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Math Help - infectious disease spread

  1. #1
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    infectious disease spread

    You are chief health inspector on a small Island whos population is 50,000. The infextious disease X has been spreading for some time and your task is to predict its future course. Disease X is not fatal provided the patient's fever is kept down, and full recovery with immunity results in 14 days after infection. Once recovered, the person is no longer infectious, According to your statistics, 2100 people are currently infected and 2500 have recovered. The rate of new infections for disease C can be calculated as 10^(-5)*S*I, where S represents the number of people in the susceptible population and I represents the number of infected persons.

    Your task is to make some short range and long term predictions. How will disease X spread over the next few dats? What is your prediction for the next month? What is the maximum numbe rof people who will be sick at once?

    where do I start?
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  2. #2
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    The usual method would be to:
    1. define the differential equations
    2. solve the differential equations
    3. solve the constants of integration from your knowledge of the number of infections today, the rate of infection today any your knowledge that at time equals infinity the entire population will have survived the infection and will be immune.

    However, the language in your question is not very precise, so I wonder if you are required to give a precise answer. Have you studied numerical methods?

    A quick spreadsheet assuming that at day 1 there is just one infected person suggests that there would be 2100 infected people at about day 20. The infection rate for the next few days would be about 1000 per day, the maximum infected people about 10,000 would occur in about a week (i.e. day 27) and within a month there would be no infections because everyone has become sick and recovered.

    The chief scientist is probably familiar with Excel but he/she has probably forgotten everything they ever knew about solving differential equations.
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