Modeling the Span of a Viral Illness as well as its Treatment

Building the Course of a Viral Illness as well as Treatment

Math Internal Assessment

Student: Xu, Dejing(Charlotte)

Treatment number: 001762023

Date: 03 26, 2010

I. Intro:

When viral particles of a specific virus enter the human body, they replicate speedily. In regarding four several hours, the number of viral particles provides doubled. The immune system does not react until you will find about 1 million viral particles in the body. The 1st response of the immune system is fever. The rise in temp lowers the pace at which the viral particles replicate to 160% just about every four several hours, but the disease fighting capability can only eradicate these particular viral particles with the rate of about 50, 500 viral debris per hour. Automobile do not seek out medical attention right away as they believe they have a prevalent cold. In the event the number of viral particles yet , reaches 1012, the person dies. The only thing could affect the progress rate is a immune system. The antiviral treatments only can easily eliminate the virus-like particles. 1)В В В В В Model the original phase from the illness for the person attacked with twelve, 000 virus-like particles to ascertain how long it will require for your body's immune respond to begin. Given: The rate is definitely 200% every 4 hour using r to represent

The first number of malware is 12, 000

Work with t to symbolize time

Use Y to represent the number ofvirus

If respect every 5 hour like a period:

Xn+1=2Xn

∴X1=X0

X2=rX

X3=r X2=r(rX)

X4= rX3=r (rX2)=r(r(rX))

∴the formula for each 1 hour would be:

Xn+1=214Xn

Seeing that X0=10, 500

Convert it to function:

Y=10, 000Г—2t4

Solve t:

When ever immune response begin to operate, Y=1, 1000, 000

one particular, 000, 000=10, 000Г—2t4

2t4=1, 000, 00010, 000

2t4=100

log100log2=t4

t= 26. 58hr

It will take 26. 58 hours pertaining to the body's immune system response to start.

hour| virus-like particles| Fever| hour| virus-like particles| Fever| 0| twelve, 000 | | 21| 380, 546 |

1| 14, 892 | | 22| 452, 548 |

2| 14, 142 | | 23| 538, 174 |

3| 16, 818 | | 24| 640, 000 |

4| twenty, 000 | | 25| 761, 093 |

5| twenty three, 784 | | 26| 905, 097 |

6| 28, 284| | 27| 1, 076, 347 | Certainly

7| 33, 636| | 28| one particular, 280, 000 | Yes

…| …| …| 29| 1, 522, 185 | Yes

20| 320, 1000 | В | 30| 1, 810, 193 | Yes

From the desk above, it determined the fact that fever commence between twenty six and27 hours which means defense mechanisms started to am employed at that time.

2)В В В В В UsingВ a spreadsheet, or, develop a style for the next stage of the illness, when the resistant response has begun but simply no medications have yet recently been administered. Make use of the model to ascertain how long will probably be before the affected person dies if the infection is usually left untreated. Given: The speed is 160% per 5 hour applying r to represent

The immune system eliminates 50000 viral every hour

The initial range of virus is definitely 1, 1000, 000

Make use of t to represent time

Work with Y to represent the number ofvirus

If respect every some hour being a period:

Xn+1=1. 6Xn-200, 1000

∴the method for every 1 hour would be:

Xn+1=1. 614Xn-50, 000

Since X0=1, 000, 000

Convert it to function:

Y=1, 000, 000Г—1. 6t4 -- 50, 000t

The table above shows that 117 hours after the resistant started to work, if zero chemical treatment was considered, people will dead. In addition to the 26 several hours before the defense mechanisms start to job which means, when the particles reach to 1012, which is between your 143th and the 144th hour, the person could die. This implies 5 days after the computer virus entered, persons will dead. Modeling recovery

An antiviral medication may be administered the moment a person seeks medical help. The medication does not affect the growth rate of the infections but with the immune response can get rid of 1 . two million virus-like particles hourly. 3)В В В В В In case the person is always to make a complete recovery, make clear why effective medication should be administered prior to the number of virus-like particles gets to 9 to 10 mil. Given: The speed is 160% per 4 hour...