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

Equations 1-5 define the prosaic SIR model. π S is the birthrate of new susceptible hosts in the environment and µ is the fractional death rate of hosts. In this context, β represents the strength of the interaction between the susceptible hosts S and the environment. This will generally be proportional to the rate of contact between the two, and will generally include a factor in it that accounts for the probability that an exposure event actually leads to a new infected host. Similarly, α characterizes the strength of interaction between infected hosts I and the environmental reservoir; it is also generally proportional to the contact rate between the two and will contain a factor accounting for the probability that when an environmental agent is exposed to infection, it will render the agent infected. ν represents the fractional recovery rate, π W is the birthrate of new uninfected environmental agents, and k is the fractional death rate of the environmental agents.