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An isolated town has a population of mud peuplei c of them are simultaneously infected with a contagious disease to which no member of the town has previously been exposed. However, v of the uninfected people have been given a (good but not perfect) vaccine against the disease. Each infected person has a 30% chance or recovering lrom the disease on any given day. Each infected person encounters several other townspeople each day. Encounters are distributed among susceptible, infected, vaccinated, and recovered people according to their proportion of the total population. (A susceptible person is a person who has never had the disease.) If an infected person encounters a susceptible person, the susceptible person has a certain (high) probability of contracting the disease. If an infected person encounters a vaccinated person, the vaccinated person has a certain (low but positive] probability of contracting the disease. An infected person who was previously vaccinated is identical to an infected person who was nevervaccinated. Let tdencte the time (in days) since the initia rnfeccion. Let 5 denote the number of people who have never had the disease or vaccine [and thus are susceptible to infectinn). Let vdenote the number of people who were vaccinated and have never had the disease. Let 1 denote the number of people cunently infected. Let R denote the number of people who have had the disease at least once and have recoveredi based on the number of encounters each infected person has and the probability of transmitting the disease to susceptible and vaccinated persons, it is computed that d3 = 7 1 SI, dV = 7 1 V], C\" = 1 1+ 1 VliD 31, d\" = 0.31; df 120GB df 60000 dt 12000 60000 Eff 5(0):5994av,1(u):o, l/(o):v, and R[u):. Use the phase plane method to nd a formula for Vin terms ofR. The sululi ll is V: Use the phase plane method to nd a formula for s in terms afR. The salu what is s+J+v+R? [Note that you do not need to do any differential equations to answer this.) The snlu is S+I+ V-l-E: Find a Formula far! in terms of R. The Eulu Suppose that v:441. How many people have had the disease at some point by the time the epidemic ends (that is, when 1:0)? Round youranswer to the nearest integer. Suppose that v=tosc. when the epidemic ends, how many people have had the disease? Round your answer to the nearest integer. Suppose that v:3436. when the epidemic ends, how many people have had the disease? Round your answer to the nearest integer. The sulu