⌚ Global Diseases Case Study

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Global Diseases Case Study



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The outbreak of severe acute respiratory syndrome SARS in — represented a serious public health threat to the international community. Its rapid spread to regions far away from the initial outbreak created great concern for the potential ability of the virus to affect a large number of countries and required a coordinated effort aimed at its containment [ 1 ]. Most importantly, it clearly pointed out that people's mobility and traveling along commercial airline routes is the major channel for emerging disease propagation at the global scale.

Spatio-temporal structures of human movements thus need to be considered for a global analysis of epidemic outbreaks [ 2 ], as for example in [ 3 ], which incorporates the airline network structure of the largest airports of the world. In this article, we present a stochastic meta-population epidemic model, based on the extension of the deterministic modeling approach to global epidemic diffusion [ 4 , 5 ], for the study of the worldwide spread of emerging diseases that includes the complete International Air Transport Association IATA commercial airline traffic database associated with urban areas census information [ 6 , 7 ].

Once the disease parameters are determined, no free adjustable parameters are left in the model. A toolkit of specific indicators that consider the stochastic nature of the process is introduced to provide risk analysis scenarios and to assess the reliability of epidemic forecasts. In particular, the predictive power of the model is linked to the emergence of epidemic propagation pathways related to the complex properties of the transportation network. The SARS epidemic is used as a case study to assess the model effectiveness and accuracy against real data. The model considers disease parameters estimated from the Hong Kong outbreak in a way consistent with the global nature of the meta-population model by including the impact of infectious individuals traveling in and out of the city.

The temporal and geographic pattern of the disease is analyzed, and the proposed toolkit of epidemic indicators is tested against empirical data. We adopt a global stochastic meta-population model that considers a set of coupled epidemic transmission models. The approach is in the same spirit as the deterministic models used for the global spread of infectious diseases and their successive stochastic generalizations [ 3 , 6 , 7 ], where each compartmental model represents the evolution of the epidemic within one urban area, and the models are coupled by air travel. The air travel data from the IATA [ 8 ] database is included in the model and determines the traveling probabilities. Each airport is surrounded by the corresponding urban area whose population is assumed to be homogeneously mixed for the disease dynamics.

Population data is collected from several census databases see [ 6 , 7 ] for more specific details. The model is fully stochastic and takes into account the discrete nature of individuals both in the travel coupling and in the compartment transitions. The transmission model within each urban area follows a compartmentalization specific to the disease under study.

In order to consider the discrete nature of the individuals in the stochastic evolution of the infection dynamics, we describe the disease propagation inside each urban area by introducing binomial and multinomial processes. Two kinds of processes are considered in the infection dynamics: the contagion process e. The second class describes a transition process, where the number of individuals changing compartment: e. Changing from a basic SIR model to a refined compartmentalization, additional processes ought to be taken into account, as the possibility of having more than one compartment able to transmit the infection, due e.

In the case of SARS, which will be addressed in the following section, the infection dynamics includes the specific characteristics of the disease under study, such as latency, hospitalization, patient isolation, and fatality rate [ 9 — 11 ]. Figure 1 illustrates a schematic representation of the compartmentalization adopted for the SARS case study, whereas the details of the stochastic discrete evolution followed by this specific compartmentalization are described in Additional file 1. Flow diagram of the transmission model. The population of each city is classified into seven different compartments, namely susceptible S , latent L , infectious I , hospitalized who either recover H R or die H D , dead D and recovered R individuals.

We assume that hospitalized as well as infectious individuals are able to transmit the infection, given the large percentage of the cases among health care workers []. The infectiousness of patients in the compartments H R and H D are assumed to be equal although this assumption can easily be changed in the model. Susceptible individuals exposed to SARS enter the latent class. Latents represent infected who are not yet contagious and are assumed to be asymptomatic, as suggested by results based on epidemiologic, clinical and diagnostic data in Canada [40].

Patients admitted to the hospital are not allowed to travel. The average death rate is denoted by d. Each compartmental model in a given urban area is then coupled to the compartmental models of other urban areas via a travel stochastic operator that identifies the number of individuals in each compartment traveling from the urban area i to the urban area j. In each city I , the numbers of passengers traveling on each connection at time t define a set of stochastic variables that follows a multinomial distribution. In addition, other routing constraints and two legs travels can be considered.

A detailed mathematical description of the traveling coupling is reported in [ 6 , 7 , 12 ]. The defined model considers stochastic fluctuations both in the individual compartmental transitions and in the traveling events. This implies that in principle each model realization, even with the same initial conditions, may be different from all the others. In this context, the comparison of a single realization of the model with the real evolution of the disease may be very misleading. Similarly, the mere comparison of the number of cases obtained in each country averaged over several realizations with the actual number of cases occurred is a poor indicator of the reliability of the achieved prediction.

Indeed in many cases the average would include a large number of occurrences with no outbreaks in a variety of countries. It is therefore crucial to distinguish in each country or to a higher degree of resolution, in each urban area the non-outbreak from the outbreak realizations and evaluate the number of cases conditionally to the occurrence of the latter events. For this reason, we define in the following a set of indicators and analysis tools that can be used to provide scenarios forecast and real world data comparison. The likelihood to experience an outbreak can be provided by analyzing different stochastic occurrences of the epidemic with the same initial conditions, and by evaluating the probability that the infection will reach a given country.

In the following we will consider statistics over 10 3 different realizations of the stochastic noise, and define the probability of outbreak in each country as the fraction of realizations that produced a positive number of cases within the country. This allows for the identification of areas at risk of infection, with a corresponding quantitative measure expressed by the outbreak probability. A more quantitative analysis is obtained by inspecting the predicted cumulative number of cases for each country, conditional to the occurrence of an outbreak in the country. The outbreak likelihood and magnitude analysis can be broken down at the level of single urban areas. In the following section we present an example of the results available at this resolution scale.

The very high potential value of forecasting tools, in a planning perspective against emerging infectious diseases, points to the necessity of assessing the accuracy of such epidemic forecasts with respect to the various stochastic elements present in the process. Indeed, the present computational approach provides meaningful predictions only if all stochastic realizations of the epidemic, with the same initial conditions and parameters, are somehow similar in intensity, locations and time evolution.

The airline network structure explicitly incorporated into the model is composed by more than 17 different connections among 3 cities. Such a large number of connections produce a huge amount of possible different paths available for the infection to spread throughout the world. This in principle could easily result in a set of simulated epidemic outbreaks that are very different one from the other — though starting from the same initial conditions — thus leading to a poor predictive power for the computational model. By contrast, while the airline network topology tends to lower the predictability of the disease evolution, the heterogeneity of the passenger volume on the various connections defines specific diffusion channels on the high traffic routes.

Ultimately, the degree of predictability is determined by the competing effects of connectivity and traffic heterogeneities [ 6 , 7 ] once the initial starting conditions and parameters of the disease are fixed [ 13 ]. The overlap function measures the similarity of two different realizations of the epidemic outbreak by comparing the evolution in time of the number of active individuals A j t in each urban area j , defined as those individuals carrying the infection. The more an outbreak is predictable, the more likely the two realizations will be similar, leading to a high value of the overlap function. In view of the strong fluctuations inherent to the infection process and the movement of individuals, the presence of an appreciable overlap can be possible only in the presence of a robust mechanism driving the disease propagation and leading to the emergence of epidemic pathways, i.

These pathways on their turn may find their origin in the large heterogeneities encountered in the traffic volume — ranging from a few passengers to 10 6 passengers per year — associated with the air travel connections. In order to pinpoint the presence of epidemic pathways, starting from identical initial conditions, one can simulate different outbreaks subject to different realizations of the stochastic noise and obtain the time evolution of the epidemic in each urban area as described in the main text. During the simulations, one observes the propagation of the virus from one country to the other by means of the air travel and thus monitors the path followed by the infection at the country level.

At each outbreak realization, it is possible to identify for each country C i the country C j origin of the infection and construct the graph of virus propagation; namely, if a latent or an infectious individuals travels from C j to C i and causes an outbreak in the country C i — not yet infected — a directed link from C j to C i is created with weight equal to 1. Once the origin of infection for C i has been identified, the following multiple introductions in C i are not considered as we are only interested in the path followed by the disease in infecting a geographical region not yet infected. After a statistically significant number of realizations, a directed weighted network is obtained in which the direction of a link indicates the direction of the virus diffusion and the weight represents the number of times this flow has been observed out of n realizations.

For each country C i we renormalize to 1 the sum of the weights on all incoming links, in order to define the probability of infection on each flow. The network of epidemic pathways is then pruned by deleting all directed links having an occurrence probability less than a given threshold, in order to clearly identify the major pathways along which the epidemic will spread. This information identifies for each country the possible origins of infection and provides a quantitative estimation of the probability of receiving the infection from each identified origin.

It is therefore information of crucial importance for the development and assessment of preparation plans of single countries. Travel advisories or limitations and medical screenings at the ports of entry — such as those put in place during SARS epidemic — might well strongly benefit from the analysis and identification of such epidemic pathways. As a concrete example of the previous modeling approach we analyze the specific case study of the SARS epidemic.

Several mathematical models have been developed since the SARS coronavirus was identified see [ 14 ] and references therein. Many of these approaches focused on localized communities, such as generic hospital populations [ 15 ], specific cities or small regions [ 9 , 10 , 16 — 27 ], whereas few others considered the role of global travel [ 3 , 28 ]. In particular, the estimates of key epidemiological parameters are traditionally obtained from fitting local models i. Such approaches assume closed boundary conditions for the region under consideration, neglecting possible movements of individuals in and out of the region. In the following we use the global computational model defined in the previous section to simulate synthetic SARS outbreak on the worldwide scale and compare with the empirical data from the real world occurrence.

The compartmentalization and the disease parameter values considered in the model are chosen according to previous studies [ 1 , 11 , 29 ]. It is worth stressing however that the compartmentalization used see Figure 1 , while borrowed from the most authoritative references on the SARS outbreak, is suffering from the approximations due to the lack of information on the social specific structure and heterogeneity that might be crucial for a full understanding of the disease. These steps correspond to the implementation in Hong Kong of containment measures and advisories effectively reducing the transmission rate [ 9 , 11 ].

It is reasonable to consider a certain reaction time delay taking place in each country from the detection of the first case to the implementation of the policies aimed at reducing the transmission rate on a national scale. In the following, we report the results for an intervention delay of 1 week. The Additional file reports the results for immediate reaction no delay and 2 weeks delay.

Initial conditions are based on available evidence on the early stages of the outbreak and assume as index patient the first case detected out of mainland China, who arrived in Hong Kong on 21 February [ 30 ]. This allows the effective consideration of the observed super-spreading events [ 31 — 34 ] and multiple transmission before the index patient was hospitalized [ 9 ]. The complete time frame under study is from T 0 days after 21 February to 11 July , date corresponding to the last daily update by the World Health Organization WHO on the cumulative number of reported probable cases of SARS [ 35 ]. The advantage with respect to previous approaches is that no closed boundaries are imposed on Hong Kong, allowing for the mobility of individuals traveling in the city and for a decrease of the pool of infectious individuals who leave the city by means of air travel.

We also tested different initial conditions that do not effectively incorporate super-spreading events with no substantial changes in the results. In Figure 2 we represent on a map the countries that are more likely to be infected with a color code, ranging from gray, signaling low outbreak probability, to red for a high probability of experiencing an outbreak. It represents a quantitative indication of the risk to which each country would be exposed in presence of a SARS-like infectious disease in which the same containment measures are implemented. It therefore provides a starting point for the development of appropriate intervention scenarios aimed at reducing that risk. The map readily identifies geographical areas with an appreciable likelihood for an outbreak.

Results: China has successfully completed the research and development of the Ebola Ad5-EBOV vaccine within 26 months, while the preparation and implementation of clinical trials took relative long time. A proliferation of literature arose between and , with a 1. Three years on from the Ebola outbreak, six Ebola-related products in China were approved by the National Medical Products Administration.

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