Models for Life by Barton Jeffrey T

Author:Barton, Jeffrey T. [BARTON, JEFFREY T.]
Language: eng
Format: epub
ISBN: 9781119039761
Publisher: John Wiley & Sons, Inc.
Published: 2016-02-01T00:00:00+00:00

When a product of two number is 0, at least one of the two numbers must be 0 so we have two cases: or .

If substitution into the S*-equation allows us to find S*:

Similarly, substitution into the R*-equation allows us to find R*:

Thus if we have found that one of our equilibrium points is given by . In context this equilibrium point corresponds to the disease not being present in the population so everyone remains susceptible.

Next we consider the case where . Solving for S* gives

Further simplification of S* yields a concise expression for S*:

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