The age–time two-dimensional model was programmed by Intel Visual Fortran on Microsoft Visual Studio to work on any computer using the Microsoft Windows platform (Microsoft, Redwood, WA). In all scenarios, the initial values of epidemiological classes were determined on the basis of data on the age distribution of measles PA antibody positivity in Japan in 2006 [32
] and coverage of measles immunization by age group (nationwide) in 2006 [33
]; simulations proceed during 2006–2007 by using the coverage of immunization in the respective year [34
]; thereafter, simulations proceed during 2008–2018 according to a scenario. For baseline scenario 1, the progression of the sectional distributions of epidemiological classes by month-old age (0–100 years of age) in March in 2008, 2013, and 2018, which were obtained by the simulation, are shown in Fig. a, b, c, respectively. The proportions of susceptible and low antibody titer classes (S, Rw, V1w) in youths and young adults (aged 10–25 years) as of March in 2013 and 2018 were estimated as 5.9 and 3.4%, respectively. The sectional distributions in Fig. d, e are limited to these three classes to show the details of the progression in the situation of youths and younger adults (<25 years old) as of March in 2013 and 2018, respectively.
Fig. 3 The sectional distributions of epidemiological classes in March in scenario 1 (Okayama city). a 2008, b, d 2013, c, e 2018. d, e Limited to susceptible (S) and low antibody titer classes (Rw, V1w). PA particle agglutination assay. The axis of ordinates (more ...)
We first compared scenario 2, that is, a higher vaccination coverage situation in Kurashiki city in the first and second stages of routine immunization, with baseline scenario 1. According to the result of the simulation, the ratio of the total number of youths and young adults at an age of 10–25 as of March, 2013 who had no or insufficient immunity (S, Rw, V1w) between scenarios 2 and 1 was 0.95:1, and the ratio as of March, 2018 fell to 0.57:1 (Fig. ).
The sectional distributions of three epidemiological classes (S, Rw, V1w) in March in scenario 2 (Kurashiki city). a 2013, b 2018. The axis of ordinates shows the number of population by month-old age
We then prepared two scenarios, namely, 3 and 4, with high and low levels of vaccination coverage, respectively, where the third and the fourth stages of measles vaccination are discontinued in 2013. The aim of these scenarios was to examine how variation introduced in vaccination coverage would influence the number of individuals potentiality susceptible to measles virus infection. The ratios for the total numbers of youths and young adults at an age of 10–25 years as of March, 2013 who had no or insufficient immunity (S, Rw, V1w) in scenarios 3 and 4 to that in baseline scenario 1 were assessed as 0.71:1 and 0.99:1, respectively (Fig. ).
The sectional distributions of epidemiological classes in March in scenarios 3 (a, b; high vaccination coverage) and 4 (c, d; low vaccination coverage). a, c 2013, b, d 2018. The axis of ordinates shows the number of population by month-old age
Finally, in scenarios 5–7, we extended the third and the fourth stages of measles vaccination until 2018. According to the results of the simulations, the proportions of individuals belonging to susceptible and low antibody titer classes (S, Rw, V1w) at an age 10–25 years as of March, 2018, for scenarios 1, 3, and 4 with the third and fourth stages discontinued in 2013 were estimated at 3.4, 2.2, and 4.0%, respectively, while those proportions for scenarios 5, 6, and 7 with the third and fourth stages extended until 2018 were estimated at very low levels of 1.3, 0.76, and 2.2%, respectively. The progress of the sectional distributions of these three classes by month-old age as of March in 2018 for scenarios 6 and 7 are shown in Fig. a, b, respectively; the progression for scenario 5 is omitted because of its similarity to Fig. a.
The sectional distributions of epidemiological classes in March 2018 in scenarios 6 (a; high vaccination coverage) and 7 (b; low vaccination coverage). The axis of ordinates shows the number of population by month-old age