Sterile insect technique Sterile insects are sometimes released as a means of

Chapter 10, Problem 31

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Sterile insect technique Sterile insects are sometimes released as a means of controlling insect populations. Fertile insects mate with the sterile individuals and therefore fail to produce offspring. The following differential equations model this idea: df dt af f f 1 s 2 tfs f 1 sd ds dt r 2 tss f 1 sd where fstd and sstd are the numbers of fertile and sterile individuals at time t, r is the rate of release of sterile insects, a is a positive birth rate constant, and t is a positive death rate constant. (a) Show that, when no sterile insects are being released (that is, where r 0), there is a locally stable equilibrium where f ^ ayt and s^ 0. (b) Show that, when sterile insects are being released (that is, where r . 0), there is a locally stable equilibrium where f ^ 0 and s^ sryt .