EHESP School of Public Health, Rennes, France

EHESP School of Public Health, Paris, France

UMR S 707, INSERM, Paris, France

MIA UR341, INRA, Jouy-en-Josas, France

UMR S 707, Université Pierre et Marie Curie-Paris 6, Paris, France

Abstract

Background

Geographical and temporal diffusion patterns of a human pandemic due to Swine Origin Influenza Virus (S-OIV) remain uncertain. The extent to which national and international pandemic preparedness plans and control strategies can slow or stop the process is not known. However, despite preparedness efforts, it appears that, particularly in the USA, Mexico, Canada and the UK, local chains of virus transmission can sustain autonomous dynamics which may lead to the next pandemic. Forecasts of influenza experts usually rely on information related to new circulating strains.

Methods

We attempted to quantify the possible spread of the pandemic across a network of 52 major cities and to predict the effect of vaccination against the pandemic strain, if available. Predictions are based on simulations from a stochastic SEIR model. Parameters used in the simulations are set to values consistent with recent estimations from the outbreak in Mexico.

Results

We show that a two-wave pandemic dynamic may be observed in Southern hemisphere because of seasonal constraints for a maximum value of the basic reproductive number (R_{0, max}) within a city equal to 1.5 and a mean generation interval (GI) of 2 days. In this case and in the absence of vaccination, attack rates may reach 46% when considering a completely susceptible population. More severe scenarios characterized by higher values of R_{0, max }(2.2) and GI (3.1) yield an attack rate of 77%. By extrapolation, we find that mass vaccination in all countries (i.e. up to 50% of the population) implemented 6 months after the start of the pandemic may reduce the cumulative number of cases by 91% in the case of the low transmissible strain (R_{0, max }= 1.5). This relative reduction is only 44% for R_{0, max }= 2.2 since most of the cases occur in the first 6 months and so before the vaccination campaign.

Conclusion

Although uncertainties remain about the epidemiological and clinical characteristics of the new influenza strain, this study provides the first analysis of the potential spread of the pandemic and first assessment of the impact of different immunization strategies.

Background

Within 15 days of the WHO's raising the pandemic threat level to 6, more countries are affected by the new Swine Origin Influenza Virus (S-OIV) further raising concerns that S-OIV may be the next pandemic influenza strain. Active autonomous chains of transmission have been reported in several countries, such as Mexico, the USA, Canada, Spain and the UK. Most information about the virus and disease so far suggests a regular influenza process with many characteristics similar to those documented in past influenza pandemics

Methods

The model implements a metapopulation approach

Coupling of local epidemic dynamics is described by population flows from city _{ij}). Transition probabilities between states are captured by distributions _{i}(_{τ}_{i}(_{i}(_{i }is the probability that a susceptible individual becomes infected at _{0, max}/

Parameter values were chosen according to qualitative knowledge or quantitative estimates. Consistent with early estimates of the basic reproductive number from data from the outbreak in Mexico _{0, max}) value of 1.5 was assumed _{0, max}, equal to 2.2, was chosen _{max }equal to 1 and 2 for the first and second pandemic profiles respectively) and _{max }equal to 4 and 7 respectively) were defined. As the average sojourn time in the exposed state for the first pandemic profile is less than a day, a time step of 0.5 days was adopted in order to correctly reproduce fast dynamic processes. The remaining parameters were identical for both pandemic profiles as detailed below. The observed seasonality in influenza transmission was incorporated using a step function: from October to March in the Northern hemisphere and the rest of the year in the Southern hemisphere the transmissibility (

Several scenarios for vaccination, introduced 6 months after the start of the pandemic, were tested for each of the two pandemic profiles. As little is known about the efficacy of a future vaccine, coverage and efficacy were combined into a unique intervention parameter through their product. Each vaccination scenario was defined by the duration of vaccination campaign and the number of cities where vaccination is implemented (all the cities or cities in developed countries only). Given that the objective is to immunize a predetermined proportion (^{d}.

First, we assumed that the vaccine was available in developed countries only and that the vaccination campaign lasted 15 days (corresponding to a proportion completely immunized in developed countries of 14%). In the second and the third scenarios, vaccination was implemented in all cities of the network over 35 and 70 days respectively (corresponding to global immunization rates of 30% and 50% respectively). Results are expressed as means calculated over 500 runs for each scenario.

Results and discussion

According to simulations from our model including a seasonal forcing in flu transmission, for R_{0, max }= 1.5 without any preventive or control measures, the pandemic would exhibit two waves (one in 2009 with a first Southern sub-wave and a second Northern sub-wave and the other in 2010), mainly owing to two successive epidemic events in Southern cities. In addition, the pattern would be different with respect to the zone considered (Figure _{0, max }= 2.2), both the first Southern wave and the following Northern wave would be tremendous in size, affecting the vast majority of susceptible individuals of these zones (86%, Table

Baseline scenario, no vaccination (R_{0, max }= 1.5 and GI = 2)

**Baseline scenario, no vaccination (R _{0, max }= 1.5 and GI = 2)**. Dynamics of the pandemic starting from Mexico City, in late March 2009, in the absence of preventive and control measures. The upper panel represents average daily incidences for Northern (green), Southern (blue), tropical (black) and all (red) cities. Plain lines correspond to means and dashed lines (for the global curve only) to .05 and .95 pointwise quantiles calculated on 500 simulation runs. The lower panel illustrates the spread of the virus through the 52 cities of the network; the predicted probability of influenza activity is represented for each city (from 0 (white) to 1 (black)).

Forecasted total attack and mortality rates for two pandemic profiles (R_{0, max }= 1.5 and GI = 2 versus R_{0, max }= 2.2 and GI = 3.1)

**Scenario**

**Total attack rate (%)**

**Total attack rate North (%)**

**Total attack rate South (%)**

**Total attack rate Tropics (%)**

**Mortality rate (%)**

R_{0, max }= 1.5

GI = 2

R_{0, max }= 2.2

GI = 3.1

R_{0, max }= 1.5

GI = 2

R_{0, max }= 2.2

GI = 3.1

R_{0, max }= 1.5

GI = 2

R_{0, max }= 2.2

GI = 3.1

R_{0, max }= 1.5

GI = 2

R_{0, max }= 2.2

GI = 3.1

R_{0, max }= 1.5

GI = 2

R_{0, max }= 2.2

GI = 3.1

No vaccination

46

77

62

86

58

86

19

62

0.14

0.23

Vaccination in developed countries (14%)

37

71

47

74

55

86

17

62

0.11

0.21

Vaccination in all countries (30%)

9

51

11

45

32

86

2

52

0.03

0.15

Vaccination in all countries (50%)

4

43

1

31

32

86

2

52

0.01

0.13

Means of attack and mortality rates in the absence of any intervention and under different vaccination scenarios are calculated on 500 simulation runs for each scenario.

Comparison between baseline scenarios (R_{0, max }= 1.5 and GI = 2 versus R_{0, max }= 2.2 and GI = 3.1), no vaccination

**Comparison between baseline scenarios (R _{0, max }= 1.5 and GI = 2 versus R_{0, max }= 2.2 and GI = 3.1), no vaccination**. Dynamics of the pandemic starting from Mexico City, in late March 2009, in the absence of preventive and control measures for two pandemic profiles (R

Owing to the scale used in Figure

In the case of a moderately transmissible virus with R_{0, max }= 1.5, 46% of the population would be infected worldwide by the end of 2010, mostly in Northern and Southern zones (Table _{0, max }= 2.2. Although these attack rates may be over-estimated because of the assumption of an entirely susceptible and completely mixing population, the predicted values are not unrealistic compared with past pandemics. However, it is difficult to provide a more accurate prediction since no information is available on the existence of cross-immunity from past flu infections.

The impact of vaccination differs according to the pandemic profiles and intervention scenarios. For the first pandemic profile (R_{0, max }= 1.5 and GI = 2), making vaccine available in developed countries only and vaccinating 14% of the population does not change the global pattern of pandemic spread but reduces the global attack rate by 20% (Figure

Vaccination in developed countries only, 14% of population are immunized (R_{0, max }= 1.5 and GI = 2)

**Vaccination in developed countries only, 14% of population are immunized (R _{0, max }= 1.5 and GI = 2)**. Dynamics of the pandemic starting from Mexico City, in late March 2009, with vaccine available only in developed countries 6 months after pandemic onset. Fourteen percent of the population in developed countries are vaccinated at a daily rate of 1%. The upper panel represents average daily incidences for Northern (green), Southern (blue), tropical (black) and all (red) cities. Plain lines correspond to means and dashed lines (for the global curve only) to .05 and .95 pointwise quantiles calculated on 500 simulation runs. The lower panel illustrates the spread of the virus through the 52 cities of the network; the predicted probability of influenza activity is represented for each city (from 0 (white) to 1 (black)).

Vaccination in all countries, 30% of population are immunized (R_{0, max }= 1.5 and GI = 2)

**Vaccination in all countries, 30% of population are immunized (R _{0, max }= 1.5 and GI = 2)**. Dynamics of the pandemic starting from Mexico City, in late March 2009, with vaccine available in all countries 6 months after the pandemic onset. Thirty percent of worldwide population are vaccinated at a daily rate of 1%. The upper panel represents average daily incidences for Northern (green), Southern (blue), tropical (black) and all (red) cities. Plain lines correspond to means and dashed lines (for the global curve only) to .05 and .95 pointwise quantiles calculated on 500 simulation runs. The lower panel illustrates the spread of the virus through the 52 cities of the network; the predicted probability of influenza activity is represented for each city (from 0 (white) to 1 (black)).

Vaccination in all countries, 50% of population are immunized (R_{0, max }= 1.5 and GI = 2)

**Vaccination in all countries, 50% of population are immunized (R _{0, max }= 1.5 and GI = 2)**. Dynamics of the pandemic starting from Mexico City, in late March 2009, with vaccine available in all countries 6 months after the pandemic onset. Fifty percent of worldwide population are vaccinated at a daily rate of 1%. The upper panel represents average daily incidences for Northern (green), Southern (blue), tropical (black) and all (red) cities. Plain lines correspond to means and dashed lines (for the global curve only) to .05 and .95 pointwise quantiles calculated on 500 simulation runs. The lower panel illustrates the spread of the virus through the 52 cities of the network; the predicted probability of influenza activity is represented for each city (from 0 (white) to 1 (black)).

The impact of vaccination is globally diminished in the case of a more transmissible influenza virus and a longer mean infectious duration (R_{0, max }= 2.2 and GI = 3.1) (Table

Comparison of vaccination impact (R_{0, max }= 1.5 and GI = 2 versus R_{0, max }= 2.2 and GI = 3.1)

**Comparison of vaccination impact (R _{0, max }= 1.5 and GI = 2 versus R_{0, max }= 2.2 and GI = 3.1)**. Box-plots represent simulated distributions of attack rates over 500 simulation runs for two pandemic profiles and four vaccination scenarios (no vaccination; vaccination of 14% of population in developed countries only, vaccination of 30% of population worldwide and vaccination of 50% of population worldwide). The vaccine was considered available 6 months after pandemic onset.

In addition to intrinsic differences in the dynamics of the two pandemic scenarios (induced by different values of R_{0, max }and of GI duration), the two-waves or one-wave patterns are partly due to seasonal forcing. As specified in the Methods, we considered that the transmissibility was 2.5 times greater during the influenza season in Northern and Southern zones (6 months in each hemisphere) than the rest of the year. In tropical regions the transmissibility was set to a constant throughout the year equal to 70% of the transmissibility during the influenza season in the North and South. The choice of a step function to represent variation in transmissibility and of the ratios between epidemic and non-epidemic seasons has a non-negligible impact on the simulated dynamic pattern. Further investigations are needed to evaluate their importance on the dynamics of the new circulating H1N1 strain.

All simulations are performed in the stochastic framework which allows capturing various effects of chance, especially at the source where the number of cases is still small. Results on final pandemic burdens, although based on stochastic runs, are quite stable and concentrated around the mean as illustrated in Figure

As little information exists on the efficacy of any future vaccine, coverage and efficacy were summarized by a single parameter representing the proportion of the population effectively immunized. This approach is a rough approximation to reality and can be interpreted in several ways. For example, a 14% vaccine-induced immunity in the population may be the result of vaccinating 20% of population with a 70% effective vaccine or of vaccinating 70% of over 60 year-olds, assuming that the latter make up 20% of the population of developed countries. It will be possible to refine this approach as age-dependent initial natural immunity and transmissibility are further characterized. Beyond the specific case of vaccination, this kind of scenario could represent any preventive and control measure designed to protect susceptible individuals.

Finally, it is interesting to note that a scenario starting in Mexico City was already identified in previous work

Conclusion

Although much remains to be done to characterize the new strain further, this study, based on models including estimates close to recently published data, shows that a multi-wave pandemic with a large attack rate is possible and may be curtailed using different immunization strategies.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

AF conceived the study. AF, EV and PYB developed the mathematical model. EV performed simulations. AF, EV and PYB analyzed the results. AF and EV drafted the manuscript. All authors read and approved the final manuscript.

Pre-publication history

The pre-publication history for this paper can be accessed here: