The Kermack€“McKendrick model was developed to explain the rapid rise and fall in the number of infected people during epidemics. This model involves the interaction of susceptible (S), infected (I), and recovered (R) people through the following mechanism:

a. Write down the differential rate expressions for S, I, and R.

b. The key quantity in this mechanism is called the epidemiological threshold, defined as the ratio of [S]k₁/k₂. When the threshold is greater than 1, the epidemic will spread; however, when the threshold is less than 1, the epidemic will die out. Based on the above mechanism, explain why this behavior is observed.

Transcribed Image Text:

S+1-»I+I S+I-