Modelling the course of a viral illness and its treatment

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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

. 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. So, for every one hour the viral particles will replicate with a value of (see figure 1-2) Therefore, the total amount of viral particles in the body for every one hour, would be equal to the start amount multiplied with 2 to the power of . So, this phase of illness can be calculated using the model
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By using the regression on the calculator, putting the values for every four hours the viral particles is replicating, I find the best fit line to be an exponential regression. ExpReg

* a=10000

* b=0,173

* r=1

* r2=1

, so the function of the graph is (see graph 1-1)

* The best fit model for the initial phase of the illness is , because this is a growth formula . So to determine the time for the body's immune response, could be solved as an inequality with a total viral ...

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