We set the number of nonimmune immigrants for the two populations to 7 and
10, respectively. All of these numbers are hypothetical.
In Fig. 21.3, we used the following specifications to calculate the number of
individuals that contract the virus:
CONTRACTION 1 ¼ BETA 1
à S 1
à I 1 þ BETA 1 2
à S 1
à I 2
ð21:1Þ
CONTRACTION 2 ¼ RATE OF CONTACT 2
à I 2
à S 2
ð21:2Þ
Can you anticipate the dynamics of the spread of the disease? The initial
outbreak will be larger than that of the previous model because the number of
susceptibles and infective individuals is larger, although the contact rates are quite a
bit smaller. What matters, though, is the product of contact rates and sizes of the
individual stocks.
Figure 21.4 shows the results for the parameter settings listed above and a choice
of DT ¼ 1. Following an initially severe outbreak, new episodes of the disease
occur at relatively constant intervals and slightly increase in their amplitude. After
only five episodes of outbreaks of the disease among S1, the disease “burns out” and
disappears from the population. Can you explain why in the very long run the
disease disappears? Plot S2 and I2 in a separate graph to help you find an answer.
Let us assume that the parameters listed above are representative of one of two
strains of the virus. The first strain—modeled above—does not move easily from
Fig. 21.3
170
21 Infectious Diseases
10, respectively. All of these numbers are hypothetical.
In Fig. 21.3, we used the following specifications to calculate the number of
individuals that contract the virus:
CONTRACTION 1 ¼ BETA 1
à S 1
à I 1 þ BETA 1 2
à S 1
à I 2
ð21:1Þ
CONTRACTION 2 ¼ RATE OF CONTACT 2
à I 2
à S 2
ð21:2Þ
Can you anticipate the dynamics of the spread of the disease? The initial
outbreak will be larger than that of the previous model because the number of
susceptibles and infective individuals is larger, although the contact rates are quite a
bit smaller. What matters, though, is the product of contact rates and sizes of the
individual stocks.
Figure 21.4 shows the results for the parameter settings listed above and a choice
of DT ¼ 1. Following an initially severe outbreak, new episodes of the disease
occur at relatively constant intervals and slightly increase in their amplitude. After
only five episodes of outbreaks of the disease among S1, the disease “burns out” and
disappears from the population. Can you explain why in the very long run the
disease disappears? Plot S2 and I2 in a separate graph to help you find an answer.
Let us assume that the parameters listed above are representative of one of two
strains of the virus. The first strain—modeled above—does not move easily from
Fig. 21.3
170
21 Infectious Diseases