Assignment A :2014/2015

1.0 Introduction:

The drug quinine remains as an important anti-malaria drug after its effectiveness was first documented about four centuries ago. When a person is given a dosage of quinine, the body metabolizes most of the quinine. It is given that a malaria patient is under a treatment of 50mg dose of quinine at the same time every day. For every 24 hours, 75% of quinine is metabolized. The first

objective of this coursework is to determine the quantity (in mg), , of quinine in the body right after

the dose for . Subsequently, from the results, a graph of versus is to be plotted

and commented. Therefore, a suitable formula is to be generated to calculate the amount of quinine in the body right after every dosage. In solving this, the method of geometric progression is to be used.

It is given that the concentration of quinine in the body is measured in mg of quinine per kg of body weight. For effective treatment, the concentration of quinine in the body must be at least 0.4mg/kg. Also given, concentration above 2mg/kg would be hazardous to the patient. Hence, the second objective of this coursework is to determine (a) the quantities of quinine in the body right before and after every dose, (b) whether the prescription is effective and safe in his body in the case of his weight is 35kg and 60kg, if the patient is given a dosage of 50mg for every 24 hours.

The last objective of this coursework is to estimate the range of dosage for every 24hours such that the prescription is effective and safe based on our own weight.

2.0 Methodology

A geometric progression (G.P.) is a sequence of numbers in which any term can be obtained from the previous term by multiplying by a certain number called the common ratio. The common ratio may have any real value. The common of a G.P., is denoted by r. The first term of a G.P. is denoted by a.

The formula of the sum of the first n terms of a G.P. is to be use to find the quantity of quinine,

in mg, in the body right after the dose is .

A malaria patient is given a treatment of 50mg dose of quinine once every 24 hours. Given that 75% of the quinine is metabolized. In other words, 25% of it retained in the body. In order to find the

quantity, in mg, of quinine in the body right after the dose, the method used is as below:

Assuming , is the first dose, which is 50mg given to a patient . From the 50mg, 25% retained in the

body. In finding the quantity of a new dose of 50mg is added to the initial 25% which was retained

in the body earlier on. In finding , another dose of 50mg is added to 25% of . These steps are

repeated till 8th dose given to the patient.

The results of to are used to plot the graph of versus n. Subsequently, the graph is to

be interpreted.

Therefore, a suitable formula, to calculate the amount of quinine in the body for every dose

is generated inductively.

Based on formula generated, it is used to find the quantity of quinine right before and after

every dose.

In finding whether the prescription is effective and safe for the weight of 35kg and 60kg, the

formula is divided by the patient’s weight. Subsequently, by referring to the results, justification can

be made whether the dosage is effective. It is effective if the concentration in the body is at least 0.4mg/kg, and if the concentration is above 2mg/kg, it would be hazardous to the patient.

By using student’s own weight, he/she has to estimate the range of dosage for every 24 hours such that the prescription is effective and safe.

3.0 RESULTS

3.1 In determining the calculations are as below, given that n=1, 2, 3, ... , 8.

3.2 From the calculation of to , the graph of versus is plotted.

In conclusion, from the calculation of to , a suitable formula to calculate the amount of

quinine in the body right after every dosage can be obtained. The formula is

The formula is obtained as below:

:

:

:

]

3.3 In the case of a patient is given a dosage of 50 mg for every 24 hours, the quantities of quinine in the body right before and after every dose are calculated as this:

n Before(quantities of quinine in the body, in mg)

After(quantities of quinine in the body, in mg)

1 0 0 + 50 = 502 50 + 12.5 = 62.5

3 15.625 + 50 = 62.625

4 16.4063 + 50 = 66.4063

5 16.6016 + 50 = 66.6016

6 16.6504 + 50 = 66.6504

7 16.6626 + 50 = 66.6626

8 16.6656 + 50 = 66.6656

For effective treatment of malaria, the concentration of quinine in the body must be at least 0.4 mg/kg. But, whenever the concentration is above 2 mg/kg, it would be hazardous to the patient. In determining whether the prescription of 50 mg for every 24 hours is effective and save, given that the patient’s body weight is 35kg, the calculation are such:

n Before / 35kg After / 35kg

1 0

2

3

4

5

6

7

8

In conclusion, the prescription of 50 mg for every 24 hours onto a patient with his weight of 35 kg is effective after the second dose and safe for all doses.

In the case of the patient’s weight of 60kg, the calculation in determining whether the same prescription of 50 mg for 24 hours is effective and safe are such:

n Before / 60kg After / 60kg

1 0

2

3

4

5

6

7

8

In conclusion, the prescription of 50 mg for 24 hours onto a patient with his weight of 60kg is seemed to be not effective as the readings are less the effective range of 0.4 mg/kg. But the prescription is still considered safe for the patient as the reading is less than 2.0 mg/kg. In fact, the reading shows that the prescription is safer on the patient with the weight of 60kg comparing to the effect of the same prescription towards the patient with his weight of 35 kg.

Taking into consideration of one’s weight of 50kg, the range of dosage for every 24 hours such that the prescription is effective and safe can be calculated as below:

Calculation of the dosage for the prescription to be safe (after the third dose):

x

Calculation of the dosage for the prescription to be effective:

x

But when the dosage is 76 mg and the number of doses given is 8,

Residue = = 2.0266 mg/kg ( danger level).

In conclusion, the prescription of 76mg is not suitable as the residue rise to the danger level. Therefore, the effective and safe dosage would be in between 64mg and 75mg.

Conclusion

In conclusion, the drug quinine remains as an important anti-malaria drug after its effectiveness was first documented about 4 centuries ago. But the dosage of quinine is not fully metabolized in the body. A portion of 25% would be retained in the body. Therefore, it is important to know the amount of quinine that stays in the body to be effective and safe. Given that it is effective if the concentration of quinine in the body is at least 0.4 mg/kg and safe if the concentration is below 2 mg/kg.

Therefore, for a patient of 35 kg, the 8 doses of 50 mg for every 24 hours are safe throughout but its effectiveness is felt after the second dose.

For a patient of 60 kg, the 8 doses of 50 mg prescribed to the patient every 24 hours, it is safe throughout as well but not effective at all in curbing the patient’s malaria disease.

For my own weight of 50 kg, a prescription of 75mg needs to be prescribed for every 24 hours in order to ensure the dose is safe for me. And a dosage of at least 64 mg needs to be prescribed to the patient to ensure the effectiveness of the dosage.