2.2. Our Model. Let's consider a model in which we add a fourth population L that are exposed but not yet showing symptoms," allow the reaction rate between those who are susceptible and those who are in the latent group to depend on time (think of this as something we can control). S' = -aSI - B(t)SL L' = a1 + B(t) SL _14 (2) 1 TR R' TL 1 TL 1 = TR Note that the equation is redundant (as was the case above). For the following questions consider the system for S, L, and I. Exercises. All of the following pertain to Equation 2. (5) Show S+L+I+R is constant, allowing us to consider only the (S, L, 1) system. (6) What do a, B, TL, and TR represent? (7) Equation 2 has a two dimensional surface of steady states; describe it. *The L stands for latent. Epidemiologists do make distinctions between 'exposed', 'latent', and asymptomatic', but we will only treat one such population and not be careful about the distinction. 2.2. Our Model. Let's consider a model in which we add a fourth population L that are exposed but not yet showing symptoms," allow the reaction rate between those who are susceptible and those who are in the latent group to depend on time (think of this as something we can control). S' = -aSI - B(t)SL L' = a1 + B(t) SL _14 (2) 1 TR R' TL 1 TL 1 = TR Note that the equation is redundant (as was the case above). For the following questions consider the system for S, L, and I. Exercises. All of the following pertain to Equation 2. (5) Show S+L+I+R is constant, allowing us to consider only the (S, L, 1) system. (6) What do a, B, TL, and TR represent? (7) Equation 2 has a two dimensional surface of steady states; describe it. *The L stands for latent. Epidemiologists do make distinctions between 'exposed', 'latent', and asymptomatic', but we will only treat one such population and not be careful about the distinction