There are many important extensions of the two-dimensional disease model (Equation 5.5.2) that include more categories of people, and that model processes of birth, death, and immunity.
1. Suppose that individuals who leave the infected class through recovery (at per capita rate μ) become susceptible again, but that individuals in the infected class also die at additional per capita rate k.
2. Suppose that one-third of the individuals who leave the infected class through recovery become permanently immune, and the other two-thirds become susceptible again.
3. Suppose that all individuals become susceptible upon recovery (as in the basic model) but that there is a source of mortality, so that both infected and susceptible individuals die at per capita rate k.
4. Suppose that all individuals become susceptible upon recovery (as in the basic model) but that there is a source of mortality, where susceptible individuals die at per capita rate k, but infected individuals die at a per capita rate that is twice as large.
5. Suppose that all individuals become susceptible upon recovery (as in the basic model) but that all individuals give birth at rate b. The offspring of susceptible individuals are susceptible and the offspring of infected individuals are infected.
6. Suppose that all individuals become susceptible upon recovery (as in the basic model) but that all individuals give birth at rate b, and that all offspring are susceptible.