In a wide variety of simple disease models, the rate of change in the number of infected people can be written as
I is the number of infected people,Sis the number of susceptible people,
¹is the total number of people in the population,bis the transmission rate of the disease, and mis the rate at which individuals leave the infected group.
Here IQ means the derivative of I with respect to time, a convention we will use throughout the paper.
Equation (1) is applicable to a wide variety of one-group models. Following Castillo-Chavez et al. , we allow bto be a function of ¹, allowing a variety of assumptions about mixing. Depending on the type of model, the per-capita removal rate,m, may include the rate of ‘‘background’’ mortality or disease-induced mortality, or transitions to immune, susceptible or quarantined compartments.]