To determine how long it will take for the body’s immune system response to begin we can substitute with the values into the formula:
Hence it will take around hours for the immune system response to begin.
In order to determine how long it will be before the patient dies if the infection is left untreated, we have to consider that after the fever begins at , will be 160% every four hours and the immune system will eliminate 50 000 viral particles per hour. Therefore the model should be developed into: where is the approximate time where the patient dies without any treatment.
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. But if the patient is to make full recovery effective medication must be administrated before the number of viral particles reaches 9 to 10 million
Let’s take a look at the course of the viral illness between 1 and 12 millions without any medication
And then let’s assume that the medication is administrated when the number of viral particles reaches about 9 millions
The growth of particles is obviously greater than number of particles that the medication and immune system response can eliminate.
If we assume that the medication is administrated somewhere around 8 millions we could see the difference. The patient will be able to make full recovery.
Another way to explain it will be that the derivative of the curve from 9 to 10 millions is greater than the curve and therefore the medication not being enough.
Doctors have calculated that the patient needs at least 90 micrograms of medication to begin and maintain the rate of 1.2 million viral particles. Over a four-hour time period of continuous intravenous dosing we will have around. Then 2.5% of this is eliminated by the kidney. Therefore we will have around 22 every hour. In order to maintain the rate of elimination we should add to 22 around 3 each hour. Hence the amount entering the body should be around 25 per hour.
where is the amount of medication entering the body every hour and is the amount of medication at hours.
As the kidneys will eliminate about 2.5% of this medication per hours that means that every four hours they will eliminate 10% of this medication.
Verification using the previous model:
should be greater than 2.35 in order for the dosage to slightly increase rather than decrease.
Hence for the patient to maintain at least 90 micrograms of the medication in his system, a dosage of about per four hours should be administrated.
We could use a spreadsheet in order to verify it. We could have different values of , where is the amount of medication per hour.
From the spreadsheet we could conclude that it is more convenient to have an amount of medication per hour greater than the amount eliminated by the kidneys.
The last possible time from the onset of infection to start the regimen of medication is approximately 46 hours. It will take about 25 hours to clear the viral particles from the patient’s system.
This graph shows the entire treatment regimen from the time the treatment begins until the viral particles are eliminated from the last possible time to start the regimen of medication.
