Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1)

Abstract

On June 11, 2009, the World Health Organization declared the outbreak of novel influenza A (H1N1) a pandemic. With limited supplies of antivirals and vaccines, countries and individuals are looking at other ways to reduce the spread of pandemic (H1N1) 2009, particularly options that are cost effective and relatively easy to implement. Recent experiences with the 2003 SARS and 2009 H1N1 epidemics have shown that people are willing to wear facemasks to protect themselves against infection; however, little research has been done to quantify the impact of using facemasks in reducing the spread of disease. We construct and analyze a mathematical model for a population in which some people wear facemasks during the pandemic and quantify impact of these masks on the spread of influenza. To estimate the parameter values used for the effectiveness of facemasks, we used available data from studies on N95 respirators and surgical facemasks. The results show that if N95 respirators are only 20% effective in reducing susceptibility and infectivity, only 10% of the population would have to wear them to reduce the number of influenza A (H1N1) cases by 20%. We can conclude from our model that, if worn properly, facemasks are an effective intervention strategy in reducing the spread of pandemic (H1N1) 2009.

Figure 1. Schematic relationship between mask wearing individuals and non-mask wearing individuals for pandemic (H1N1) 2009.

The arrows that connect the boxed groups represent the movement of individuals from one group to an adjacent one. Non-mask wearing susceptible individuals (S) can either become exposed (E) or susceptible wearing a mask . Non-mask wearing exposed individuals (E) can either become infectious non-mask wearing (I) or mask wearing exposed (). Non-mask wearing infectious individuals (I) can either recover (R), die (D), or become infectious wearing a mask (). Mask wearing susceptible individual () can either become an exposed mask wearer () or a non-mask wearing susceptible (S). Mask wearing exposed individuals () can either become an infectious mask wearer () or a non-mask wearing exposed individual (E). A mask wearing infectious individual () can either recover (R), die (D), or stop wearing the mask while they are still infectious (I).

Figure 2. Cumulative Number of Cases for N95 Respirator.

Without any interventions the number of cumulative cases is shown by the solid blue line. As expected when the mask is more effective or more people wear a masks, then the number of cumulative cases decreases. Note how effective the N95 is when only 10% of the population wears a respirator.

Figure 3. Cumulative Number of Cases for Surgical Masks.

The same pattern that was seen in Figure 2 with respirators is also seen here: as the masks effectiveness is higher the number of cumulative cases decreases and the number of cases also decreases if a higher percentage of people wear masks. However, the difference in the number of cumulative cases is not nearly as large when surgical masks are worn; this is due to their lower effectiveness.

Figure 4. Sensitivity to .

The number of cumulative cases is very sensitive to the value of the uncontrolled effective reproduction number ( ). Higher values of result in a larger number of cumulative cases. A large difference in the number of cases is seen when the is equal to 1.83 and when is equal to 1.7; for such a slight difference in the difference in the number of cases is quite large.

Figure 5. Sensitivity to the Number of Initial Cases.

The model is sensitive to the number of index cases. In a population of one million if the number of index cases is 10 there are significantly fewer cases than if the number of index cases is 1000 or 10,000.

Figure 6. Sensitivity to the Percentage of the Population Wearing Masks.

The fraction of the population wearing masks greatly affects the number of cases. Even if only 10% of the population wears masks the number of cumulative cases is significantly reduced; however, the graph shows that the number of cases is drastically reduced if 25% of people wear masks.

Figure 7. Sensitivity to When Masks Are Implemented.

Masks should be implemented as soon as possible. There is a large difference in the number of cases when masks are implemented at 100 infectious individuals versus waiting until there are 1000.

Figure 8. Sensitivity to Who Wears Masks.

In order to achieve the greatest possible reduction in the cumulative number of cases both infectious individuals and susceptible and exposed individuals should wear masks. If only infectious individuals wear masks the number of cases is not significantly reduced.