PMC

Average monthly position of poliomyelitis centroids for each of the four time periods defined in : Period I (July 1910–March 1917); Period II (April 1917–November 1941); Period III (December 1941–May 1955); Period IV (June 1955–December 1971). State centroids are plotted as the grey circles for reference.

Average monthly rate of poliomyelitis notifications (per 100,000 population) by state, conterminous U.S., 1910–1971. Rates are mapped for each of the four major periods of poliovirus transmission defined in . (A) Period I, July 1910–March 1917. (B) Period II, April 1917–November 1941. (C) Period III, December 1941–May 1955. (D) Period IV, June 1955–December 1971.

Monthly rate of poliomyelitis notifications (per 100,000 population) in the conterminous U.S., July 1910–December 1971. Time intervals associated with major periods of poliovirus transmission as defined in are indicated. Source: Series constructed from state-level notifications included in the Public Health Reports (Washington, DC: Government Printing Office, 1910– 1951) and Morbidity and Mortality Weekly Report (Atlanta, GA: ).

Geographical centroids of poliomyelitis activity in the U.S., 1910–1971, I: state geographical centers. Graphs plot the monthly coordinates for longitude (upper graph) and latitude (lower graph) as computed from Equations () and () using raw (fine line traces) and deseasonalized (heavy line traces) disease notification rates (per 100,000 population). To assist interpretation, the longitudes and latitudes of representative states are indicated, as is the average longitude and latitude of the forty-nine states. Time intervals associated with major periods of poliovirus transmission as defined in are indicated.

Trends in the velocity of poliomyelitis epidemics in the U.S., 1910–1971. For each of the epidemics identified in , graphs plot four alternative measures of epidemic velocity. (A) Average time to infection, , scaled to the duration of the epidemic. (B) Standard deviation, s, scaled to the duration of the epidemic. (C) Skewness, b ₁. (D) Kurtosis, b ₂. Linear trend lines have been fitted to the distributions by ordinary least squares. Time intervals associated with major periods of poliovirus transmission as defined in are indicated.

Geographical centroids of poliomyelitis activity in the U.S., 1910–1971, II: largest metropolitan centers. The line traces plot, on a monthly basis, the difference between the location of the poliomyelitis centroid computed using (i) the map coordinates of largest metropolitan center in each state as the denominator in Equations () and (), and (ii) the map coordinates of the state geographical centers. The difference was defined as (i) minus (ii). The upper graph plots longitude differences, the lower graph latitude differences. Spatial coincidence of the centroids calculated using the two different denominator definitions will produce a difference of zero. The histogram plots the frequency distribution of the differences in poliomyelitis centroid locations (in miles) using the two different definitions of ‘‘center.’’

Diffusion of poliomyelitis in the U.S., 1910–1971. Bar charts plot the monthly values of the spatial autocorrelation coefficient, Moran’s I, as a standard Normal deviate for different diffusion processes. (A) Contagious diffusion. (B) Hierarchical diffusion. (C) Mixed contagious–hierarchical diffusion. Values of Moran’s I are plotted on the basis of raw (left-hand charts) and deseasonalized (right-hand charts) notification rates. Horizontal lines at z = 1.65 mark the statistically significant I coefficients at the p = 0.05 level in a one-tailed test for positive spatial autocorrelation. Time intervals associated with major periods of poliovirus transmission as defined in are indicated.

Diffusion of poliomyelitis in the U.S., 1910–1971. Graphs plot cross-correlation functions (CCFs) between the monthly poliomyelitis case rate (per 100,000 population) and the spatial autocorrelation coefficient, Moran’s I, calculated for three different diffusion processes: contagious diffusion;hierarchical diffusion; and mixed contagious–hierarchical diffusion. CCFs are plotted for each of the four major periods of poliovirus transmission defined in . (A) Period I, July 1910–March 1917. (B) Period II, April 1917–November 1941. (C) Period III, December 1941–May 1955. (D) Period IV, June 1955–December 1971. In each instance, the lag k at which the maximum CCF value occurs is indicated.