Hello tutors, I need help with the following biological growth problem. I would appreciate any help as I remotely know how to begin this problem. Thanks!

Consider a model of disease spread that contains a compartment for the density of susceptible (S) individuals, infective (I) individuals, and chronic carrier (C) individuals. The chronic carriers (C) become infected such that they do not show symptoms of the disease, remain infected forever, and will continually transmit the disease to susceptibles (S). dtdS=ISSC+I

dtdI=ISI

dtdC=SC where is the average infection rate from infectives to suscetpibles, is the average infection rate from susceptibles to chronic carriers, and is the recovery rate from infectives back to susceptibles. a) Is the total density of individuals, N = S + I + C, constant in time or does it change in time? Use the equations above to prove your answer. Can you use your result to reduce the number of independent variables and equations?

b) Find all of the fixed points for this system

c) To see if a newly introduced disease will spread, which fixed point should you examine and perform stability analysis?

d) Perform linear stability analysis to determine what conditions will allow the disease to spread by finding the Jacobian matrix at the fixed point in part (c), and then computing the eigenvalues of this Jacobian. Hint: You can use a matrix with reduced equations if you can do so.