Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility

Abstract

Background: On 11 June the World Health Organization officially raised the phase of pandemic alert (with regard to the new H1N1 influenza strain) to level 6. As of 19 July, 137,232 cases of the H1N1 influenza strain have been officially confirmed in 142 different countries, and the pandemic unfolding in the Southern hemisphere is now under scrutiny to gain insights about the next winter wave in the Northern hemisphere. A major challenge is pre-emptied by the need to estimate the transmission potential of the virus and to assess its dependence on seasonality aspects in order to be able to use numerical models capable of projecting the spatiotemporal pattern of the pandemic.

Methods: In the present work, we use a global structured metapopulation model integrating mobility and transportation data worldwide. The model considers data on 3,362 subpopulations in 220 different countries and individual mobility across them. The model generates stochastic realizations of the epidemic evolution worldwide considering 6 billion individuals, from which we can gather information such as prevalence, morbidity, number of secondary cases and number and date of imported cases for each subpopulation, all with a time resolution of 1 day. In order to estimate the transmission potential and the relevant model parameters we used the data on the chronology of the 2009 novel influenza A(H1N1). The method is based on the maximum likelihood analysis of the arrival time distribution generated by the model in 12 countries seeded by Mexico by using 1 million computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects.

Results: We found the best estimate R0 = 1.75 (95% confidence interval (CI) 1.64 to 1.88) for the basic reproductive number. Correlation analysis allows the selection of the most probable seasonal behavior based on the observed pattern, leading to the identification of plausible scenarios for the future unfolding of the pandemic and the estimate of pandemic activity peaks in the different hemispheres. We provide estimates for the number of hospitalizations and the attack rate for the next wave as well as an extensive sensitivity analysis on the disease parameter values. We also studied the effect of systematic therapeutic use of antiviral drugs on the epidemic timeline.

Conclusion: The analysis shows the potential for an early epidemic peak occurring in October/November in the Northern hemisphere, likely before large-scale vaccination campaigns could be carried out. The baseline results refer to a worst-case scenario in which additional mitigation policies are not considered. We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs.

Figure 1

Schematic illustration of the GLobal Epidemic and Mobility (GLEaM) model. Top: census and mobility layers that define the subpopulations and the various types of mobility among those (commuting patterns and air travel flows). The same resolution is used worldwide. Bottom: compartmental structure in each subpopulation. A susceptible individual in contact with a symptomatic or asymptomatic infectious person contracts the infection at rate β or r_ββ [30,32], respectively, and enters the latent compartment where he is infected but not yet infectious. At the end of the latency period, each latent individual becomes infectious, entering the symptomatic compartments with probability 1 - p_a or becoming asymptomatic with probability p_a [30,32]. The symptomatic cases are further divided between those who are allowed to travel (with probability p_t) and those who would stop traveling when ill (with probability 1 - p_t) [30]. Infectious individuals recover permanently with rate μ. All transition processes are modeled through multinomial processes.

Figure 2

Illustration of the model's initialization and the results for the activity peaks in three geographical areas. (a) Intensity of the commuting between US and Mexico at the border of the two countries. (b) The 12 countries infected from Mexico used in the Monte Carlo likelihood analysis. The color scale of the arrows from red to yellow indicates the time ordering of the epidemic invasion. Panels (c), (d) and (e) show the daily incidence in Lower South America, South Pacific and North America/Western Europe, respectively. The shaded area indicates the 95% confidence interval (CI) of the peak time in the corresponding geographical region. The median incidence profiles of selected countries are shown for the two values defining the best-fit seasonality scaling factor interval.

Figure 3

Delay effect induced by the use of antiviral drugs for treatment with 30% case detection and drug administration. (a) Peak times of the epidemic activity in the worst-case scenario (black) and in the scenario where antiviral treatment is considered (red), for a set of countries in the Northern hemisphere. The intervals correspond to the 95% confidence interval (CI) of the peak time for the two values defining the best-fit seasonality scaling factor interval. (b, c) Incidence profiles for Spain and Germany in the worst-case scenario (black) and in the scenario where antiviral treatment is considered (red). Results are shown for α_min = 0.6 only, for the sake of visualization. A delay of about 4 weeks results from the implemented mitigation.