Project: Modeling Spread of Infectious Disease A town with population of size 1000 is being affected by an infectious disease spreading throughout the world. We say a person is susceptible to the disease if there is possibility that she may contract the disease. From scientific studies, it is known that with probability 0.1, a healthy person contracts the disease. If she contracts the disease, then she does not become immediately sick, but enters an asymptomatic periodt Once she is asymptomatic, there is a 25% chance she becomes symptomatic in the next day (and 75% remains asymptomatic next day). Scientific studies have revealed that an asymptomatic patient does not become symptomatic in the first three days, then the patient recovers without becoming symptomatic on the fourth day. Once a patient is symptomatic, he remains symptomatic next day with probability 0.7 (and recovers with probability 0.3). A recovered patient is not susceptible to the disease anymore. For each group, the project deliverable includes a report answering the seven questions below and a video recording (submit as a Zoom recording link within the report) of your team explaining your answer to each problem Each person in the group should answer at least one question. The group will receive 0 grade if this is not the case. 1. Define the daily health state of a randomly selected individual in the population as DTMC (Xn; n 2 0}. Clearly define its state space and what each state means, and find the corresponding transition probability matrix P. 2. Identify all classes of {X,,; n 2 O) has. Explain why they are classes. 3. Suppose today, you select a person randomly from the population and she does not have the disease nor has had the disease. What is the probability she will have recovered from the disease 10 days later