Question

A flu virus is spreading through a city with a population of 25,000. The disease is spreading at a rateproportional to the product of the number of people who have it and the number who don't. Supposethat 100 people had the flu initially and that 400 people had it after 10 days. How many people willhave the fu after 20 days?

Answer 1

Using the principles of the susceptible-infected-recovered model in epidemiology, and supposing that the growth of the virus spread is exponential, we estimate that the number of flu-infected individuals in the city would reach approximately 1600 by day 20.

Step-by-step explanation:

The problem described is a classic representation of a differential equation that models population growth and the spread of diseases, also known as a susceptible-infected-recovered (SIR) model in epidemiology. This model uses differential equations to describe how a disease can spread through a population. In this problem, given that the rate of spread is proportional to the product of those who have it and those who don't, we can deduce that the mechanism of the spreading is similar to that of exponential growth.

Based on the information given for the first 10 days, the number quadrupled from 100 to 400, meaning that the virus is spreading at a high pace. If we suppose that the growth of infection is exponential, then, in the next 10 days (from day 10 to day 20), the number of infected people is likely to quadruple again, going from 400 to 1600.

Please note, this analysis assumes that the conditions remain constant over time, which in real-life situations may not be accurate. Changes in factors such as immunity, behavior, policies, and medication could significantly alter the outcomes.

Learn more about Exponential Growth