Question

(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and = a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y The y-nullclines are y = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (31,91) and (12,42), where we order them so that 21 <12- The equilibrium with the smaller e-coordinate is (31,91) = The equilibrium with the larger 2-coordinate is (22,42) c) The linearization of the system of differential equations at the equilibrium (11,yı) gives a system of the form (0%) -4(1) where A=

Answer 1

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