Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions

Abstract

Background: The highly pathogenic H5N1 avian influenza virus, which is now widespread in Southeast Asia and which diffused recently in some areas of the Balkans region and Western Europe, has raised a public alert toward the potential occurrence of a new severe influenza pandemic. Here we study the worldwide spread of a pandemic and its possible containment at a global level taking into account all available information on air travel.

Methods and findings: We studied a metapopulation stochastic epidemic model on a global scale that considers airline travel flow data among urban areas. We provided a temporal and spatial evolution of the pandemic with a sensitivity analysis of different levels of infectiousness of the virus and initial outbreak conditions (both geographical and seasonal). For each spreading scenario we provided the timeline and the geographical impact of the pandemic in 3,100 urban areas, located in 220 different countries. We compared the baseline cases with different containment strategies, including travel restrictions and the therapeutic use of antiviral (AV) drugs. We investigated the effect of the use of AV drugs in the event that therapeutic protocols can be carried out with maximal coverage for the populations in all countries. In view of the wide diversity of AV stockpiles in different regions of the world, we also studied scenarios in which only a limited number of countries are prepared (i.e., have considerable AV supplies). In particular, we compared different plans in which, on the one hand, only prepared and wealthy countries benefit from large AV resources, with, on the other hand, cooperative containment scenarios in which countries with large AV stockpiles make a small portion of their supplies available worldwide.

Conclusions: We show that the inclusion of air transportation is crucial in the assessment of the occurrence probability of global outbreaks. The large-scale therapeutic usage of AV drugs in all hit countries would be able to mitigate a pandemic effect with a reproductive rate as high as 1.9 during the first year; with AV supply use sufficient to treat approximately 2% to 6% of the population, in conjunction with efficient case detection and timely drug distribution. For highly contagious viruses (i.e., a reproductive rate as high as 2.3), even the unrealistic use of supplies corresponding to the treatment of approximately 20% of the population leaves 30%-50% of the population infected. In the case of limited AV supplies and pandemics with a reproductive rate as high as 1.9, we demonstrate that the more cooperative the strategy, the more effective are the containment results in all regions of the world, including those countries that made part of their resources available for global use.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1. Representation of the Metapopulation Model Adopted

The model includes 3,100 airports in 220 countries worldwide. The map portrays the locations of urban airports worldwide; geographical data are obtained from open sources on the Internet and mapped with ArcGIS software (http://www.esri.com/software/arcgis). A schematic illustration represents the patch or metapopulation model adopted, in which the total population is divided into subpopulations each corresponding to the urban area surrounding each airport. Filled circles inside each subpopulation represent individuals, and the colors correspond to a specific stage of the disease. Homogeneous mixing for the infection dynamics is assumed inside each urban area, and different urban areas; subpopulations are coupled by means of air travel, according to the International Air Transport Association traffic fluxes.

Figure 2. Flow Diagrams of the Transmission Models

The compartmentalization schemes adopted in the baseline scenario (left) and in the presence of intervention with the use of therapeutic AV treatment (right) are shown. “Sympt. T” and “Sympt. NT” correspond to infected symptomatic individuals allowed to travel and not allowed to travel, respectively. “Infect. AV” indicates infectious individuals under AV treatment, who are therefore not allowed to travel (NT).

Figure 3. Baseline Scenario: Probability of Global Outbreaks and Expected Evolution for a Pandemic Seeded in Hanoi

(A) Probability of observing a global outbreak after one year from the beginning of the epidemic, for the values R0 = 1.1, 1.5, 1.9, and 2.3. A global outbreak occurs when more than one country reports infected cases, while the absence of a global outbreak is given by an epidemic affecting the initially seeded country only. Two different dates for the start of the pandemic are shown: October (left) and April (right). The average attack rates in the case that a global outbreak occurs are also reported, by showing the average number of cases per 1,000 at the end of the first year. Results are obtained from n = 500 different realizations of the noise. (B) Timing of the influenza pandemic in the six regions under study, for R0 = 1.5 and R0 = 1.9, for two different initial dates: October (left column) and April (right column). Sporadic activity occurs when the average prevalence reports (10−2 − 1) cases per 1,000, while epidemic activity is defined by more than one case per 1,000. The average profile is obtained by considering all runs for each region that experienced an outbreak in the region itself during the time window investigated. The thick vertical line corresponds to one year after the start of the pandemic.

Figure 4. Baseline Scenario: Probability of Global Outbreaks and Expected Evolution for a Pandemic Seeded in Bucharest

(A) Probability of observing a global outbreak after one year from the beginning of the epidemic. In the case of outbreaks starting in April, the reproductive rate is effectively reduced to a value smaller than one because of seasonal effects. This effect makes global outbreaks unlikely. (B) Timing of the influenza pandemic in the six regions under study. Results for different values of the reproductive rates are shown: R0 = 1.5 and R0 = 1.9 for a pandemic starting in October, and R0 = 1.9 and R0 = 2.3 for a pandemic starting in April. Results shown refer to the average profiles in each region when a global outbreak affecting more than 100 countries occurs, thus showing a typical timeline of a pandemic when affecting all regions.

Figure 5. Intervention Scenario with Maximal AV Coverage: Probability of Global Outbreaks for a Pandemic Seeded in Hanoi in October

Probability of observing a global outbreak after one year from the beginning of the epidemic, for the values R0 = 1.1, 1.5, 1.9, and 2.3. A maximal coverage with unlimited AV supplies in all hit countries is assumed. Symptomatic cases receive AV drugs with rate pAV = 0.7/d (A), 0.5/d (B), and 0.3/d (C).

Figure 6. Importance of Air Travel in the Worldwide Spread of Pandemic Influenza

The two snapshots show the countries in orange that have a nonnull probability of being infected by the time Vietnam (seeded country) experiences an attack rate of 10−6 (A) and 10−5 (B) cases. Results refer to a pandemic originated in Hanoi in October with R0 = 1.9, with the assumption of unlimited AV supplies available. A country is defined as infected (experiencing an outbreak) if at least one generation of secondary cases occurs. Although the number of cases inside Vietnam is very low, the virus has already propagated out of the initial borders to other countries, thus providing several different seeds for the worldwide spread of the disease. Maps are obtained from open source geographic data and plotted with ArcGIS software.

Figure 7. Intervention Scenario with Limited AV Supplies: Schematic Representation of the Implemented Containment Strategies and Corresponding Probability of Global Outbreaks, for a Pandemic Seeded in Hanoi in October

(A) The stockpile available in the prepared countries is shown according to the different interventions. An initial stockpile able to cover 10% of the population of prepared countries is assumed. In the uncooperative strategy (left), the totality of these resources is used exclusively for national purposes. The cooperative strategy I (center) is based on the global redistribution of one-tenth of the resources stockpiled by prepared countries, which will thus be able to count on supplies covering 9% of their own population. In the cooperative strategy II (right) the amount provided for global sharing is increased to one-fifth, with a corresponding decrease of the supplies from 10% to 8% in the prepared countries stockpiles. (B–D) Probability of observing a global outbreak after one year from the start of the pandemic in Hanoi, when AV intervention is applied within cooperative or uncooperative strategies. The assumed protocol considers a rate distribution pAV = 0.5/d, whenever AV stockpiles are available. The probability of a global outbreak occurring is subdivided into four bins, according to the number of infected countries (see Figure 3A).

Figure 8. Intervention Scenarios with Limited AV Supplies: Global Attack Rates

(A), (C), and (E): Behavior in time of the cumulative number of symptomatic cases per 1,000 people, for a pandemic starting in Hanoi in October, according to different AV repartition strategies and to the baseline case. Given the rate of distribution pAV, the value of the reproductive rate R0 up to which cooperative strategies effectively contain the pandemic are reported, R0 = 1.9 and pAV = 0.7/d (A), R0 = 1.7 and pAV = 0.5/d (C), R0 = 1.5 and pAV = 0.3/d (E). (B), (D), and (F): Average number of cases after the first year versus different values of the reproductive rate R0, for a pandemic starting in Hanoi in October. Error bars represent the standard deviation around the average value. Different intervention strategies are compared to the baseline case. Different values of AV distribution rates are shown: pAV = 0.7/d (B), 0.5/d (D), and 0.3/day (F). While cooperative strategies always outperform the uncooperative one, the benefit provided by the redistribution of AV resources decreases as pAV decreases, for fixed values of R0.

Figure 9. Intervention Scenarios with Limited AV Supplies: Expected Pandemic Evolution

Average prevalence profiles expected in the baseline case and the different intervention scenarios under study for a pandemic starting in Hanoi in October. Profiles for six global regions (A) are shown together with six illustrative examples of countries profiles (B), each taken from the corresponding region. For the sake of simplicity, only one cooperative strategy is shown, namely cooperative strategy II. Here R0 = 1.7 and AV drugs, when available, are distributed to symptomatic infectious individuals who enter the AV treatment with a rate pAV = 0.5/d. The first 12-month period after the start of the pandemic is shown. The average attack rate after one year is reported for all regions/countries and containment strategies.