Dialog System for Modeling Multidimensional Demographic Processes

W O R K I N G P A P E R

DIALOG SYSTEM FOR YODELING .MULTIDIMENSIONAL DENCGRAPHIC PROCESSES

Sergei Scherbov Anatoli Yashin V l a d i m i r G r e c h u c h a

June 1 9 8 6 I@-86-929

I n t e r n a t i o n a l I n s t i t u t e for Applied Systems Analysis

NOT FOR QUOTATION WITHOUT THE PERMISSION OF THE AUTHORS

DIALOG SYEVEM FOR MODEUNG

MULTIDIMEWSIONAL DEMOGRAPHIC PROCESSES

Sergei Scherbov AnatoLi Y a s h i n V l a d i m i r Grechucha

June 1986 WP-86-29

Working P a p e r s a r e interim r e p o r t s on work of t h e International Institute f o r Applied Systems Analysis and have received only limited review. Views o r opinions expressed h e r e i n do not necessarily r e p r e s e n t those of t h e Institute o r of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

DIALOG EXSl%M FOR MODELZNG

MULTIDIMENSIONAL DEMOGRAPHIC PROCESSES Sergei Scherbov*, Anatoli Yashin**, I?ladimir Grechucha***

1.

INTRODUCTION

A growing understanding of t h e importance of demographic p r o c e s s e s in social and economic development places g r e a t e r demands on t h e quality of demographic r e s e a r c h and on t h e adequacy and convenience of tools used in t h e analysis of a population's c h a r a c t e r i s t i c s .

Multistate population models recently became popular in t h e study of many as- p e c t s of demographic transitions, such as migration, marriage, changes of health s t a t u s , social status, occupation, e t c . [1,2].

Computer programs and software packages were developed t o realize such models [3,4]. However, most of t h e s e allow analysis of systems only when fertility, mortality, o r transition coefficients do not depend o n time. Some a u t h o r s have overcome t h i s drawback [5,6] and have c r e a t e d t h e opportunity t o analyze a l t e r n a - tive evolutions of t h e system under various scenarios of n a t u r a l and mechanical reproduction of t h e population. However, t h e s e programs are not always ap- p r o p r i a t e f o r u s e by t h e many demographers and health specialists who are not deeply involved in computer modeling. The software is often not flexible enough t o enable choices of and changes in t h e variables t h a t determine t h e scenarios, t h e r e p r e s e n t a t i o n of t h e r e s u l t s , and t h e control of modeling itself.

The most important disadvantage of t h e s e packages is t h e inability t o commun- i c a t e interactively with t h e model. A s e x p e r i e n c e shows, interactively working with computers essentially r e d u c e s t h e time s p e n t on model design and debugging.

I t a l s o creates additional opportunities f o r model analysis.

=Sergei Scherbov, All Union Institute of Syetems Studies, USSR Academy of Sciences, Proepect 60 Let Octyabria, 9, 117312 Moscow, USSR.

xxAnatoli Yashin, Population Program, IIASA, A-2361 Laxenburg, Austria.

===Vladirnir Crechucha, All Unlon Institute of Systems Studles, USSR Academy of Sciences, Pros- pect 60 Let Octyabria, 9, 117312 Moscow. USSR.

Thus, t h e r e is a necessity t o c r e a t e a user-friendly system t h a t allows a more effective analysis of demographic processes.

In this p a p e r a n interactive system t h a t uses t h e multistate demographic models is described. The system provides t h e opportunity t o p r e p a r e s c e n a r i o s , change coefficients of t h e model during t h e modeling p r o c e d u r e , and p r e s e n t in- termediate results. The p a p e r uses some r e s u l t s of r e s e a r c h conducted at VNIISI and at IIASA: namely, t h e design of t h e man-machine modeling system [7] and t h e modeling of multistate demographic processes [3,4,8.9].

2. REQUIREMENTS FOR THE DIALOG SYSTEM OF MODELING

The f i r s t version of t h e i n t e r a c t i v e system w a s based on t h e following main re- quirements.

(1) The dialog system should be simple in t h a t t h e command language should b e as close t o n a t u r a l as possible. Since t h e system is oriented toward non- specialists in computer science, t h e leading r o l e in t h e dialog should b e played by t h e system itself. The u s e r should only answer simple questions o r s e l e c t instructions from t h e menu.

(2) An opportunity t o c o n t r o l t h e modeling p r o c e d u r e should b e provided; t h a t is, one should have t h e opportunity t o s t o p modeling, change t h e control vari- ables, and t h e n start modeling again.

(3) Visual display of t h e modeling r e s u l t s should be provided. One should b e a b l e t o obtain t a b l e s and g r a p h s (on g r a p h i c display, p r i n t e r , o r p l o t t e r ) during t h e modeling.

(4) The system should provide opportunities f o r flexible s c e n a r i o setting. For demographic and medical demographic models t h e opportunity t o set s c e n a r i o s f o r such v a r i a b l e s as age-specific mortality, age-specific f e r t i l i t y , c r u d e b i r t h r a t e s , transition intensities, etc., should b e provided. The system should a l s o provide t h e opportunity t o set t h e functions in t e r m s of tables, and contain some s t a n d a r d functional forms, such as exponential, l i n e a r , e t c . (5) The system should enable t h e u s e r t o change t h e s t r u c t u r e of t h e model o r in-

c o r p o r a t e a new one from t h e class of discrete-time Markov processes. The opportunity t o change dialog in a c c o r d a n c e with t h e changes in model t y p e should b e provided.

(6) The opportunity t o easily t r a n s f e r t h e model from one computer t o a n o t h e r should b e provided.

3. DESCRIPTION OF THE MODEL

A detailed mathematical description of t h e multistate population dynamics i s given by Rogers [9,10]. I t h a s been shown t h a t t h e dynamic of t h e population can b e described by t h e equation

where K c h a r a c t e r i z e s t h e population according t o a g e groups and different s t a t e s at times t and t

+

h , h i s t h e time interval as well as t h e a g e interval, and G i s t h e growth matrix:

The f i r s t row of matrix G consists of t h e matrices B

( z ) ,

B ( z )

= (q)

h ^{C [P(O)}

⁺

I ] [ F ( z )

+

F ( z

+

h ) S ( z ) ]

where F ( z ) i s t h e diagonal matrix f o r b i r t h r a t e s of people aged

z

t o

z +

h y e a r s old in different states. The P matrix contains t h e survival probabilities from a g e

z

until z

+

^{h .} The e n t r i e s under t h e main diagonal of t h e G matrix determine t h e survival coefficients,

The transition probabilities a r e calculated in t h e same manner as f o r increment- decrement life tables. A t f i r s t t h e observed coefficients a r e grouped into t h e ma- t r i x :

where Mid ( z ) is t h e age-specific annual death rate in s t a t e i , and M i j ( z ) is t h e age-specific annual transition rate from state j t o state i

.

The probability matrix P is calculated as follows

The C matrix determines t h e state in which newborns a p p e a r in connection with t h e i r parents' state. Thus, t h e rows of t h e C matrix r e p r e s e n t t h e states of t h e newborns and t h e columns r e p r e s e n t t h e states of t h e parents. If, s a y , C ( i

,

j )

=

1 then t h e p a r e n t s are in state j and t h e children will a p p e a r in state i . The C ma- t r i x satisfies t h e usual probabilistic constraints: C (i , j )

r

0 , C (i , j )

=

1.

j

Just [ l l ] h a s shown t h a t t o complete t h e female dominant two-sex model a diagonal matrix xf h a s to b e defined. I t s elements are t h e ratios of males to females born by a woman in each state. Usually t h e s e r a t i o s are identical. Thus

where

and b? and b{ denote t h e number of male and female births. For t h e female projec- tion t h e f i r s t row of t h e growth matrix is given by elements

gf ( z )

= (+)cx~

[ P f ( 0 )

+

I ] [ F ( X )

+

F ( z +h ) s f ^{( 2} ) I

The s u p e r s c r i p t f indicates t h a t t h e survivorship proportions and probabilities of female population are used. The projection of t h e male population is performed in two steps. First t h e total (male and female) population at e x a c t a g e 0 i s calculated by

~ ' ( 0 )

= Z

[ F ( z )

+

~ ( z + h ) ~ f ( z ) l t K f ( z ) X

K' ( 0 ) i s now input to t h e projection of males. The male population in t h e f i r s t a g e group at time t +h c a n easily b e derived by means of

where t h e elements sj- of

Xn

a r e 1

-

^sj-f. The o t h e r a g e groups a r e c a r r i e d for- ward by

t ' h ~ m ( ~ + h ) = S ~ ( Z ) ~ K ~ ( Z ) f o r h S z S n - h , where n stands f o r t h e last a g e group.

4. THE STRUCTURE OF THE INTEBACTIW SYSTEM

The block scheme f o r t h e dialog system, which satisfies most of t h e numerated r e - quirements, i s r e p r e s e n t e d in Figure 1. The u s e r starts t h e system by typing t h e name of t h e loading module SPAT. The rest of t h e dialog with t h e system i s contin- ued in t h e menu mode. The job control block a s k s t h e u s e r which of t h e blocks i s t o have control:

(1) Initialization.

(2) Modeling.

(3) S c e n a r i o setting.

(4) Result r e p r e s e n t a t i o n .

The u s e r t y p e s t h e number and t h e r e s p e c t i v e block controls t h e system.

4.1. Model Initialization

During model initialization t h e file with t h e initial d a t a i s r e a d . This file should b e p r e p a r e d in a p a r t i c u l a r form, described in t h e Appendix A . l and A.2. The model initialization p r o c e d u r e i s n e c e s s a r y in t h e following cases:

(a) Before s t a r t i n g work with a model.

(b) Before a new start of t h e modeling p r o c e d u r e (starting a new scenario. f o r example).

(c) When choosing a new t y p e of model (medical demographic o r demographic) o r a new model (another country o r region) without exiting t h e system.

job control

Figure 1. S t r u c t u r e of t h e dialog system.

4.2. Scenario Setting

The system p r o v i d e s flexible a n d convenient setting of t h e c o n t r o l variables.

These variables, which determine t h e s c e n a r i o , can b e set as a t a b l e in t h e in- t e r a c t i v e mode, when some fixed time points c o r r e s p o n d t o t h e values of t h e s c e n a r i o v a r i a b l e s o r as a function of time.

Any model's p a r a m e t e r o r exogenous v a r i a b l e c a n b e chosen as a s c e n a r i o variable, s i n c e t h e s c e n a r i o determines t h e number of given variables. During t h e modeling p r o c e d u r e t h e values of t h e s c e n a r i o v a r i a b l e s are calculated f o r any time in t h e s c e n a r i o block, based on information determined by t h e u s e r in t h e block f o r s c e n a r i o setting. If f o r some v a r i a b l e t h e s c e n a r i o i s n o t set, its value is specified as a default value (calculated from initial d a t a ) and is unchangeable dur- ing t h e p r o c e s s of modeling.

A s c e n a r i o s e t t i n g block allows t h e u s e r to:

(1) Set t h e s c e n a r i o on fertility.

(2) Set t h e s c e n a r i o on mortality.

(3) Set t h e s c e n a r i o on migration o r transitions between states.

(4) Set t h e s c e n a r i o by a v a r i a b l e name.

(5) S a v e t h e s c e n a r i o .

(6) Read a s c e n a r i o from t h e file.

4.2.1.

Scenario Setting for Fertility. Mortality, and Migration

S c e n a r i o s on f e r t i l i t y a n d mortality are determined f o r one o r s e v e r a l states (re- gions). The system a s k s t h e state of d e p a r t u r e and t h e state of destination f o r set- ting transition s c e n a r i o s .

The g r o s s f e r t i l i t y (GRRN), mortality (GDRN), and migration (GMRN) rates are t a k e n as s c e n a r i o variables. In modes 1, 2, and 3 when t h e nonnegative values of GRRN, GDRN, a n d GMRN are set, only t h e area under t h e age-specific rates of fer- tility, mortality, and migration (RATF, RATD, a n d RATM) changeable; t h e s h a p e of t h e age-specific rates is unchangeable.

F o r negative values, GRRN, GDRN, and GMRN act as switches, which i s dis- cussed l a t e r .

The s c e n a r i o v a r i a b l e can have up t o 1 0 values. The time and t h e values are specified a s follows:

During simulation t h e values of t h e s c e n a r i o v a r i a b l e s in between t h e given points are calculated using l i n e a r interpolation.

If t h e v a r i a b l e i s specified as a function of time, t h e values of t h e r e s p e c t i v e coefficients t h a t determine t h i s function are determined. Note t h a t e a c h new set- ting of t h e values f o r some s c e n a r i o v a r i a b l e cancels values a l r e a d y specified.

4.2.2. Setting a Scenario by the Variable Name

The system provides a n opportunity f o r s c e n a r i o setting according t o t h e v a r i a b l e name. For t h i s p u r p o s e , t h e u s e r should have t h e list of t h e v a r i a b l e names (iden- t i f i e r s ) (Appendix A.4). Let, f o r instance, t h e u s e r know t h a t t h e identifier of t h e v a r i a b l e f e r t i l i t y coefficient f o r t h e f i r s t region in t h e l i s t of regions in t h e model i s GRRN(1). Then, being in mode 4 one should t y p e t h e name GRRN(1) and, follow- ing t h e dialog, t y p e t h e d e s i r a b l e values.

In t h i s case t h e r e i s t h e opportunity t o set age-specific f e r t i l i t y , mortality, and transition rates. Knowing t h e r e s p e c t i v e identifier o n e can determine t h e s c e n a r i o value of t h e coefficient for given states and a g e groups. If at t h e same time t h e value of t h e s c e n a r i o v a r i a b l e for a g r o s s rate, s a y , f e r t i l i t y GRRN, i s set positive, t h e n t h e a r e a u n d e r t h e c u r v e RATF will change and will equal t h e new value, but t h e form of t h e c u r v e will not change. If GRRN i s negative, t h e n i t will no longer b e a g r o s s r e p r o d u c t i o n rate, b u t act a s a switch.

In t h i s case no normalization and age-specific coefficients will s t a y t h e same, e x c e p t f o r t h o s e t h a t t h e s c e n a r i o h a s specified. The area u n d e r t h e a g e distribu- tion RATF will change. Note t h a t t h e initial values of g r o s s rates are calculated according to initial p a t t e r n s of f e r t i l i t y , mortality, and migration.

4.2.3. Using the Mode of Scenario Setting by the Variable Name for Model Debugging

When working with t h e model i t is sometimes n e c e s s a r y t o look a t t h e c u r r e n t value of v a r i a b l e s t h e r e p r e s e n t a t i o n of which i s not provided in t h e program. The mode of s c e n a r i o setting by t h e v a r i a b l e name c a n b e used f o r t h i s p u r p o s e , since during s c e n a r i o setting in t h i s mode t h e c u r r e n t value of t h i s v a r i a b l e i s printed f i r s t . Then t h e u s e r decides whether t o leave t h e v a r i a b l e unchanged o r s e t i t t o a new value. Thus, t o use t h i s mode f o r model debugging, one needs to know only t h e identifiers of t h e v a r i a b l e s , which are given in t h e Appendix A.4.

4.2.4. Saving the Scenario

Creation of t h e s c e n a r i o can b e time-consuming, especially if t h e number of con- t r o l v a r i a b l e s i s high. Since one sometimes needs t o work with t h e same s c e n a r i o again, t h e s c e n a r i o c a n b e saved. The u s e r should provide t h e name of t h e s c e n a r i o in o r d e r t o d o this, and t h e information about t h e s c e n a r i o will b e written t o a disk file.

4.2.5. Reading the Scenario from the File

To work with a s c e n a r i o t h a t h a s a l r e a d y been c r e a t e d by t h e u s e r or h a s been saved f r o m t h e dialog system, t h e r e is t h e opportunity t o r e a d t h e s c e n a r i o from t h e file. F o r t h i s p u r p o s e , t h e u s e r t y p e s t h e name of t h e file where t h e s c e n a r i o i s written. The file with t h e s c e n a r i o is p r e p a r e d according t o t h e following r u l e s : a ) t h e s t r i n g i s r e a d as a comment if t h e f i r s t c h a r a c t e r i s ' c ' ;

b ) t h e s c e n a r i o v a r i a b l e is defined as t h e following function:

where, t l , t 2

,...,

tn are time points, Yl,Y2

,....

Yn are values of t h e s c e n a r i o variable;

c ) t h e s t r i n g c a n b e t r a n s f e r r e d at any place;

d) a few s c e n a r i o v a r i a b l e s c a n b e defined in t h e file;

e ) only one s c e n a r i o c a n b e defined in t h e file.

After t h e s c e n a r i o h a s been r e a d , t h e u s e r c a n deal with i t as if i t had just been c r e a t e d : o n e c a n add t h e new v a r i a b l e values, change t h e values of t h e old vari- a b l e s , etc.

4.3. Modeling

The simulation is performed in t h e modeling block. Modeling can b e done in s e v e r a l time intervals. When t h e system a s k s "ENTER TIME SPAN", t h e l a s t y e a r of model- ing should b e specified by t h e u s e r . If t h e modeling p r o c e d u r e i s s t a r t e d a f t e r t h e model initialization, t h e n t h e time from t h e file used f o r initialization is t a k e n as t h e initial time f o r t h e modeling interval. The modeling s t e p coincides with t h e width of t h e a g e group. The modeling interval c a n consist of o n e o r s e v e r a l steps.

During t h e modeling p r o c e d u r e t h e u s e r h a s t h e following opportunities:

(1) After completing t h e modeling p r o c e s s f o r t h e f i r s t time i n t e r v a l , one c a n continue modeling. For t h i s p u r p o s e one should specify t h e end point of t h e new time interval. The end point of t h e previous time i n t e r v a l i s considered as t h e initial point f o r a new i n t e r v a l of modeling.

(2) One c a n r e p r e s e n t t h e r e s u l t s of modeling a f t e r e a c h specified modeling i n t e r - val (dumping).

(3) One c a n obtain r e s u l t r e p r e s e n t a t i o n a f t e r e a c h s t e p of t h e modeling p r o c e s s . (4) One can change t h e values of t h e s c e n a r i o v a r i a b l e s and introduce new

s c e n a r i o variables.

(5) One c a n s t o p modeling and start modeling again with a new model without exit- ing t h e dialog system.

4.4. Representation of Modeling Results

A r e p r e s e n t a t i o n block r e a l i z e s t h e output of t h e produced r e s u l t s during t h e p r o - cess of modeling (printing d a t a during t h e r u n ) , as w e l l as a f t e r completion of t h e modeling interval (dumping data).

During t h e modeling p r o c e s s information is r e p r e s e n t e d in t e r m s of t a b l e s and i s written into t h e file associated with unit number 2 a f t e r e a c h s t e p (not t h e modeling interval). The l i s t of t a b l e s is given in t h e menu. When dumping d a t a , t h e r e s u l t a p p e a r s on t h e s c r e e n .

In o r d e r t o achieve more independence from t h e available hardware environ- ment ( t h e size of t h e terminal s c r e e n o r t h e width of t h e p r i n t e r p a p e r ) , a s p e c i a l table g e n e r a t o r w a s developed. This helps t o easily a d a p t t h e r e p r e s e n t a t i o n form f o r t h e r e s u l t s of modeling t o t h e p a r t i c u l a r t y p e and configuration of t h e comput- er. I t a l s o allows deletion of c o n s t r a i n t s r e l a t e d t o t h e number of states and a g e groups in t h e model, which usually produce problems in r e p r e s e n t a t i o n of t h e r e s u l t s .

After completing t h e modeling p r o c e d u r e t h e r e s u l t s c a n b e r e p r e s e n t e d as:

(1) C u r r e n t values of t h e demographical v a r i a b l e s in t h e form of tables.

(2) P i e c h a r t s of t h e population s t r u c t u r e at t h e c u r r e n t time.

(3) A histogram of t h e age-specific population s t r u c t u r e in e a c h state (group) at t h e c u r r e n t time.

(4) The population size in e a c h state (group) s t a r t i n g from t h e initial time of modeling until t h e c u r r e n t y e a r .

(5) A new version of t h e system will include g r a p h i c r e p r e s e n t a t i o n of t h e popula- tion as a function of time and a g e using a three-dimensional plot.

The g r a p h i c information c a n b e r e p r e s e n t e d e i t h e r by g r a p h i c display o r p l o t t e r .

5. REALIZATION

The dialog system w a s c r e a t e d f o r use on t h e VAX 11/780. However, at e a c h s t a g e of i t s design, e f f o r t s were developed t o make t h e system as machine independent as possible. The programming language used i s FORTRAN 77, which minimizes t h e ef- f o r t r e q u i r e d t o t r a n s f e r t h i s system t o a n o t h e r computer.

Programs f o r t h e g r a p h i c r e p r e s e n t a t i o n of r e s u l t s are machine-dependent.

For instance, IIASA uses t h e NEWPLOT system. During modeling t h e r e s u l t s are written in some auxilliary d a t a file. The call t o t h e NEWPLOT comes from t h e pro- grams of t h e dialog systems written in FORTRAN. The NEWPLOT system uses a com- mand file, which should b e p r e p a r e d beforehand, r e a d s t h e d a t a from t h e auxilli- a r y d a t a file, and plots t h e r e s p e c t i v e g r a p h s . Control i s t h e n t r a n s f e r r e d b a c k t o t h e dialog system. Thus, t h e u s e r should create t h e s p e c i a l command file f o r t h e NEWPLOT system, which t h e n starts execution from t h e dialog system. In t h e new version of t h e dialog system, formation of t h e command file f o r t h e NEWPLOT sys-

tem i s realized automatically from the main system. The generalized version of the system, which takes into account s e x composition of the population, i s now being developed f o r PCs.

Appendixes

A1

Input

Data

File

Before using t h e system t h e u s e r should p r e p a r e t h e initial d a t a file. The d a t a a r e r e a d in f r e e format from t h e device with a logical number of 4. The name of t h e in- put file i s requested by t h e system at t h e beginning of t h e dialog. This file contains t h e following information:

(1) The t i t l e of t h e d a t a file

-

one r e c o r d containing information about t h i s d a t a file (the form of t h e note i s a r b i t r a r y ) .

(2) The model's p a r a m e t e r s .

NA

-

t h e number of t h e a g e groups, NA 5 1 8 in t h i s version of t h e model.

NSEXES

-

t h e number of s e x e s ( 1 o r 2).

NR

-

t h e number of regions o r s t a t e s , NR 5 1 5 in t h i s version.

NY

-

t h e size of t h e a g e c o h o r t , usually NY

=

1 o r NY

=

5.

NU

-

t h e number of s t r i n g s in t h e t i t l e of t h e system.

INIT

-

t h e initial y e a r of modeling.

NG

-

switch of t h e model type.

SEXRAT

-

t h e r a t i o of female t o male newborns.

NAGE(NA+l)

-

a r r a y of a g e boundaries.

NG

=

0 c o r r e s p o n d s t o t h e model t y p e in which a newborn a p p e a r s in t h e same s t a t e as t h e p a r e n t s . In t h i s c a s e t h e

C

matrix i s identical. When t h e switch NG

=

1 t h i s c o r r e s p o n d s t o t h e model where all newborns a p p e a r in t h e same state.

NDAT

-

switch of t h e initial d a t a type.

NDAT

=

1 c o r r e s p o n d s to t h e case when f e r t i l i t y , mortality, and migration are given in absolute numbers. If NDAT

=

2, t h e coefficients of f e r t i l i t y , mortali- t y , a n d migration a r e given.

The t i t l e of t h e system. This is t h e number of r e c o r d s t h a t will b e s e e n o n t h e display after a l l d a t a f r o m t h e file have been r e a d .

The name of t h e c o u n t r y or t h e system of t h e states (groups).

Data. For e a c h state (group) should b e given:

t h e d a t a f o r state 1, t h e d a t a for state 2, t h e d a t a f o r state NR.

The d a t a f o r e a c h state includes t h e following information:

The name of t h e region or s t a t e , which may contain up to 8 symbols.

The population's a g e s t r u c t u r e at time INIT.

Fertility. The age-specific p a t t e r n i s specified. When NDAT

=

1 th e b i r t h s are given in absolute numbers. When NDAT

=

2 t h e b i r t h rates are specified.

Mortality

-

t h e age-specific mortality i s specified. When NDAT

=

1 i t i s given in absolute numbers. If NDAT

=

2 t h e mortality rates are specified.

Transitions from one given state to a n o t h e r . When b i r t h a n d death are speci- fied in absolute numbers, then t h e a g e s t r u c t u r e of transitions should a l s o b e specified in terms of absolute numbers. If b i r t h and death are specified by rates, then age-dependent transition rates should a l s o b e specified.

The last sentence in t h e d a t a file i s t h e word END.

k 2 . Example of the Initial Data File

S t r i n g s which start with t h e symbol

*

are comments given to facilitate understand- ing of t h e s t r u c t u r e of t h e initial d a t a file. In r e a l initial d a t a files, a l l such com- ments are prohibited.

* ^1. The title of the data file.

country 1

:

- ^{2 regions} - two sexes: male,female

* 2. Model's parameters.

* ^{NA NSEXES NR NY NU} INIT NG NDAT SEXRAT

* 3. Age intervals for which data are given

* 4. Title in the system.

MLnTIREGIONAL POPULATION SIMULATION for

hypothetical country starting year 1975

* ^5. Name of the country or the states of the system.

COUNTRY

* ^6. Data for the first state.

*a) Name of the state.

NORTH

* Data for female.

*b) Population age structure.

*e)Transitions from 1 to 1.

*f)Transitions from 1 to 2.

* Data f o r m a l e .

* g ) Population age structure.

*i)Transition from 1 t o 1.

0. 0. 0 . 0. 0.

0 . 0 . 0. 0. 0.

*j)Transition from 1 t o 2.

* 7. Data f o r the second state.

SOUTH

62653.

100196.

52249.

0 . 7.

221.

287.

108.

19.

0.

0.

62653.

100196.

52249.

221.

287.

108.

19.

0.

0.

-

17

-

A.3

Example o f Dialog: U n d e r l i n e d Symbols are Introduced b y U s e r

I N T E R A C T I V E S Y S T E M for Multistate Population Simulation

Version 1.00

(C) Copyright 1986 VNIISI Moscow.

(C) Copyright 1986 IIASA Laxenburg

to continue press <return>:

0 - exit

1 - model initialization 2 - ^modelling

3

-

scenario setting 4 - results presentation

to start or to restart model you must first initialize it enter number:l

enter, please, name of the file with data

for the country you want to deal with: country.dat

MULTIREGIONAL POPULATION SIMULATION for

hypothetical country starting year 1975 to continue press <return>:

0

- exit

1 - model initialization 2 - modelling

3 - scenario setting

4

-

results presentation

enter number:3

0

- ^exit

1 - fertility (grr) 2 - mortality (gdr)

3 - transitions and morbidity

( g m r )

4 - varible by name 5 - save scenario

6 - read scenario from the file enter number:l

1 - ^NORTH

2 - ^SOUTH

3 - exit to previous level

you are setting fertility scenario enter region number:l

there was no scenario set for this variable the default value is 1.4698

1 - do not change default value 2 - set new scenario

enter number:2

enter new scenario in format

:

t ime value (to end press

^ z

and then <return>) 1980 1.7

1985 1 . 8

- 2

0 - ^exit

1 - fertility (grr) 2 - mortality (gdr)

3 - transitions and morbidity _(mu-) 4 - varible by name

5 - save scenario

6 - read scenario from the file enter number:O

0

- ^exit

1 - model initialization 2 - ^modelling

3 - scenario setting

4 - results presentation

enter number:2

enter end of time interval:1990 current time - ¹⁹⁸⁰

current time - 1985 current time - ¹⁹⁹⁰ 0 - ^exit

1 - model initialization 2 - ^modelling

3 - scenario setting 4 - results presentation enter number:4

0 - exit

1 - printing data during run 2 - dumping data

enter number:2 exit

age-specif ic rates gross rates

expectancies births, deaths transition flows

indices of labory activity summary tab 1 e

population distribution

percentage population distribution graphics

enter nurnber:8 enter sex

:

1 - ^{female, 2} - ^{male, 3 -total}

enter number: 2

population distributions by age and regions variant: male year: 1990

,

I

1 NORTH SOUTH COUNTRY 1

I I

I I

8

I

I a

01 155075. 65460. 220535. 1

I ,

5 : 147895. 63967. 211862. 1

I ,

101 119060. 59686. 178746. 1

I

I

15: 125832. 63020. 188852. 1

a

I

20: 159963. 80531. 240494. :

I

I

25: 195148. 96560. 291708. :

I

I

301 178302. 78842. 257144. 1

I ,

35 : 177265. 77129. 254395. 1

I

I

40

1

110612. 66918. 177530.

1

I

I

45 1 117336. 87764. 205100. 1

I ,

50 1 156183. 95139. 251322. 1

I

I

551 125737. 70186. 195924.

1

I ,

60: 99460. 54082. 153543. 1

I

I

65 : ^{72265. 37571. 109836.}

¹

I

I

70 : 40498. 25305. 65803. 1

I ,

75 : 65611. 49526. 115138.

1 1

total 1 2046244. 1071686. 3117930.

1

...

t o continue press < r e t u r n > : exit

age-specif ic r a t e s gross rates

expectancies births, deaths transition f l o w s

indices of labory activity summary table

population distribution

percentage population distribution graphics

enter number:3 enter s e x :

1 - ^female, 2 - ^male, 3 -total

enter number:l

life expectancies variant: female year: 1990

I

I

I

NORTH SOUTH

I

a , ^I

I I I

:

NORTH 1

67.010 3.068 I

:

SOUTH

I 4.180 67.780 :

I

I

total

1

71 .I89 70.848 : ...

to continue press <return>:

exit

age-specific rates gross rates

expectancies births, deaths transition f lows

indices of labory activity summary table

population distribution

percentage population distribution graphics

enter number:2 enter sex:

1 - ^female,

2

- male, 3 -total enter number:l

gross rates variant: female year: 1990

I

I

I

NORTH SOUTH

:

1 t I

I I I

1

gross fert. ratel 1.800 1.571 : : gross mort. rate: 1.342 1.431

1

: gr. mob.tot.ratel 0.098 0.070 :

1 NORTH 1

0.000 0.070 :

1 SOUTH

0.098 0.000

₁

...

to continue press <return>:

exit

age-specific rates gross rates

expectancies births, deaths transition flows

indices of labory activity summary table

population distribution

percentage population distribution graphics

enter number:lO 0 - exit

1 - population structure in

%

2 - age-specific fertility per 1000 3 - age-specific mortality per 1000 enter number:2

enter sex:

1 - ^{female, 2} - male, 3 -total enter number:l

0 - exit to previous level 1 - NORTH

2

- SOUTH 3 - COUNTRY

--- ^>2

0 - ^exit

1 - population structure in

%

2 - age-specific fertility per 1000 3 - age-specific mortality per 1000 enter number:l

enter sex:

1 - ^female, 2 - ^male, 3 -total enter number:l

0 - exit to previous level 1 - NORTH

2

-

SOUTH 3

- ^COUNTRY

--- ^>I

A.4. List of Variables for the Multistate Demographic Model

In

t h e following, indices in b r a c k e t s denote:

X

-

^{a g e ,}

1,J

-

number of states

IS

-

index of t h e s e x (1

-

female, 2

-

male, 3

-

t o t a l )

Population

POPR(X,I,IS)

-

population by a g e , state, a n d s e x PDTOT(X,IS)

-

population by a g e a n d s e x

PTOTR(1,IS)

-

population by state a n d s e x

PRCPDR(1,IS)

-

p e r c e n t of population d i s t r i b u t i o n by state a n d s e x POPTOT(1S)

-

t o t a l number of people in population a n d s e x

Fertility

RATF(X,I)

-

f e r t i l i t y rate by a g e of mother a n d state

BIRTH(X,I)

-

number of newborn by a g e of m o t h e r a n d by state BR(1,IS)

-

f e r t i l i t y rate by state a n d s e x of newborn

B(1,IS)

-

number of newborn by state a n d s e x BRTOT(1S)

-

t o t a l f e r t i l i t y rate by s e x of newborn BTOT(1S)

-

t o t a l number of newborn by s e x

GRR(1)

-

g r o s s f e r t i l i t y rate by state

GRRN(1)

-

s c e n a r i o g r o s s f e r t i l i t y rate by state or a switch if

<

⁰

Mortality

RATD(X,I,IS)

-

mortality rate by a g e , state, a n d s e x DR(1,IS)

-

mortality rate by state and s e x

D(1,IS)

-

number of d e a d by state and s e x DRTOT(1S)

-

t o t a l mortality rate by s e x

DEATH(X,I,IS)

-

number of dead by age, s t a t e , and sex DTOT(1S)

-

total number of dead by sex

GDR(1,IS)

-

g r o s s mortality r a t e by s t a t e and sex

GDRN(1,IS)

-

scenario gross mortality rate by s t a t e and sex o r a switch if

<

⁰

EXL(I,J,IS)

-

a v e r a g e time spent in s t a t e I f o r those who were born in s t a t e J by sex

EXLT(1,IS)

-

time t h a t a n a r b i t r a r y individual spent in s t a t e I by sex

Transitions between States

OMIG(X,I,J.IS)

-

number of transitions from state J t o state I by a g e and sex RATM(X,I,J,IS)

-

transition r a t e from s t a t e J t o state I by a g e and sex GMR(I,J,IS)

-

gross transition rate from J t o I by sex

GMRN(I,J,IS)

-

scenario gross transition rate from J t o I by sex o r a switch if

<

0

FMGR(1,IS)

-

number of transitions from J t o I by sex FMGRA(1,IS)

-

number of a r r i v a l s by s t a t e and sex FMGRD(1,IS)

-

number of d e p a r t u r e s by s t a t e and sex

FMGRR(I,J,IS)

-

transition r a t e from s t a t e J t o state I by sex FMGRDR(1,IS)

-

rate of d e p a r t u r e s by state and sex

FMGRAR(1,IS)

-

r a t e of a r r i v a l s by s t a t e and sex DFMGR(1,IS)

-

saldo of transitions by s t a t e and sex FMGRT(1S)

-

total number of transitions by sex

Indices of Labor Force Participation

ACT(1,IS)

-

number of individuals of active age (from 15 t o 6 4 ) by s t a t e and sex

RETM(1,IS)

-

number of elderly by state ( 6 5 y e a r s and o v e r ) and sex CHLD(1,IS)

-

number of children up t o 15 by s t a t e and sex

PASS(1,IS)

-

number of children up t o 15 and elderly of 65 y e a r s and o v e r by s t a t e and sex

ACTR(1,IS)

-

p r o p o r t i o n of individuals of a c t i v e a g e by state and s e x up t o 15 and 65+

PRPA(1,IS)

-

dependency r a t i o ( ) by state and s e x 1 5

-

⁶⁵

CHLDR(1,IS)

-

p r o p o r t i o n of children by s t a t e and s e x RETMR(1,IS)

-

p r o p o r t i o n of elderly by state and s e x

ACTTOT(1S)

-

t o t a l number of individuals of a c t i v e a g e by s e x CHLT(1S)

-

t o t a l number of children by sex

RETMT(1S)

-

total number of elderly by s e x PASST(1S)

-

t o t a l number of dependents by s e x

ACTTR(1S)

-

p r o p o r t i o n of individuals of a c t i v e a g e by s e x CHLDTR(1S)

-

p r o p o r t i o n of children by s e x

RETMTR(1S)

-

p r o p o r t i o n of elderly by s e x PRPTOT(1S)

-

dependency r a t i o by s e x

Other Indices

AGEM(1,IS)

-

a v e r a g e a g e by state and s e x AGEMT(1S)

-

a v e r a g e a g e by s e x

RNINC(I.IS)

-

n a t u r a l growth rate by state and s e x

RMINC(1,IS)

-

^growth rate d u e to transitions by state and s e x RNINCT(1S)

-

t o t a l growth rate by s e x

REFERENCES

[I] Keyfitz, N. (1980) MuLtidimensionaLity i n P o p u L a t i o n A n a L y s i s , Research Report RR-80-33 (Laxenburg, Austria: International Institute f o r Applied Systems Analysis).

[2] Yashin, A. (1977) MethodoLogicaL Aspects of ModeLing a n d D e c i s i o n Making in t h e HeaLth C a r e S y s t e m , Collaborative P a p e r CP-77-4

(Laxenburg, Austria: International Institute f o r Applied Systems Analysis).

[3] Willekens, F. and Rogers, A. (1978) S p a t i a L P o p u L a t i o n AnaLysis: Methods a n d C o m p u t e r P r o g r a m s , Research Report RR-78-18 (Laxenburg, Austria:

International Institute f o r Applied Systems Analysis).

[4] Willekens. F. (1979) C o m p u t e r P r o g r a m for Increment-Decrement (UuLtistate) Life TabLe AnaLysis: A User's ManuaL to L i f e i n d e c , Working P a p e r WP-79-102

(Laxenburg, Austria: International Institute f o r Applied Systems Analysis).

[5] Ramachandran, R. (1980) S i m u L a t i o n of MuLtiregionaL P o p u L a t i o n Change:

A n AppLication t o BeLgium (Brussels: Brije Universiteit).

[6] Scherbov, S. and Usbeck, H. (1983) S i m u L a t i o n of MuLtiregionaL P o p u L a t i o n Change: A n AppLication to t h e G e r m a n Democratic RepubLic, Working P a p e r WP-83-6 (Laxenburg, Austria: International Institute f o r Applied Systems Analysis).

[7] Gelovani, V.A. (1980) Man-machine modeling system of t h e global development processes, S y s t e m S t u d i e s A n n u a l , 155-173 (Moscow: VNIISI) (in Russian).

[8] Scherbov, S.Y. and Grechucha, V.A. (1984) Modeling of multiregional demo- graphic development, Materials of t h e Third All-Union School Seminar on S y s - t e m s A n a L y s i s of Social-EconomicaL ProbLems of RegionaL Development (No- vosibirsk) (in Russian).

[9] Rogers. A. (1975) I n t r o d u c t i o n to MuLtiregionaL MathematicaL D e m o g r a p h y . (New York: John Wiley).

[ l o ] Rogers, A. (Ed.) (1980) E s s a y s in MuLtistate MathematicaL D e m o g r a p h y , Research R e p o r t RR-80-10 (Laxenburg, Austria: International Institute f o r Applied Systems Analysis).

[ll] Just, P. (1983) Two P r o g r a m Packages for D e r i v i n g MuLtistate-MuLtiregion Life Tables a n d Two-Sex (Female D o m i n a n t ) P o p u L a t i o n P r o j e c t i o n s , Working P a p e r WP-83-10 (Laxenburg, Austria: International Institute f o r Applied Sys- tems Analysis).