Effects of reactive social distancing on the 1918 influenza pandemic.

The 1918 influenza pandemic was characterized by multiple epidemic waves. We investigated reactive social distancing, a form of behavioral response where individuals avoid potentially infectious contacts in response to available information on an ongoing epidemic or pandemic. We modelled its effects on the three influenza waves in the United Kingdom. In previous studies, human behavioral response was modelled by a Power function of the proportion of recent influenza mortality in a population, and by a Hill function, which is a function of the number of recent influenza mortality. Using a simple epidemic model with a Power function and one common set of parameters, we provided a good model fit for the observed multiple epidemic waves in London boroughs, Birmingham and Liverpool. We further applied the model parameters from these three cities to all 334 administrative units in England and Wales and including the population sizes of individual administrative units. We computed the Pearson's correlation between the observed and simulated for each administrative unit. We found a median correlation of 0.636, indicating that our model predictions are performing reasonably well. Our modelling approach is an improvement from previous studies where separate models are fitted to each city. With the reduced number of model parameters used, we achieved computational efficiency gain without over-fitting the model. We also showed the importance of reactive behavioral distancing as a potential non-pharmaceutical intervention during an influenza pandemic. Our work has both scientific and public health significance

Comparison between the observed and simulated patterns of influenza mortality in 334 administrative units.

<p>(a) Observed data. (b) Simulated data that considers school term, temperature, and behavioral changes. (c) Without behavioral changes. Administrative units are ordered in descending population sizes from top to bottom.</p

Contour plots of the cumulative number of deaths with (panel a) and (panel b).

<p><i>N</i> = 2,000,000, <i>S</i>₀ = 0.8<i>N</i>, <i>I</i>₀ = 100, <i>g</i>⁻¹ = 8, <i>γ</i>⁻¹ = 4, <i>ϕ</i> = 0.01. <i>κ</i> represents the intensity of reactive social distancing behavior, and <i>λ</i> represents the rate of decay of reactive social distancing behavior.</p

Cumulative number of weekly mortality using different values of <i>κ</i> and <i>λ</i>.

<p>With <i>N</i> = 2,000,000, <i>S</i>₀ = 0.8<i>N</i>, <i>I</i>₀ = 100, <i>g</i>⁻¹ = 8, <i>γ</i>⁻¹ = 4 and <i>ϕ</i> = 0.01, the effects of <i>κ</i> and <i>λ</i> on the simulated weekly mortalities are shown in panels (a) and (b) respectively. In panels (a), we fixed <i>λ</i>⁻¹ = 10 days, and the cumulative weekly mortalities are 16% smaller when we have <i>κ</i> = 10,000 than <i>κ</i> = 1,000. In panel (b), when we fixed <i>κ</i> = 10,000, the cumulative weekly mortalities will be 27% smaller when we have <i>λ</i>⁻¹ = 5 days than <i>λ</i>⁻¹ = 20 days.</p

Summary of all parameters estimated in the best-fit model using the Power function.

<p>Distinct parameters could have different values for the three cities. Common parameters have the same values for all three cities.</p

Simulation comparison of the three behavioral functions using the same parameter settings: <i>N</i> = 4000,000, <i>κ</i> = 1350.

<p>Black line, red dashed line and blue dotted line represent Power function, Hill function and modified-Hill function, respectively.</p

Schematic diagram showing the transmission dynamics during an influenza pandemic.

<p><i>S</i>, <i>I</i> and <i>R</i> denote the number of susceptible, infectious, and recovered individuals, respectively; <i>D</i> denotes the number of infected individuals who are no longer infectious and are progressing to death in influenza or pneumonia causes; <i>M</i> denotes the cumulative number of influenza-related deaths; and <i>W</i> denotes recent influenza mortality, a proxy indicator for the perception of pandemic severity.</p

Comparison among the values of three behavioral functions with their best-fitted <i>κ</i>.

<p>Comparison among the values of three behavioral functions with their best-fitted <i>κ</i>.</p

Estimated daily basic reproductive number (thin red curve), effective reproductive number (bold blue curve) and weekly influenza mortality (shaded region).

<p>The average basic reproductive number is 3.24 in the three cities.</p