Bimodal distributions of counts with one mode at zero are often seen in medical research. In a health survey parents were asked the number of days their children missed their activities (Y(1)) and the number of days their children spent in bed (Y(2)) due to illness in the past four weeks. Both variables exhibited zero inflation. We consider a bivariate Poisson-Poisson regression model, in which the two variables are regarded as indicators of an unobserved health status variable. Based on this, we further develop a bivariate Poisson-Poisson model that constrains Y(1)>or=Y(2). It is often claimed that there is a critical window of growth and nutrition in foetal life and infancy during which subsequent health status is affected. It is not clear whether the claim is true and whether childhood growth matters more. We analyse the bivariate data in relation to weight-for-age in infancy and weight gain from infancy to age 7 years. The findings do not support the existence of a critical window in infancy. There is some indication that childhood weight gain might affect health status.