Numerous infectious diseases are associated with a substantial mortality risk. Examples include malaria, measles, whooping cough, SARS, and dengue fever, among others. How do we explore the consequences of infection-induced mortality? Specifically, how do we incorporate a mortality probability into the SIR equations? The obvious approach would be to add a term such as −mI to the basic equation, where m is a per capita disease-induced mortality rate for infected individuals. However, this may be tricky to interpret biologically or estimate from data. Instead, it is preferable to think about the probability, ρ, of an individual in the I class dying from the infection before either recovering or dying from natural causes.
We initial consider the case of density-dependent transmission, where as total population size N decreases, due to disease-induced mortality, there is reduced interaction between hosts. To make the dynamics clearer we switch to considering the number or density (rather than proportion) of individuals.