(a) The flow diagram (3) below represents an SIS model. (3) S + B A I...

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(a) The flow diagram (3) below represents an SIS model. (3) S + B A I where the parameters ß and y are positive constants. (i) Write down the equations that govern the system (3), and describe the interac- tions in this system. Briefly explain why we can eliminate I. [3 marks] (ii) Find the steady states and determine their stability and show that the presence of the disease depends on an inequality involving R, = BN/y, where N is the total population size. [7 marks] (iii) Explain what Ro represents and use it to derive the condition for the disease eradication. [2 marks] (a) The flow diagram (3) below represents an SIS model. (3) S + B A I where the parameters ß and y are positive constants. (i) Write down the equations that govern the system (3), and describe the interac- tions in this system. Briefly explain why we can eliminate I. [3 marks] (ii) Find the steady states and determine their stability and show that the presence of the disease depends on an inequality involving R, = BN/y, where N is the total population size. [7 marks] (iii) Explain what Ro represents and use it to derive the condition for the disease eradication. [2 marks]

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