hi please looking for help

EEE HE E The transmission of an infectious disease within a population of individuals (measured in the hundreds of thousands) can be modelled with the following system of rst-order ordinary dif- ferential equations dy =y'=a:ryby dt da: :r" or dt ya! where :r(t) represents the number of healthy individuals that are susceptible to infection and y(t) represents the number of infectious individuals capable of causing infection, for given values of the parameters a > 0 and b > 0. The term may represents the gain in infected individuals, with susceptible individuals being lost at the same rate. The term elm represents the rate at which infectious individuals recover from the disease, and these recovered individuals are no longer susceptible to re-infection. 1. Determine the equations for the nullclines of the system. . Find an expression for the equilibrium points of the system. 9am Use the chain rule to derive a rstorder ODE for the trajectories in the my phase plane. Express this ODE in the form 'Ly = dm 9091' where re) and 9(y) are functions which you need to determine. 4. Rewrite the above ODE in differential form. 5. Use the solution method for exact equations to nd the general solution to the ODE in 4. You MUST use the exact method, including the test for exactness, even though the equation is separable. 6. Determine the particular solution for the phase trajectory that satises the initial conditions 3(0) = 1 and y(0) = 0.2