Based on a mathematical model of human T-cell leukemia virus type I (HTLV-I) transmission, the non-vanishing condition of HTLV-I was derived, and the effect of changes in breastfeeding patterns on the prevalence of HTLV-I was evaluated. The non-vanishing condition was shown to be a>1/(1+b), where a is the probability of mother-to-child transmission and b is the probability of husband-to-wife transmission. This condition implies that If a Is under 0.5, HTLV-I cannot be sustained In populations over a long term. The age-specific prevalences in 1985 were calculated under this model and the assumption of changes In breast-feeding over the period 1925-1985, based on information from many surveys on breast-feeding in Japan. The prevalence increased with age, like the prevalences observed in many populations in Japan. These findings suggest that the probability of mother-to-child transmission had been over 0.5 and was reduced by the spread of compound milk and the shorter duration of breast-feeding in recent years in Japan, and that it has resulted in a decrease in HTLV-I carriers among younger age groups.
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