3. The SEIR model is a compartmental model for tracking the dynamics of infectious diseases. The SEIR model divides the population into compartments: (S)usceptible, (E)xposed, (I)nfected, and (R)ecovered. Susceptible individuals become exposed if they interact with an infected individual. After some lag time, exposed individuals develop an infection. Infected individuals recover from the disease and are no longer susceptible. a. Draw a diagram of the SEIR model that shows (1) the compartments and (2) directions and rates (use a different variable for each rate) that individuals can change from one compartment to another. Show the system of differential equations that describes the model you have drawn. Hint: Four boxes connected by arrows where each arrow should be associated with a rate, and four differential equations where each equation corresponds to a compartment. b. Model the system using ordinary differential equations. Use the same rate variables defined in part (a). C. How does the system in (a) change if some individuals are vaccinated (i.e., they become immune to exposure, as if they had experienced the disease and then recovered)? Redraw the diagram and update the system of ordinary differential equations. Show all work to get full credit. d. How does the system in (b) change if birth and natural (non-disease-related) death are introduced? Redraw the diagram and update the system of ordinary differential equations. Show all work to get full credit