Modeling Complex Sd

Modeling Complex SD DELAYS AND TABLES

Dennis T. Beng Hui, De La Salle University-Manila

Types of Rate Equations (Var.kl = …) „ „ „ „ „ „ „

Constant*Level.k Level.k/life (goal.k-level.k)/adjustment aux.k*level.k level.k/aux.k norm.k+effect.k norm.k*effect.k Dennis T. Beng Hui, De La Salle University-Manila

The Spreading Virus Problem „

Virus starts with a few people who are susceptible to the virus. These susceptible people will become infected and in turn become sick. Once people get sick, they start taking medicine, as time progresses, these people will slowly get cured and on their way to recovery. Dennis T. Beng Hui, De La Salle University-Manila

The Spreading Virus Problem Susceptible People

Recovered People Infected People

Sick People

Dennis T. Beng Hui, De La Salle University-Manila

Examples of Delays: Delay1 R SYMP.KL=DELAY1 (INF.KL, TSS) Where

TSS = time to show symptoms INF = infection rate SYMP = symptom rate

Incubate

Healthy INF

Sick SYM

Delay1(INF.KL,TIME)

Dennis T. Beng Hui, De La Salle University-Manila

Recovered REC

Examples of Delays: Delay3 SYMP.KL=DELAY3 (INF.KL, TSS) Where

Susceptible

TSS = time to show symptoms INF = infection rate SYMP = symptom rate

INFC

INC1

Sic

Incubate3

Incubate2

Incubate1

INC2

Delay3(INFC.KL,TSS)

Dennis T. Beng Hui, De La Salle University-Manila

INC3

Effect of Delays „

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What happens to the diagram if there is an incubation period? What do you think is the behavior of the levels and the rates in this system? SMOOTH – delay command for information. Ex. smooth1, smooth3

Dennis T. Beng Hui, De La Salle University-Manila

Effect of Delays

Dennis T. Beng Hui, De La Salle University-Manila

The TABLE COMMAND

„

TABLE – use to describe a variable that is not a simple algebraic equation SYNTAX:

A T

VAR.K = TABLE (table_name, input_to_table, min-x, max-x, x-inc) table_name = y0/y1/y2/ … /yn

„

NOTE: n is equal to the number of x points available between min-x up to max-x.

Dennis T. Beng Hui, De La Salle University-Manila

TABLE Example A SALESMEN.K = TABLE (TSE, DDRM.K, 0, 10, 1) T TSE = 400/388/348/292/212/152/100/60/32/12/8 R ORDERS.KL = SALESMEN.K*SALES/PERSON.K Where TSE = table for SALEMEN DDRM.K = delivery delay (level or auxiliary variable, or even a rate variable) X

0

1

2

3

4

5

6

7

8

9

10

Y

400

388

348

292

212

152

100

60

32

12

8

Dennis T. Beng Hui, De La Salle University-Manila

TEST Commands RAMP - continuous growing or declining linear function of TIME. Var = RAMP(A,B) Where A = represents the slope of the linear function B = represents the starting time of the ramp „ NOISE - The noise function allows us to vary the value of a variable by –0.5 to 0.5. This command allows us to exhibit a little bit of randomness, but still maintaining the pattern of behavior. NOISE exhibits a uniform distribution. Var = A*NOISE()+B Where A and B are constants and that the value of Var is centered between A and B. „

Dennis T. Beng Hui, De La Salle University-Manila

TEST Commands „

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PULSE – creates a sudden increase in the behavior and drops back to its original state. PULSE(HEIGHT,WIDTH,FIRST,INTVL) – from VENSIM -A pulse of height , starting at time FIRST and every INTVL lasting WIDTH time units. STEP – creates a step change in the behavior and does not return to its original state. STEP(H,T) – from VENSIM - Returns 0 till time T and then H.

Note: DYNAMO commands for PULSE and STEP will have a slightly different syntax. Dennis T. Beng Hui, De La Salle University-Manila