A virus infects by contact and if you are first infected you stay a carrier for unlimited time. In an isolated population with P inhabitants the the rate of infections by time (in moths after 1/1 2020) is proportional with the product of 1 the amount infected, meaning people that are infectious, 2 the amount not infected, meaning people that can be infected, which means the functions follows logistic growth. A tenth of the population is infected 1/1 2020. If a fifth of the population is infected one month later, how many are infected one year later?
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