(a) Given the epidemic model dx = -x(n+1-x), where x = n at T-0. Where x(t) is the number of susceptible and T = Bt. dT (1) Use the substitution x = = to solve the equation. (6 marks) If the contact rate is 0.001 and the number od susceptible (n) is 2,000. Initially, determine (ii) (iii) (iv) (v) (v) The number of susceptible left after 3 weeks. (2 marks) The density of susceptible when the rate of appearance of new cases is maximum. (2 marks) The time in weeks at which the rate of appearance of new cases is maximum. (2 marks) (2 marks) The maximum rate of appearance of new cases. The epidemic curve. (1 mark)