### Analysis of an Infectious Disease Transmission Model Consider the scenario from the problem above. Let's suppose we are now dealing with an infectious disease that is transmittable via contact with an infected person. As before, define: - \( S \) = number of the people in the population who are susceptible - \( I \) = number of the people in the population who are infected - \( t \) = time since outbreak observed, days However, let's assume the following: - Each day, 4% of people who are susceptible become infected and 4% of infected people become immune. - Each infected person will infect 3 susceptible people per day. - Some people who are infected do not become immune but instead are once again susceptible to getting the disease again – suppose this is 7% of all infected people. - Finally, each day 2% of people who are susceptible take a vaccine and so become immune. **Note:** Remember that all people who are immune are out of the picture of our model. ### Tasks **Note:** You will **not** be solving this system of differential equations! #### a.) Draw a diagram Draw a diagram similar to that of our "tank" problems that shows the transition rates between the two groups. Though we are not dealing with water and chemicals, we can still think about the "flows" in an analogous way. #### b.) Write a system of differential equations Write a system of differential equations for \( \frac{dS}{dt} \), \( \frac{dI}{dt} \) to model the rate of change of the number of susceptibles and infecteds. #### c.) Find any equilibrium point(s) of this system Explain what this point(s) mean in the context of the problem. If applicable, you can round to two decimal places (e.g., 213.135 rounds to 213.14). #### d.) Classify the equilibrium point(s) What does this say about the long-run nature of this disease for the two groups considered?