The only morbidity response we considered was acute gastroenteritis. According to Teunis et al. (1999), the modeling of Pill/inf mainly depends on three components: (1) an infected host, defined as many living pathogens present in (parts of) the gut; (2) a hazard of illness, defined as a certain nonzero hazard of becoming ill during infection; and (3) the duration of infection, defined as the length of the period that colonization persists. As illness is conditional on infection, the infection duration is the key variable used to construct the dose–morbidity relationship. A host with strong defenses against the pathogen is assumed to clear infection rapidly, while a pathogen that is highly virulent is assumed to sustain intra-intestinal growth for a long period, namely, to induce a long duration of infection. Thus the probability of illness, given infection, is calculated by Equation (6):
where D represents exposure dose, and γ and σ are scale and shape parameters, respectively, for the gamma distribution of infection duration (Teunis et al. 1999). The parameters involved in Equation (6) were determined by fitting the dose–illness data obtained from several human volunteer experiments, as shown in Table 4.