Background A hepatitis A epidemic occurred among men who have sex with men (MSM) in Japan in 2017–2018. In this study, we employ a parsimonious mathematical model to epidemiologically investigate the dynamics of infection, aiming to evaluate the effectiveness of campaign-based interventions among MSM to raise awareness of the situation. Methods A mathematical model describing a mixture of human-to-human transmission and environmental transmission was fitted to surveillance data. Taking seasonally varying environmental transmission into account, we estimated the reproduction number of hepatitis A virus during the course of epidemic, and, especially, the abrupt decline in this reproduction number following campaign-based interventions. Results The reproduction number prior to the countermeasures ranged from 2.6 to 3.1 and then began to decrease following campaign-based interventions. After the first countermeasure, the reproduction number decreased, but the epidemic remained supercritical (i.e., Rt > 1). The value of Rt dropped well below one following the second countermeasure, which used web articles to widely disseminate information about the epidemic risk. Conclusions Although the effective reproduction number, Rt, changes because of both intrinsic and extrinsic factors, the timing of the examined countermeasures against hepatitis A in the MSM population was consistent with the abrupt declines observed in Rt. Even without vaccination, the epidemic was brought under control, and risky behaviors may have been changed by the increase in situation awareness reached through web articles.

In this paper, we formulate an age-structured epidemic model for the demographic transition in which we assume that the cultural norms leading to lower fertility are transmitted amongst individuals in the same way as infectious diseases. First, we formulate the basic model as an abstract homogeneous Cauchy problem on a Banach space to prove the existence, uniqueness, and well-posedness of solutions. Next based on the normalization arguments, we investigate the existence of nontrivial exponential solutions and then study the linearized stability at the exponential solutions using the idea of asynchronous exponential growth. The relative stability defined in the normalized system and the absolute (orbital) stability in the original system are examined. For the boundary exponential solutions corresponding to infection-free or totally infected status, we formulate the stability condition using reproduction numbers. We show that bi-unstability of boundary exponential solutions is one of conditions which guarantee the existence of coexistent exponential solutions.