Linear Ordinary Differential Equations: A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and...

Linear Ordinary Differential Equations:

A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and noninfected persons, who are assumed to move freely among each other. Set up the model. Find the equilibrium solutions and indicate their stability or instability. Solve the ODE. Find the limit of the proportion of infected persons as time approaches infinity and explain what it means