• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Modelling the course of a viral illness and its treatment

Extracts from this document...


Modelling the course of a viral illness and its treatment Description (from assignment) When viral particles of a certain virus enter the human body, they replicate rapidly. In about four hours, the number of viral particles has doubled. The immune system does not respond until there are about 1 billion viral particles in the body. The first response of the immune system is fever. The rise in temperature lowers the rate at which the viral particles replicate to 160% every fours hours, but the immune system can only eliminate these particular viral particles at the rate of about 50 000 viral particles per hour. Often people do not seek medical attention immediately as the think they have a common cold. If the number of viral particles, however, reaches 1012, the person dies. Modelling infection 1. A patient is infected with 10 000 viral particles. Every four hours, the viral particles doubles = 200% (see figure 1-1).The viral particles replicate every four hours. ...read more.


By using the exponential regression, putting in the values (see figure 2-1). I find the function and by solving e0,1137=1,125. I will get a function that looks like this So the growth factor after 26,6 hours when the human body has fever is 112,5 % found through regression.. However, the immune system will eliminate 50000 viral particles per hour so I need to subtract 50000 from the total amount. Which means, . Since a person will die if the number of viral particles reaches 1 million (1012), we can estimate the time using the model. Vn=1012, so 117,3 hours is the remaining time after the immune system have responded. So to find the total amount of time the patient have before he dies can be found be adding the time it takes from when the patient is infected to the immune system response adding with the times before it exceed 1012 viral particles. ...read more.


This makes me see the small differences in the precision of the values Applying your model 7. If the patient is a young child instead of an adult, than the models have to be modified carefully. The immune system of a child is weaker than an adult, so this means the immune system would respond later than an adult. Therefore, a child would die earlier of the amount of viral particles than an adult if left untreated, because the body of a child is smaller and the immune system eliminates less particles. The amounts of dosage and medications also have to be reduced, since a body of a child can not handle as much compared to an adult body. So the time to start the regimen of medication also have to start earlier, since a child is smaller than an adult and the body can not handle the same amount of viral particles. So the models of immune response have to be increased and the medication has to be decreased. Appendix Graph 4-1 ?? ?? ?? ?? Kien Vu ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. A logistic model

    The model considers an annual harvest of 1x104 fish. A population collapse occurs after year 25. From figure 7.2 one can observe the chronic depletion of the fish population as a consequence of excessive harvest. If one continues with the model into year 26 the population turns negative, and this means the death of the last fish in the lake.

  2. Statistics project. Comparing and analyzing the correlation of the number of novels read per ...

    30 Girls 2 2 3 4 18 1 30 Total 7 8 8 7 19 11 60 Expected values So X�= 26.5 P=0.0 Since P<0.05, at 5 % level, we reject Ho There for type of books read and gender are dependent Pearson's correlation coefficient Next was the Pearson's correlation co-efficient.

  1. Modelling the course of viral illness

    Hence if the patient receives any treatment it will take about 144 hour before he dies. An antiviral medication can be administrated as soon as a person seeks medical attention. The medication does not affect the growth of rate of the viruses but together with the immune system response can eliminate 1.2 million viral particles per hour.

  2. Modelling the amount of a drug in the bloodstre

    menu and there will different items of functions to specify your list of data. For this assignment one will choose equations he is most familiar with. In this case four of the optional items were chosen: * Linear regression ( ax+b)


    Using a spreadsheet, or otherwise, develop a model for the next phase of the illness, when the immune response has begun but no medications have yet been administered. Use the model to determine how long it will be before the patient dies if the infection is left untreated.

  2. Virus Modelling

    Then I will show how and when medicine can be administered and I'll portray its effects on the patient. To help recover the patient, I will determine how much medicine is required and at what levels. I will also explain how additional dosage can help maintain the medication level.

  1. Creating a logistic model

    18 60000 1 19 60000 1 20 60000 1 As we have done before, we should also use the GDC to find an estimate for the logistic function: However, the function that the calculator gives is just an estimate, so it is safe for us to round off this function

  2. Mathematics IA - Particles

    At this point I decide that I want to find out how long the patient will live for if he goes untreated. I presume that once the immune system responds the particles will not double every four hours, but instead they will increase by 160%.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work