In a Model of Epidemics, the Number of Infected Individuals $\frac { d y } { d t } = 0.6 y - 0.0002 y ^ { 2 }$

question 87

Essay

In a model of epidemics, the number of infected individuals in a population at a time is a solution of the logistic differential equation $\frac { d y } { d t } = 0.6 y - 0.0002 y ^ { 2 }$ , where y is the number of infected individuals in the community and t is the time in days.(a) Describe the population for this situation.(b) Assume that 10 people were infected at the initial time t = 0. Find the solution for the differential equation.(c) How many days will it take for half of the population to be infected?

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