Linearisation of an epidemic model. Consider the following model for the spread of a disease, with susceptibles constantly renewed by births at a constant overall birth rate of μ: S^'=-βS I μ, I^'=βS I-γI (a) Show that the only equilibrium point is (γ/ β, μ/ γ). (b) Linearise the system and determine the behaviour of the trajectories near the equilibrium point. (c) Discuss, briefly, the implications for the time-dependent behaviour of both S(t) and I(t) . | Numerade
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