Question1.(20pts) Considering a Prey-Predator Model different from the one we introduced in class: (a,b,c,f,e are all positive numbers) { = ar bay - er? -fy + cry (a) Compute the x and y nullclines for the system and calculate all the fixed points (b) Analyze and sketch the direction of flow over the x - y plane (c) Judge the stability properties for all the fixed points. (d) Confirm your analysis with phase-plane plotting (use Matlab for the plot). Question2.20pts) Suppose we have certain disease model: { = BS als = aIS - MI where I is the diseased population and S is the susceptible population. a, 8 and are model parameters. (a) Explain the meaning of the model equations (b) Suppose the diseased ones recover at rate y. Analyze the equilibria, their stability and draw related phase-plane plots to confirm your analysis (use Matlab for the plot). (c) Suppose instead recovering, diseased individuals generate uninfected offspring, but do so at a reduced rate (multiply 8 by a value less than 1). Do a similar analysis as in (b) Question1.(20pts) Considering a Prey-Predator Model different from the one we introduced in class: (a,b,c,f,e are all positive numbers) { = ar bay - er? -fy + cry (a) Compute the x and y nullclines for the system and calculate all the fixed points (b) Analyze and sketch the direction of flow over the x - y plane (c) Judge the stability properties for all the fixed points. (d) Confirm your analysis with phase-plane plotting (use Matlab for the plot). Question2.20pts) Suppose we have certain disease model: { = BS als = aIS - MI where I is the diseased population and S is the susceptible population. a, 8 and are model parameters. (a) Explain the meaning of the model equations (b) Suppose the diseased ones recover at rate y. Analyze the equilibria, their stability and draw related phase-plane plots to confirm your analysis (use Matlab for the plot). (c) Suppose instead recovering, diseased individuals generate uninfected offspring, but do so at a reduced rate (multiply 8 by a value less than 1). Do a similar analysis as in (b)