EEA algorithm model in estimating spread and evaluating countermeasures on high performance computing

doi:10.4236/jbise.2009.21008

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J. Biomedical Science and Engineering, 2009, 2, 41-50

Published Online February 2009 in SciRes. http://www.scirp.org/journal/jbise JBiSE

EEA algorithm model in estimating spread and

evaluating countermeasures on high performance

computing

Si-Yuan Liu1,3, Chao Liu2, Yu Liu4, Yi-Ming Luo3, Gao-Jin Wen1, Jian-Ping Fan1

1Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China. 2Institute of Computing Technology, Chinese Academy of Sci-

ences, Beijing, China. 3Hong Kong University of Science and Technology, Hong Kong, China. 4Royal Institute of Technology, Stockholm, Sweden. Correspon-

dence should be addressed to Si-Yuan Liu (liusiyuan@ict.ac.cn).

Received March 12th, 2008; revised December 7th, 2008; accepted December 29th, 2008

ABSTRACT

This work started out with the in-depth feasibil-

ity study and limitation analysis on the current

disease spread estimating and countermea-

sures evaluating models, then we identify that

the population variability is a crucial impact

which has been always ignored or less empha-

sized. Taking HIV/AIDS as the application and

validation background, we propose a novel al-

gorithm model system, EEA model system, a

new way to estimate the spread situation,

evaluate different countermeasures and analyze

the development of ARV-resistant disease

strains. The model is a series of solvable ordi-

nary differential equation (ODE) models to es-

timate the spread of HIV/AIDS infections, which

not only require only one year’s data to deduce

the situation in any year, but also apply the

piecewise constant method to employ multi-

year information at the same time. We simulate

the effects of therapy and vaccine, then evaluate

the difference between them, and offer the

smallest proportion of the vaccination in the

population to defeat HIV/AIDS, especially the

advantage of using the vaccination while the

deficiency of using therapy separately. Then we

analyze the development of ARV-resistant dis-

ease strains by the piecewise constant method.

Last but not least, high performance computing

(HPC) platform is applied to simulate the situa-

tion with variable large scale areas divided by

grids, and especially the acceleration rate will

come to around 4 to 5.5.

Keywords: EEA, ODE, HIV/AIDS, Spread Esti-

mating, Countermeasure Evaluation, High Per-

formance Computing

1. INTRODUCTION

There is an ancient Arabic saying, those who predict the

future, lie, even if they think they are telling the truth.

This saying succinctly sums up the great uncertainty in

projecting the future, especially for a complex problem

such as HIV/AIDS spread estimation issues. As the HIV/

AIDS pandemic enters its 27th year, both the number of

infections and number of deaths due to the HIV/AIDS

continue to leap. Even though an enormous amount of

effort, our global society remains uncertain on how to

most effectively estimate the spread of this disease,

evaluate different countermeasures to it and allocate

resources to fight this epidemic.

Nevertheless, attempts to predict future trends and

prevalence of HIV/AIDS have been carried out with a

wide range of errors, using the following methods for

estimating HIV/AIDS prevalence, such as

back-calculation method, “ratio” method, multiplying

the estimated annual HIV/AIDS cases by 20, using the

results of serological surveys and extrapolating these

data to the total 15-49 years old population and some

recently developed methods, the workbook method, and

the special computer models [1,2].

Based on the differential equation theory，we propose

a novel algorithm model system, EEA model system, a

new way to estimate the spread of HIV/AIDS, evaluate

different countermeasures to HIV/AIDS and analyze the

development of ARV-resistant disease strains. It is a se-

ries of solvable ordinary differential equation (ODE)

models to estimate the spread of HIV/AIDS infections,

which not only require only one year’s data to deduce

the situation in any year, but also apply the piecewise

constant method to employ multi-year information at the

same time, overcoming the limitation of the classic in-

fection model (SI model) which ignores the change of

the population, and the scarcity and error of data.

We simulate the effects of therapy and vaccine, then

evaluate the difference between them, and offer the

smallest proportion of the vaccination in the population

to defeat HIV/AIDS, especially the advantage of using

the vaccination while the deficiency of using therapy

separately. At last, we analyze the development of

ARV-resistant disease strains by the piecewise constant

method.

42 S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-50

According to our models, we can firstly outline the

spread period of HIV/AIDS without any control in a

country can be reasonably divided into three main peri-

ods (Figure 1.) [3,4]: free spread period, burst spread

period and stable spread period.

In recent years, the demand on modeling capability

has increased rapidly in the areas of disease analysis,

drug design study, environmental assessment, etc.

Most modeling approaches are still based on the tra-

ditional single-CPU reservoir simulators and have

reached their limits with regard to what can be ac-

complished with them. During the same period, high

performance computing (HPC) technology has in-

creasingly been recognized as an attractive alternative

modeling approach to resolving large-scale or multi-

million-cell simulation problems [5]. As a result, par-

allel computing techniques have received more atten-

tion in this modeling community.

2. AN IDEAL MODEL TO ESTIMATE THE

SPREAD OF HIV/AIDS

Build a solvable model to estimate the proportion of the

number of HIV/AIDS infections in the population for

any country in any year, in the absence of any additional

interventions. Model 1

2.1. Assumptions and Definitions

Ⅰ. All the derivatives referred in the equations exist.

Ⅱ. t is time (unit: year).

N (t) is the population of the country at t.

N (t) obeys Logistic Population Model

Ⅲ. The crowd is divided into the susceptible crowd

and the infective crowd.

i (t) is the proportion of the infected population in the

total population at t.

The rest of the N (t) is the susceptible crowd.

Ⅳ. Two main transmission ways:

Cross infections: T-1

Figure 1. Proportion of infections in the Population 1990 to 2050

Sharing drug injecting equipment and transfusion of

blood or blood-derived products. Vaginal intercourse

without a condom (man to woman and woman to man)

and anal sex without a condom (both partners are at risk).

We assume as the average number of persons infected by

an HIV patient per year. Single-chain infections: T-2

An infected mother to her baby during pregnancy, at

childbirth, or by breast feeding. And is the birth rate of

infected infants in infected crowd per year.

Ⅴ. 3

is the rate of patient death.

2.2. Design of the Model

Through the first transmission way, every patient can

infect 1(1( ))

−

healthy people, so there are

1(1( )) ()( )

ititNt− people infected every year.

Through the second transmission way, the number of

infected people is 2()()

Ntit .

We can get

()

123

()()()(1- ())()()-()()

titKNtit itKNtKNtit

dt =+

(1)

After deduce, we can get

123 1

'( )

'( )()i(t)( )(t)

N( )

itK KKitKi

=+− −−,

So that we can get

1321 )()())(ln()( tiKtitN

KKKti −−−+=

′

The following question is how to solve those equa-

tions. Based on the classic Logistic population model, N

(t) should satisfy

2bNaN

dN +−=

Its solution is

cea

tN −

=)( , where

and

are constants. c

is determined by initial condition.

After fitting, we find out, for the countries in the chart,

is smaller than

by several orders of magnitude

averagely. So we let

= 0 in computation.

The population data of China in this diagram come

from[13].Then,

() t

tce

−

≈ (2)

So ln

)(t is a constant value for the same

country.

Let a=1

)(ln

)(

321 tN

KKKb−−+= (3)

and add the initial condition I (t0) = c, meaning c is the

proportion of the infected people at t0, then we can get

S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-51 43

'( )()()

()

itaitbit

it c

=− +

⎧

⎨

⎩ (4)

Finally we get

)(0

)(

ttb

−−

= (5)

where a, b are undetermined coefficients.

When it comes to how to get a and b, we believe the

best way is to get the statistical value of 1

, 2

, 3

and ))(ln( tN

d, then get a and b by (3). Of course this

will burden the workload of the public health department,

but that worth it greatly, because these two constants will

tell people the destination and rapidity of the HIV/AIDS

infections.

It’s easy that

lim( )

→∞

b (6)

That means, without any additional interventions, the

proportion of infected population will steadily come to

b. Meanwhile b indicates the speed of i (t) which tends

to limit. So the larger the value of b of a country is, the

faster the rate of change in the number of HIV/AIDS

infections for this country, and the more attention should

be paid to this country. So based on abundant data, it’s

significant to estimate the value of a and b. Then we can

realize the potential destroy of HIV/AIDS to a country.

It is a pity that we can not get the believable conclu-

sion about 1

, so we have to apply the fitting

method as a makeshift.

The detailed method is as the followings.

Because the solution of (4) exists and only exists, we

can get a series of equations about a and b by referring to

the data between 1995 to 1997, and get a series of ap-

proximate solutions, while the rest of the data are ap-

plied to test the model.

The reason why we take the data in early times is that

in those days the infection situation we take as without

too many additional interventions which is very neces-

sary and reasonable for our model.

Also we can forecast the trend of HIV/AIDS infec-

tions in a country, especially the coming of the peak and

the appropriate time to take appropriate measures to

control the situation.

Table 1. Data of china

Year 1997 1999 2001 2003

Number

of HIV/AIDS

infections

300,000

[8]

500,000

[12]

660,000

[10]

840,000

[10]

This model ignores some additional interventions, but

is easy to be modified to satisfy the requirements in the

following models, focusing on two interventions: provi-

sion of antiretroviral (ARV) drug therapies, and provi-

sion of a hypothetical HIV/AIDS preventative vaccine.

The data in Figure 2 refer to Table I.

The situation of the spread of HIV/AIDS in China

accords with our three main periods (as Figure 3 shows).

The spread of HIV/AIDS in China is in the free spread

period.

3. MODELS TO EVALUATE COUNTER-

MEASURES TO HIV/AIDS

Based on the estimating model, we take the following

scenarios into consideration to build three models to

solve different problems and come to the significant re-

sults.

1. Antiretroviral (ARV) drug therapy. Model 2.1

2. A preventative HIV/AIDS vaccine. Model 2.2

3. Both ARV provision and a preventative HIV/AIDS

vaccine. Model 2.3

Assume in these scenarios that there is no risk of

emergence of drug-resistant strains of HIV which we

will examine this issue later.

3.1. Model in Scenario 1: Antiretroviral (ARV)

Drug Therapy

3.1.1. Assumptions and Definitions

First, based on , , and in ⅠⅡⅣⅤ Model 1.

And,

.Ⅲ

i(t) is the percentage of the infection in the population

(N (t)) at t, which is infective.

r(t) is the percentage of patients accepting ARV in the

population at t (() ()rt it

≤

These people take the lower death rate p and are

stopped to take the infection actions, while all the

non-infected are susceptible.

Figure 2. Number of infections in China 1995 to 2010

44 S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-50

Figure 3. Proportion of infections in population China, 2000 to 2100

Ⅵ.

∀ n, ∃ n

r s.t.

max |()|

ntn

rtr

−<≤

− is very small, so,

rtr ≈)( , at 1−n＜t≤n

During solve the equation, we consider r (t) is a con-

stant in the same year, that is, when n≤t＜1

() n

rt r=, where n is the number of years.

We can assert the expression of i(t), which is not a ap-

proximate solution calculated by computer simulation.

Meanwhile, from the subsequent data, we can find out

there is no obvious error. Actually, our calculated result

is very accurate.

And because we can take )(ln

)( tN

d as a constant

value (see (1)), the deformation course of the equation

will be

11 23

(((1) )),

dN di

iN KiKrKKcN

dt dt

+=−+−+−−

2(),=−++−

di aibraic

where 2

11 23

(((1) ))+=−+−+−−

dN di

iN KiKrKKcN

dt dt,

and n

c=(a-b-p)r .

These are all undetermined coefficients, while n

r is

determined by outside conditions.

With an initial condition, () (01),

in ii=≤≤

'()

() (1)

iaibraic

inin tn

⎧=−+ +−

⎪

⎨=≤≤+

⎪

⎩

Let 1(1)

iin

+=+, we can backwards calculate all the

values in n years.

Similarly we can get

'()

(1)( 1)

iaibraic

inin tn

⎧=−+ +−

⎪

⎨+= ≤≤+

⎪

⎩

Let ()

iin=, so we can calculate forwards. Then we

finish the solving course of Model 2.1.

Now we consider how to apply it into the numeric

calculation.

First, based on assumptions IV, a and b here are the

same with those are in the Model 1.

So we can continue to use the precious fitted data in

Model 1, while r (n) is determined by outside aid and the

population in this country which is given before. So

based on the above solving course of the two problems,

we just have to get the proportion of the infections in the

population in any year after the appearance of HIV/

AIDS, and put the data into them inductively to forecast

or backdate the value of t in this country in any year.

Then the calculation of the rate of the change of the

infections this year is as follows, ()( )

dNiaN ir

−

(1) ()ib Ni

−

++ , where N can be looked up in the

data[13], while ln

b= can be fitted by the

least-square estimation based on N, which is different

for different countries.(Figure 1)

3.1.2. Model Analysis and Application

The following results base on the credible data from [10] [12].

From the diagram (Figure 4), we can find out the effect

Figure 4. Rate of change in the number of HIV/AIDS in-

fections for Russia from 2005 to 2050

Figure 5. Rate of change in the number of HIV/AIDS

infections for Russia from 2002 to 2050

S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-51 45

of the Antiretroviral (ARV) drug therapy is tiny, as Rus-

sia is in Burst Spread Period, despite of the number of

infections who received the treatment is very large.

However, if the therapy can be offered earlier, the ef-

fect is delectable. As we can see in the diagram (Figure

5) below, about 280,000 infections have received ARV

treatment every year since 2002. At that time, Russia is

in the end of Free Spread Period. So the ARV drug ther-

apy should be offered as early as possible (better before

the Burst Spread Period).

So what is the effect of the ARV drug therapy? Based

on our model, we can find out it will delay the coming of

the infection peak. As what the following diagram shows,

the peak will come late at least 5 years, which means we

have 5 more precious years to solve it.

3.2. Model in Scenario 2: Preventative HIV/

AIDS Vaccine

3.2.1. Assumptions and Definitions

First, based on , , and . And,ⅠⅡⅣ Ⅴ

Ⅲ’’.

We assume vaccine is fully effective without any inef-

ficacy and drug-resistant strains, and it will give the pa-

tient whole life immunity.

i(t) is the percentage of the infections in the popula-

tion (N (t)) at t, which is infective.

s(t) is the percentage of vaccine injections in the

population at t, which is not susceptible.

The rest of the N (t) is the susceptible crowd.

Ⅶ

∀ n, ∃ n

s s. t. 1

max|( )|

ntn

−<≤ − is very small, so,

sts ≈)( , when n-1＜t≤n.

During solving the equation, we consider r(t) is a

constant in the same year, that is, when 1ntn≤≤+,

() n

ts=, where n is the number of years.

So we can directly deduce the expression of i(t),

which is not a approximate solution calculated by com-

puter simulation. Meanwhile, from the subsequent data,

Figure 6. Proportion of infections in the population for

Russia from 1999 to 2050

we can find out there is no obvious error. Actually, our

calculated result is very accurate.

And because we can take ln()

()

dNt

dt as a constant

value (Model 1), the deformation course of the equation

will be

11 23

(((1) )),

dN di

iN KiKsKKiN

dt dt

+=−+−+−

2(),

di aibs a i

dt =−+ − (7)

where 1,1 2 3(ln)

aKbK KKN

==+−− , and these

are all undetermined coefficients, while n

is deter-

mined by outside conditions.

With an initial condition, () ,(01)

in ii=≤≤

'()

()( 1)

iaibsai

inin tn

⎧=−+ −

⎪

⎨

≤≤+

⎪

⎩ (8)

So we can get

()()

()

() ()/()

(1)

bas tn

ai sb

itb asae

ntn

−− −

+−

=− −

≤<+

(9)

Similarly we can get

'()

(1)( 1)

iaibsai

inin tn

⎧=−+ −

⎪

⎨

=≤≤+

⎪

⎩

E.2-2-3’

()()

()

() ()/()

(1)

bas tn

ais b

itb asae

ntn

−− −

+−

=− −

≤<+

(10)

Then we finish the solving course of Model 2.1.

From (11), we can get lim( )

it s

→∞ =−, so when

, i(t)=0. That is, when b

≥, maybe we will clear

up HIV/AIDS. That means, when the percentage of vac-

cine injections in the population is lower than b/a, the

percentage of the infections in the population will finally

tend to b/a-s, so only when it equals to or is higher than

b/a, we can finally defeat HIV/AIDS. That really pro-

vides a great meaning suggestion to the government

layout and deployment.

Now we consider how to apply it into the numeric

calculation.

First, it’s not hard to find out, a, b here have the same

definitions with those are in the Model 1. So we can

continue to use the precious fitted data in Model 1,

while s(n) is determined by outside aid and the popula-

tion in this country which is given before. So based on

46 S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-50

the above solving course of the two problems, we just

have to get the proportion of the infections in the popu-

lation in any year after the appearance of HIV/AIDS, put

the data into the inductive formula,

() lim()

nxn

iinix

→−

== ,

so we can forecast or backdate the value of t of this

country in any year.

3.2.2. Model Analysis and Application

Take the situation in Brazil as an example to explain our

model and result.

The reason why we take Brazil as an example is that

the percentage of ARV treatment there has come to 100

%. [12] So we believe it’s reasonable and representative

to select Brazil to show the effect of the vaccination.

So in Brazil we let the proportion of vaccination is

0.081, which approximates to b/a (refer to Model 1).

When we use the vaccine measurement in 2010, the rate

of change in the number of HIV/AIDS infections will

slow down obviously. So if the proportion of vaccination

is over 0.08 every year (see Figure 7), and the trend of

defeating HIV/AIDS maybe will appear.

So we come to the conclusion: Compared with ARV

treatment, vaccination is a better way to clear up the

HIV/AIDS, which has the following advantages:

Less cost

Convenient application

Better efficiency in short period

Clearing up HIV/AIDS finally

But, it’s a pity that the efficient vaccine is not avail-

able now.

4. MODEL IN SCENARIO 3: BOTH ARV

PROVISION AND PREVENTATIVE HIV/

AIDS VACCINE

4.1. Assumptions and Definitions

First, based on , , ⅠⅡⅣ，Ⅴ，Ⅵ，and . And,Ⅶ

’’’

Ⅲ

i(t) is the percentage of the infection in the popula-

Figure 7. Proportion of infections in population Brazil from

2000 to 2050

tion (N (t)) at t, which is infective.

s(t) is the percentage of patients accepting ARV in the

population at (() ())tst it

≤

. These people take the lower

death rate p and are stopped to take the infection actions,

while all the non-infected are susceptible.

r(t) is the percentage of vaccine injection in the popu-

lation at t, which is not susceptible.

4.2. Design of the Model

During solving the equation, we consider r(t) and r(t) are

constants in the same year, that is,

when 1ntn

≤

<+,

()

rt r

⎧

⎨

⎩, where n is the num-

ber of years.

So we can directly deduce the expression of i(t),

which is not a approximate solution calculated by com-

puter simulation. Meanwhile, from the subsequent data,

we can find out there is no obvious error. Actually, our

calculated result is very accurate.

And because we can take ln( )

()

dNt

dt as a constant

value (Model 1), the deformation course of the equation

will be

11 23

(((1) )),

dN di

iN KiKsrKKicN

dt dt

+=−+−++−−

2(),

di aibsar aic

−+− +−

where 1,1 2 3(ln )

aKbK KKN

==+−− , and

(1 )

ca sr

−, and these are all undetermined coeffi-

cients, while n

s is determined by outside conditions.

With an initial condition, () ,(01)

in ii=≤≤

'(() )r(-as+b+lnN-p)

(1)( 1)

iaibrsai

inin tn

⎧

⎪

⎨

⎪

⎩

=−+ +−−

+= ≤≤+

(11)

()

dbr sa

+− ,

(ln())

crasbp N

=−+−+, (1)ntn≤≤ +.

Similarly we can get

'(())r(-as+b+lnN-p)

(1)( 1)

iaibrsai

inin tn

⎧

⎪

⎨

⎪

⎩

=−+ +−−

+= ≤≤+

(12)

()(((1) 4

(2)

)4 )

itarctgt nca d

arctgdi aca dd

ca d

=−−−−

−+

+−+

−

(13)

where

S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-51 47

()

dbr sa=+ −,(ln())

crasbp N

=−+−+ ,

(1)ntn≤≤ +.

Then we finish the solving course of Model 2.1

First, it’s not hard to find out, a, b here have the same

definitions with those are in the Model 1. So we can

continue to use the precious fitted data in Model 1, while

s(n) is determined by outside aid and the population in

this country which is given before. So based on the

above solving course of the two problems, we just have

to get the proportion of the infections in the population

in any year after the appearance of HIV/AIDS, and put

the data into the above formulas inductively, to forecast

or backdate the value of t of this country in any year.

Then the calculation of the rate of the change of the in-

fections this year is as follows,

()( )(1)()( )

dNiaN irisbN irpNr

nn nn

=−−−++−+,

where N can be looked up in the data that ICM provides,

while ln

= can be fitted by the least-square es-

timation based on N, which is different for different

countries.

4.3. Model Analysis and Application

In this model, we can estimate the expected rate of

change in the number of HIV/AIDS infections for a

country under realistic assumptions for two scenarios:

Antiretroviral (ARV) drug therapy and a preventative

HIV/AIDS vaccine.

Take the situation in India as an example to explain

our model and result [12].

The reason why we take India as an example is that

India, a developing country, will have the largest popula-

tion in the world in the not far future.

As the above two conclusions we come to, the effi

ciency of vaccination is better than treatment. So in the

Figure 8. Rate of change in the number of HIV/ADIS infections

for India from 2005 to 2050

less fund situation, vaccination is the first choice.

To India, a developing country with a very large

population, should apply vaccination, under the condi-

tion, certain amount of treatment.

5. Models to Analyze the Development

of ARV-resistant Disease Strains

We will re-formulate the three models developed in last

section, taking into consideration the following assump-

tions about the development of ARV-resistant disease

strains.

A person receiving ARV treatment with adherence

below 90 percent has a 5 percent chance of producing a

strain of HIV/AIDS which is resistant to standard

first-line drug treatments. Second-and third-line ARV

drug therapies are available, but assume that these drugs

are prohibitively expensive to implement in countries

outside of Europe, Japan, and the United States. Model 3

5.1. Assumptions and Definitions

First, based on , , ,, ⅠⅡⅣⅤⅥ，and .Ⅶ

And,

’’’

Ⅲ

i(t) is the percentage of the infection in the population

(N (t)) at t, which is infective.

r(t) is the percentage of patients accepting ARV in the

population at t (() ()

tit

≤

These people take the lower death rate p and are

stopped to take the infection actions, while all the

non-infected are susceptible.

s(t) is the percentage of vaccine injection in the popu-

lation at t, which is not susceptible.

Ⅷ

p in ’’’ is the functi

Ⅲon of t , and

∀

∃

p s.t. max|( )|

ntn

−

−<≤ is very small, so,

p(t) n

≈

, at 1ntn

−

<≤.

5.2. Design of the Model

At first, we have to do some necessary modifications.

The development of ARV-resistant disease strains

doesn’t have effect on the model without ARV treatment,

Model 2.2. So we just have to focus on Model 2.1 and

Model 2.3. Because of the similarity between these two

models, we just take Model 2.1 as an example.

The development of ARV-resistant disease strains will

cause the rising of the proportion of the patients with

ARV treatment, that is, p is bigger. To get the more general

result, we assume p is the function of t, p(t).

Remain the rest of the assumptions, the model will be

modified into

(( )())( )(1())(()( ))

() ()(()())()()

()() nn

dNtitKNtititrt

KNtit rtptNrt

Nnin Ni

⎧

⎪

⎨

⎪

⎩

=−−

+−− −

48 S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-50

Just as how we deal with r(t) and s(t), we assume

p(t) (1)

pn tn=≤<+

Then deduce functions, we get

2()

()ntn1

di aibar ic

in i

⎧

⎪

⎨

⎪

⎩

=−+ +−

=≤≤− ()

and

()

(1)ntn1

di aibar ic

in i+

⎧

⎪

⎨

⎪

⎩

=−+ +−

+= ≤≤− ()

where 1

aK,= b=12

KK lnN

+− , c=(a+b-n

)

r, ( nZ∈).

The solutions of the above questions is uniquely exists,

and have the expressions, which we will not give unnec-

essary details to.

Then with m

ii()limi(x)

m→

== , we can get a satisfied

curve of the rate of the change of infections starting at

one point.

5.3. Model Analysis and Application

The result of the model is as the following diagram

shows (Figure 9).

We take India as an example to explain the result.

(HIV/AIDS infections data from [10])

The development of ARV-resistant disease strains will

cause the rising of the proportion of the patients with

ARV treatment. And India has a long way to solve the

HIV/AIDS problem.

We can satisfy all the requirements in the last section,

under the conditions in this section, using our models

with the similar methods, so we will not give unneces-

sary details to the realization of other models in this sec-

tion.

Figure 9. Rate of change in the number of HIV/ADIS infections

for India from 2005 to 2050

6. HIGH PERFORMANCE COMPUTING

PLATFORM

Dawning 4000L, IDC data processing machine, as Fig-

ure 10, shows, located in Shenzhen Institute of Ad-

vanced Technology, Chinese Academy of Sciences, has

been designed to provide more than 3 teraflops comput-

ing capability with 644 processors, 644GB physical

memory and 100 terabytes storage. The machine can be

upgraded online to 6.75 teraflops computing capability

with 1300 processors, 4000GB physical memory and

600 terabytes storage.

The computing capability of the common PC will be

enough for our model, while in simulating a large scale

and establish the relation between time and variation

ratio in real time, especially when amount of data be-

come very large, the performance of database manage-

ment system will drop sharply , ability of data of or-

ganization and management weaken greatly , can't real-

ize the rapid searching for the a great deal of data .And

what is more, it can even cause the breakdown of system

when amount of data is getting larger, so high perform-

ance computing platform will come to be necessary.

Each CPU will compute the variable situation in a

certain area which divided by grids (P( ):( )nMn n→, P

is the processor, M is the certain area, and n is the

number. As Figure 11 shows, with the communication in

the results, finally, we can get the whole situation in a

large scale area, such as a country, a continent and the

global world, and the acceleration rate will come to

around 4 to 5.5.

7. CONCLUSION AND FUTURE WORK

We identify the scenarios and problems in spreading and

countermeasures evaluating, and propose a novel algo-

rithm model system, the EEA model system, with three

distinctive main conclusions. First, three main periods

spread of HIV/AIDS, and finally comes to the stable

spread period. Secondly, the limitations and applications

of the antiretroviral (ARV) drug therapies. Thirdly the

minimum proportion of vaccination in a country to

eliminate HIV/AIDS.

Based on the design, analysis, and application of our

model system which based on high performance com-

puting platform, we can safely draw the conclusion that

the EA model system exploits a new way to estimate the

spread of HIV/AIDS, evaluate different countermeasures

to HIV/AIDS and analyze the development of

ARV-resistant disease strains and will behave a great

positive effect on defeating HIV/ AIDS.

The future work we should focus on is the im prove-

ment of algorithm for this issue on the HPC platform to

arise the accuracy of estimation, the stability of coun-

termeasures evaluation and identification of more sig-

nificant issues, such as this model maybe will be appli-

cable for the terrorist infection spreading and counter

measures evaluation.

S. Y. Liu et al. / J. Biomedical Science and Engineering 2 (2009) 41-51 49

Figure 10. High-performance Computing Platform

Figure 11. Computation and communication in the CPUs

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