Population dynamics of HTLV‐I infection: A discrete‐time mathematical epidemic model approach

Human T‐cell Leukaemia Virus Type 1 (HTLV‐I) is a retrovirus that causes Adult T‐cell Leukaemia (ATL). The transmission routes of HTLV‐I are (i) from infected mothers to their newborn babies, (ii) from infected males (husbands) to females (their wives) by long‐term sexual intercourse, and (iii) from infected females (wives) to males (their husbands). Eshima et al. (2001) analysed a continuous‐time HTLV‐I model with no age structure in the population. In this paper, we consider the population dynamics of HTLV‐I infection in a discrete‐time mathematical model incorporating an age structure. The necessary and sufficient condition for the extinction of HTLV‐I is derived from the mathematical model. A simulation of the HTLV‐I infection based on the model demonstrates a rapid reduction of the HTLV‐I infection proportion in Japan.