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(13) Suppose it is known that the population of a community is 20, 000 . Dur- ing the beginning of the current COVID-IQ pandemic (that is, at time t = 0 ), it is reported that 50 people are carrying the disease (caused by SARS-CoV-2 virus). The rate at which the virus spreads can be modeled by the ordinary differential equation (ODE): I ' = k (at + ht? ) ; I (0) = 50 where I (t) denotes the number of infected individuals. Suppose the model ts very well with the rst 12 days' infected data (see, Table 1) and therefore the parameters are estimated as: k = 0.09, a = 100, b = 1. We can apply this model to predict the number of individuals who will be- come infected in near future. Such projections will help the community to take the necessary measures so that the spread of the SERSCOV2 virus can be prevented or controlled. Now answer the following sub-questions: (i) At the pandemic peak, the number of infected individuals will reach to the maximum. 80 it's important to predict the peak time (in days). According to the model, when will the peak of the infection arise ? (ii) Find the number of individuals of the community who is likely to become infected at the pandemic peak if I (t) follows the cubic form: 01 + 02152 +c3t3 where (:1 = 50.02 = g and c3 = %. (iii) Identify the appropriate time (interval) after when the infection is about to decrease. Tablezl Number of COVID-IQ infected people in the community No. 0mm W No. 0mm -Ei'l--M