Need help - especially with number 4

Q2. Consider the following discrete-time model of the dynamics of an epidemic system made of a growing susceptible (- healthy) population (x) and an infected (ill) population (v), with x20, y2 0, a > 0, b > 0, c > 0 and K > 0. K is the carrying capacity of the environment. It is assumed that (i) the susceptible population grows until the total population reaches the carrying capacity of the environment; (ii) the interaction between susceptible and infected populations causes infection (i.e., susceptible individuals turning into infected ones); and (iii) the infected individuals recover and become susceptible again at a certain rate. Answer the following. Explain how each of the above three assumptions were represented in the equations. (5x3 15 points) 1. 2. Find the equilibrium points. There are three such points. (7x3 21 points) 3. Conduct linear stability analysis for each of the three equilibrium points, and discuss the conditions (regarding the parameter values of a, b, and c) under which they are stable/unstable. (8x3-24 points) Conduct numerical simulations of this model with carrying capacity K-0.5 and initial populationsxo 0.1 for several different parameter values of a, b, and c, to confirm the prediction of stabilities derived in the previous question. (10 points) 4