for Disease Prevention and Control called the attention in March 2012 to the risk of measles in Ukraine among visitors to the 2012 UEFA European Football Championship. Large populations of supporters travelled to various locations in Poland and Ukraine, depending on the schedule of Euro 2012 and the outcome of the games, possibly carrying the disease from one location to another. In the present study, we propose a novel two-phase multitype branching process model with immigration to describe the risk of a major epidemic in connection with large-scale sports-related mass gathering events. By analytic means, we calculate the expected number and the variance of imported cases and the probability of a major epidemic caused by the imported cases in their home country. Applying our model to the case study of Euro 2012 we demonstrate that the results of the football games can be highly influential to the risk of measles outbreaks in the home countries of supporters. To prevent imported epidemics, it should be emphasized that vaccinating travellers would most efficiently reduce the risk of epidemic, while requiring the minimum doses of vaccines as compared to other vaccination strategies. Our theoretical framework can be applied to other future sport tournaments too.

The European Centre for Disease Prevention and Control reported a measles outbreak in Ukraine with more than 11,000 cases from the beginning of 2012 until the end of June 2012 [

We introduce a discrete time Markov chain model, which is an adaptation of a multitype Galton-Watson process with immigration to give a mathematical model for the evolution of the epidemic. Thus, we calculate the risk of epidemics connected to sports-related mass gathering events. Our model consists of two parts, the first one describing the spread of the disease during the championship in the host country, while the second part models the spread of the disease by fans returning to their home countries.

We apply our model to the special case of measles epidemics in Ukraine during the Euro 2012. Four of the eight host cities of this championship are in Ukraine (Kiev, Kharkiv, Lviv and Donetsk); one of these, Lviv, is situated in the western region where the prevalence is the highest and vaccination coverage remained the lowest in the country. Games of the group phase took place in the four Ukrainian cities for groups B and D including Denmark, Germany, Netherlands, Portugal and Ukraine, England, France, Sweden [

The rest of the paper is organized as follows. In Section

Since the supporter group spends a relatively short time in the infected area, it is possible that nobody gets infected, in which case there is no increased chance for epidemic in the home country. It is also clear that the risk of a huge epidemic is larger when five infected individuals arrive home (maybe to different parts of the country) than in the case when only one infectious supporter arrives. The fact that the number of infected supporters is zero, one, or five is just a matter of chance; thus, a deterministic model does not serve for our purposes in this case. It is well known (see [

To describe the importation dynamics in the simplest manner, as a mathematical model, we propose a branching process with immigration. For simplicity, consider a single supporter population

In the following we describe the exact mathematical model.

Let

It is easy to show that the recursion

Up to now we did not use any particular property of the branching structure. However, note that in our case we have the following. The immigrants are always of type-1; thus, the generating function is in fact a one-variable function, that is,

Phase 2 starts with the infected vector

Now, all who were infected after this step spend their infectious days in the home country, so the process now is a simple single type Galton-Watson process with offspring generating function

If this simple Galton-Watson process is critical or subcritical, that is,

In this section we apply the results to the measles epidemic in Ukraine during the 2012 UEFA European Football Championship. For illustratory purposes, we have chosen France as a prototype for describing the results. In fact, as being amongst the four favourites for the European championship title [

France is eliminated in the group stage, thus playing only three games in Ukraine between June 11 and June 19 (hypothetical case);

France finishes second in the group and is eliminated in the quarterfinals, playing four games in Ukraine between June 11 and June 23 (this is what actually happened);

France finishes second in the group, and gets into the final, thus playing six games between June 11 and July 1, all in Ukraine (hypothetical case).

The movement of France during Euro 2012 and the dates of games. The solid arrow corresponds to the group stage, the dashed arrow corresponds to additional games in scenarios (b) and (c), and the dot-dashed arrow corresponds to the hypothetical case of getting into the final (scenario (c)). The dotted arrows represent the movement of Italy (chosen randomly for illustratory purposes) during the tournament.

We assume that the supporter population is staying in Ukraine as long as the team continues to play games. The total length of stay would be the length of games plus one extra day due to international travel, and thus in the three cases we have

For our computations we set

By the nature of the immigration and the offspring distributions it is natural to assume that these are Poisson, or compound Poisson distributed. We calculate the extinction probabilities in two cases: when the offspring and immigration distributions are Poisson distributions and when they are negative binomial distributions. In the appendix we explicitly calculate some relevant quantities. We assume that the expectations of the total number of daily new infections from the local population (

Assuming that both the immigration and the offspring distributions are Poisson, we have

A random variable

Figure

The probability of a major epidemic as the function of the effective reproduction number in France in the Poissonian case (a) and in the negative binomial case (b). The parameters are

Comparing Figures

The extinction probabilities cannot be computed explicitly. This is because

We compare the effectiveness of three potential vaccination strategies in reducing the risk of imported major epidemic:

vaccination of the general population in France;

vaccination of the general population in Ukraine;

vaccination of football-associated travellers between France and Euro 2012 venues.

To consider (i), note that increasing the vaccination rate

The probability of a major epidemic as the function of the immunization rate in France. The parameters are

The solid curve is the expectation of the total number of imported cases in scenario (b) in the function of the immunization rate in France. At least with probability 0.75 the number of imported cases is smaller than the dashed curve and with probability 0.9 is smaller than the dot-dashed curve (calculated from Chebyshev’s inequality). The parameter values are the same as in Figure

Figure

On the other hand, elevating the vaccination level

The probability of a major epidemic as the function of the immunization rate in Ukraine. The parameters are

Targeted vaccination of football visitors reduces both

The probability of a major epidemic as the function of the immunization rate in the supporter group. The parameters are

In contrast to Euro 2012, here we descriptively review the measles outbreaks which are likely associated with Euro 2008 and other mass gathering events. The 2008 UEFA European Football Championship (Euro 2008) took place in Austria and Switzerland from 7 to 29 June 2008. Significant measles outbreaks were reported in both of the host countries before the championship [

For Euro 2008 we chose Germany as the German national team reached the final of the championship, which means that their supporters spent 21 days in Austria and Switzerland, and WHO reports a suboptimal coverage of 83–89% for the second dose of measles-containing vaccine in Germany [

Data from 2008 show that in several participating countries (e.g., France, Germany, Spain, and Switzerland) there were increases in the number of measles cases after Euro 2008 compared to the same period of the year in 2007 [

As pointed out in [

After Euro 2012, another sports related mass gathering event followed, the Summer Olympic Games in London. There were several alerts about measles in connection with the Olympic Games [

We constructed and applied a stochastic model to investigate the risk of imported epidemics caused by visitors returning from a sports related mass gathering event to their home countries after the tournament. For the sake of simplicity, we considered a single supporter population, while a realistic situation of course involves many additional complicating factors including movements within the host country and interactions between supporters and local population. We introduced a discrete time Markov chain model with two phases, which is an adaptation of a multitype Galton-Watson process with immigration as a mathematical model and derived several analytical relations for the expectations, variances and probabilities regarding key aspects of the process.

We applied our theoretical model to the measles epidemics in Ukraine during the 2012 UEFA European Football Championship, selecting the national team of France for illustratory purposes. Due to the uncertainties in social parameters, we considered a wide interval for the transmission rate between local and visitor populations. Our approach clearly demonstrated that the travel patterns depend on the schedule and the results of the football games, showing that the probability of a major measles epidemic in France could be greatly elevated by the successful outcomes of French games. Namely, the more successful the national team is in a football tournament, the higher the risk of a post-tournament imported measles epidemic would be in the home country. More importantly, we have compared different vaccination strategies and our study theoretically demonstrated that the risk of an imported measles epidemic by the visitors to Euro 2012 and other mass gatherings would be most efficiently reduced by vaccinating the visitors (travellers). Of course, vaccinating the entire French population would also be effective (which actually prevents the country from not only the risk from Euro 2012 but also any other epidemics to be imported), but in theory this option requires us to secure millions of doses. The optimal control by effectively targeting travellers is novel both in practical and theoretical sense, because the condensed interventions among travellers have been shown not to be very effective in preventing an epidemic (e.g., pandemic influenza) as long as there are arbitrarily large number of travellers. We have shown that it is worth focusing on travellers when the number is finite and in the manageable order. Unvaccinated travellers would likely be covered within a few thousand doses, and thus any country to respond to the associated risk is suggested to consider this option.

We compute explicitly the expectation and variance of the overall number of infectious individuals arriving home after day

Assuming Poissonian offspring and immigration distribution, we have the following:

In the negative binomial case for the different scenarios we have

Also note that in both cases the variance is large compared to the expectation, implying that the probability of no imported cases is large.

A. Dénes and G. Röst were supported by the European Research Council Starting Investigator Grant no. 259559, the Hungarian Scientific Research Fund OTKA K75517, and Bolyai Scholarship of the Hungarian Academy of Sciences. P. Kevei was supported by the TÁMOP-4.2.1/B-09/1/KONV-2010-0005 Project and the Hungarian Scientific Research Fund OTKA PD106181. H. Nishiura received funding support from the JST PRESTO Program and The University of Hong Kong Seed Funding Program (Grant Code: 10208192).