Waterborne, abiotic and other indirectly transmitted (W.A.I.T.) infections are defined by the dynamics of free-living pathogens and environmental reservoirs

Miles D. Miller-Dickson; Victor A. Meszaros; Francis Baffour-Awuah; Salvador Almagro-Moreno; C. Brandon Ogbunugafor

π S is the birthrate (via migration or first-time use) of new members into a given community of injection drug users (constant in this model). This includes those who may be returning to the population of IDU after recovering from HCV. π T represents the rate that individuals enter the infected stage coming from an unsuccessful treatment program. φ represents the daily fraction of individuals infected with HCV who spontaneously clear the infection. c represents the rate of sharing a needle with another user (infected or otherwise) per capita. β represents the probability that an uninfected individual will convert to HCV+ after injection with an infected needle. µ is the combined fractional death and IDU cessation rate (individuals who leave the IDU community). π I represents the rate of migration of early stage infected individuals into the study population of IDU (assumed to be constant). ω is the daily fraction of earlystage infected individuals who progress to the late-stage of infection. τ is the daily fraction of infected individuals who go into treatment. π N is the rate of introduction of uninfected needles into the population of IDU. γ is the average number of injections per user per day. ζ represents the probability that a new needle becomes infected after use by an infected user. k u is the daily fraction of uninfected needles which are discarded. k i is the daily fraction of infected needles which are discarded. Lastly, is the fraction of infected needles which become uninfected in the period of a day due to deactivation (or "death") of virus populations on the needle. Parameter values and sources can be seen in Table II .