Population Projection of the Districts Noakhali, Feni, Lakhshmipur and Comilla, Bangladesh by Using Logistic Growth Model

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1 Pure nd Appled Mthemtcs Journl 017; 6(6): do: /j.pmj ISSN: (Prnt); ISSN: (Onlne) Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model Tnjm Akhter, Jml Hossn *, Slm Jhn Deprtment of Appled Mthemtcs, Nokhl Scence nd Technology Unversty, Nokhl, Bngldesh Eml ddress: (T. Akhter), (J. Hossn), (S. Jhn) * Correspondng uthor To cte ths rtcle: Tnjm Akhter, Jml Hossn, Slm Jhn. Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model. Pure nd Appled Mthemtcs Journl. Vol. 6, No. 6, 017, pp do: /j.pmj Receved: October 8, 017; Accepted: December 4, 017; Publshed: Jnury, 018 Abstrct: Uncontrolled humn populton growth hs been posng thret to the resources nd hbtts of Bngldesh. Populton of dfferent regon of Bngldesh hs been ncresng drmtclly. As thrvng country Bngldesh should rtstclly del wth ths ssue. Ths work s ll bout to estmte the populton projecton of the dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh. By consderng logstc growth model nd mkng use of lest squre method nd MATLAB to compute populton growth rte nd crryng cpcty nd the yer when populton wll be nerly hlf of ts crryng cpcty nd shown populton projecton for the bove mentoned dstrcts nd gve comprson wth ctul populton for the sme tme perod. Also estmte future pcture of populton for these dstrcts. Keywords: Populton, Crryng Cpcty, Growth Rte, Vtl Coeffcent, Lest Squre Method 1. Introducton Populton projecton s one of the most nttve concerns to ssure rpd, effectve nd sustnble dvncement for humn. It s useful tool to demonstrte the mgntude of current problems nd lkely to estmte the future mgntude of the problem. In rpdly chngng current world, populton projecton hs become one of the most momentous problems. Populton sze nd growth n country bldly nfluence the stuton of polcy, culture, educton nd envronment etc of tht country nd cost of nturl sources. Those resources cn be exhusted becuse of populton exploson but no one cn wt tll tht. Therefore the study of populton projecton hs strted erler. The projecton of future populton gves future pcture of populton sze whch s controllble by reducng populton growth wth dfferent possble mesures. Chnges n populton sze nd composton hve mny socl, envronmentl nd poltcl mplctons, for ths reson populton projecton often serve s bss for producng other projectons (e.g. brths, household, fmles, school). Every development plns contn future estmtes of ntons need s well s for polcy formulton for sectors such s lbour force, urbnzton, grculture etc. Any ntve or centrl government s contrbuton cn be extreme n performng tsk of long term effect f they hve fesble sttstcs prtculrly wth ncontrovertble presumptve ulteror scenro of the concern demogrphy. For mxml possble pproxmton mthemtcl nd sttstcl nlyss re requred. Thus from nlyss populton projecton cn be done bsng on the prevous dt. For such pproch to get better result, mthemtcl modelng hs become brod nterdscplnry scence tht uses mthemtcl nd computtonl technques to model nd elucdte the phenomen rsng n lfe scences. Effort n ths work s to model the populton growth pttern of Nokhl, Fen, Lkhsmpur & Comll usng Logstc growth model. For the purpose of populton modelng nd forecstng n vrety of felds, ths model s wdely used [1]. In wde rnge of cses n model the growth of vrous speces, frst order dfferentl equtons re very effectve. As populton of ny speces cn never be dfferentble functon of tme, t would pprently mpossble to mmc nteger dt of populton

2 165 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model wth dfferentl equton of contnuous vrble. In cse of lrge populton, f t s ncresed by one, then the chnge s very smll compred to the gven populton []. Logstc model lso tells tht the populton growth rte decreses s the populton reches the sturton pont of the envronment. In ths pper, the governng enttes.e. the crryng cpcty nd the vtl coeffcents for the populton growth were determned usng the lest squre method.. Development of Logstc Growth Model The mthemtcl model of populton growth proposed by Thoms R. Mlthus n 1798 s d P t dt ( ) P ( t ) = (1) Equton (1) s frst order lner dfferentl equton; representng populton growth n ths cse hs soluton P t ( ) 0 t = Pe () Ths s known s the soluton of Mlthusn growth model. Accordng to del concepton f the populton contnues to grow wthout bound nture wll tke over n the long run. In such stuton, brth rtes tend to declne whle deth rtes tend to ncrese for the lmted food resource. As long s there re enough resources vlble, there wll be n ncrese n the number of ndvduls, or postve growth rte. As resources begn to slow down, hence model ncorportng crryng cpcty, proposed by Belgn Mthemtcn Verhulst, s more resonbly consderble thn Mlthusn lw. Logstc model llustrtes how populton my ncrese exponentlly untl t reches the crryng cpcty of ts envronment. When populton reches the crryng cpcty, growth slows down or stops ltogether. Verhulst showed tht the populton growth depends both on the populton sze nd on how fr ths sze s from ts upper lmt,.e., ts crryng cpcty [3]. Hs modfcton of Mlthus's model encompss n ddtonl bp ( t) term where nd b re clled the vtl coeffcents of the populton [4]. Thus the modfed equton s of the form. d P t dt ( ) ( ) ( ) ( ) P t bp t = (3) Equton (3) provdes the rght feedbck to lmt the populton growth s the ddtonl term wll become very smll nd tend to zero s the populton vlue grows nd gets closer to. Thus the second term reflectng the competton b for vlble resources tends to constrn the populton growth nd consequently growth rte. The Verhulst s equton (3), wdely known s the logstc lw of populton growth, s nonlner dfferentl equton. Dscrdng t, equton (3) cn be rewrtten s d P P bp = (4) dt Seprtng the vrbles n equton (4) nd ntegrtng we obtn So tht 1 1 b dp t f + P = + bp 1 ( logp log ( bp )) = t + f (5) Usng t = 0 nd P = P0, we see tht Equton (5) becomes 1 f = logp log bp ( 0 ( 0 )) 1 1 ( ) ( logp log ( bp) ) = t + logp0 log ( bp0 ) Solvng for P yelds P = b 1 b + 1 e P0 t If we tke the lmt of equton (6) s t, we get (snce 0 > ) P mx (6) = lm P = (7) t b Then the vlue of, b nd P mx were determned by usng the lest squre method. Dfferentton of equton (6) twce wth respect to t gves t t ( ) t ( + ) 3 d P F e F e = 3 dt b F e where F = b 1. P0 Snce t the nflecton pont, the equton (8) representng second dervtve of P must be equl to zero. Ths s possble f (8) t F = e (9) lnf t = (10)

3 Pure nd Appled Mthemtcs Journl 017; 6(6): For ths vlue of t or tme the pont of nflecton occurs, tht s, when the populton s hlf of the vlue of ts crryng cpcty. Hence, the coordnte of the pont of lnf L nflecton s,. If the tme when the pont of nflecton occurs s t = t, then t F e we use ths new vlue of F nd replce b equton (6) wll be P = L ( t t ) 1+ e t = becomes F = e. If by L, then (11) Let coordntes of the ctul nd tht of the predcted, t, M respectvely wth the populton vlues be ( t m ) nd ( ) sme bscss whch cn be presented n the sme fgure. M m ndctes the error n ths cse. To ensure tht error ( ) s postve, we squre ( M m). Thus, for curve fttng, totl squred error denoted by l hs the form m ( ) j j (1) l = M m j= 1 It s cler tht equton (1) n connecton wth equton (11) contns three prmeters M, nd t. To elmnte L we let To get equton (11) s h = P = Lh (13) 1 ( t t ) 1+ e (14) In equton (1), usng the vlue of P from equton (13) nd by propertes of nner product, we get, m ( ) j j = ( M j mj ) + + ( Mn mn ) l = M m j= 1 ( Lh m ) ( Lh m ) = ( Lh m Lh m ) = n n ( Lh, Lh ) ( m, m ) = 1 n 1 n = LH G 1 1, n n = L H, H L H, G + G, G where H = h1, h, hn nd G = m1, m, mn Thus l = L H, H L H, G + G, G (15) Dfferenttng l once wth respect to L prtlly nd equtng t to zero, we get Ths gves, L H, H H, G = 0 H, G L = (16) H, H From equton (13) by substtutng ths vlue of L, we obtn H, G l = G, G (17) H, H The equton (17) s n error functon tht contnng just two prmeters nd t whch re determned by MATLAB progrm. The vlues of the prmeters were n equton (16) to get the vlue of L. 3. Results 3.1. Populton Projecton of Nokhl Dstrct Usng Logstc Growth Model We fnd tht vlues of nd t re nd 15 respectvely usng ctul populton vlues, ther correspondng yers from Tble 1 nd usng MATLAB progrms. Thus, the populton growth rte of Nokhl s nerly 1.8% per nnum nd populton sze wll be hlf of ts lmtng vlue or crryng cpcty n the yer 15. From equton (0) by usng vlues of nd t nd MATLAB progrm, we get L = P mx = (18) Ths s the predcted lmtng vlue of the populton of Nokhl. Then, equton (7) gves b = = (19) The ntl populton wll be P 0 = 57744, f we let t = 0 to correspond to the yer 001. Substtutng the vlues of P 0, b nd nto equton (6), we get P = (0) 0.018t e To compute the predcted vlues of the populton, the equton (0) ws used. The tme t the pont of nflecton s found from equton (10) by usng vlues of, b nd P 0 nd t s t 14 (1) Ths vlue when dded to the ctul yer correspondng to t = 0,.e., 001 gves 15 s erler found s the vlue of t. From equton (0) by usng ths vlue of t, we obtn b =

4 167 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model Thus, n the yer 15 the populton of Nokhl dstrct s predcted to be whch s hlf of ts crryng Tble 1. Actul nd predcted vlues of populton of Nokhl. cpcty. The tble below shows predcted nd ther correspondng ctul populton vlues: Yer Actul Populton Growth Rte Predcted Populton Yer Actul Populton Growth Rte Predcted Populton Source: Populton nd Housng Census 011, Zll Report: Nokhl, Bngldesh Sttstcl Bureu, Bngldesh [5]. The followng s the grph of ctul populton nd predcted populton vlues gnst tme. 3.3 x ctul populton predcted populton Populton Tme Fgure 1. Grph of ctul populton nd predcted populton vlues gnst. Below s the grph of predcted populton vlues gnst tme. Equton (0) ws used to compute the vlues. Fgure. Grph of predcted populton vlues gnst tme.

5 Pure nd Appled Mthemtcs Journl 017; 6(6): Populton Projecton of Fen Dstrct Usng Logstc Growth Model of P 0, b nd nto equton (6), we get We fnd tht the vlues of nd t re nd 95 respectvely by usng ctul populton vlues, ther correspondng yers from Tble nd usng MATLAB progrms. Thus, the vlue of the populton growth rte of Fen s nerly 1.4% per nnum nd the populton sze wll be hlf of ts lmtng vlue or crryng cpcty n the yer 195. From equton (16) by usng vlues of nd t nd MATLAB progrm, we get L = P mx = () Ths s the predcted lmtng vlue of the populton of Fen. Then, equton (11) gves b = = (3) The ntl populton wll be P 0 = , f we let t = 0 to correspond to the yer 001. Substtutng the vlues Tble. Actul nd predcted vlues of populton of Fen P = 0.014t e (4) + To compute the predcted vlues of the populton, the equton (4) ws used. The tme t the pont of nflecton s found from equton (10) by usng vlues of, b nd P 0 nd t s t 94 (5) Ths vlue when dded to the ctul yer correspondng to t = 0,.e., 001 gves 95 s erler found s the vlue of t. From equton (4) by usng ths vlue of t, we obtn b = Thus, n the yer 95 the populton of Fen dstrct s predcted to be whch s hlf of ts crryng cpcty. The tble below shows the predcted populton vlues nd ther correspondng ctul populton vlues. Yer Actul Populton Growth Rte Predcted Populton Yer Actul Populton Growth Rte Predcted Populton Source: Populton nd Housng Census 011, Zll Report: Fen, Bngldesh Sttstcl Bureu, Bngldesh [6]. The followng s the grph of ctul populton nd predcted populton vlues gnst tme. 1.5 x ctul populton predcted populton 1.4 Populton Tme Fgure 3. Grph of ctul populton nd predcted populton vlues gnst tme.

6 169 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model Below s the grph of predcted populton vlues gnst tme. Equton (4) ws used to compute the vlues Fgure 4. Grph of predcted populton vlues gnst tme Populton Projecton of Lkhshmpur Dstrct Usng Logstc Growth Model We fnd tht the vlues of nd t re nd 75 respectvely by usng ctul populton vlues, ther correspondng yers from Tble 3 nd usng MATLAB progrms. Thus, the vlue of the populton growth rte of Lkhshmpur s nerly 1.5% per nnum nd the populton sze wll be hlf of ts lmtng vlue or crryng cpcty n the yer 75. From equton (16) by usng vlues of nd t nd MATLAB progrm, we get L = P mx = (6) Ths s the predcted lmtng vlue of the populton of Lkhshmpur. Then, equton (11) gves b = = (7) The ntl populton wll be P 0 = , f we let t = 0 to correspond to the yer 001. Substtutng the vlues P = 0.015t e (8) + To compute the predcted vlues of the populton, the equton (8) ws used. The tme t the pont of nflecton s found from equton (10) by usng vlues of, b nd nd t s t 74 (9) Ths vlue when dded to the ctul yer correspondng to t = 0,.e., 001 gves 75 s erler found s the vlue of. From equton (8) by usng ths vlue of t, we obtn b = Thus, n the yer 75 the populton of Lkhshmpur dstrct s predcted to be whch s hlf of ts crryng cpcty. The tble below shows the predcted populton vlues nd ther correspondng ctul populton vlues. of P 0, b nd nto equton (6), we get Tble 3. Actul nd predcted vlues of populton of Lkhshmpur. Yer Actul Populton Growth Rte Predcted Populton Yer Actul Populton Growth Rte Predcted Populton Source: Populton nd Housng Census 011, Zll Report: Lkhshmpur, Bngldesh Sttstcl Bureu, Bngldesh [7].

7 Pure nd Appled Mthemtcs Journl 017; 6(6): The followng s the grph of ctul populton nd predcted populton vlues gnst tme x ctul populton predcted populton Populton Tme Fgure 5. Grph of ctul populton nd predcted populton vlues gnst tme. Below s the grph of predcted populton vlues gnst tme. Equton (8) ws used to compute the vlues Fgure 6. Grph of predcted populton vlues gnst tme Populton Projecton of Comll Dstrct Usng Logstc Model We fnd tht vlues of nd t re nd 05 respectvely usng ctul populton vlues, ther correspondng yers from Tble 4 nd usng MATLAB. Thus, the vlue of the populton growth rte of Comll s nerly 1.6% per nnum nd the populton sze wll be hlf of ts lmtng vlue or crryng cpcty n the yer 05. From equton (0) usng vlues of nd t nd MATLAB progrm, we get

8 171 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model L = P mx = (30) Ths s the predcted lmtng vlue of the populton of Comll. Then, equton (11) gves b = = (31) The ntl populton wll be P 0 = , f we let t = 0 to correspond to the yer 001. Substtutng the vlues P 0, b nd nto equton (6), we get To compute the predcted vlues of the populton, the equton (3) ws used. The tme t the pont of nflecton s found from equton (10) by usng vlues of, b nd P 0 nd t s t 04 (33) Ths vlue when dded to the ctul yer correspondng to t = 0,.e., 001 gves 05 s erler found s the vlue of t. From equton (3) by usng ths vlue of t, we obtn b = P = 0.016t 1 6.e (3) + Tble 4. Actul nd predcted vlues of populton of Comll. Thus, n the yer 05 the populton of Comll dstrct s predcted to be whch s hlf of ts crryng cpcty. The tble below shows the predcted populton vlues nd ther correspondng ctul populton vlues. Yer Actul Populton Nturl Growth Predcted Populton Yer Actul Populton Nturl Growth Predcted Populton Source: Populton nd Housng Census 011, Zll Report: Comll, BngldeshSttstcl Bureu, Bngldesh [8]. The followng s the grph of ctul populton nd predcted populton vlues gnst tme. 5.8 x ctul populton prdcted populton 5.4 Populton Tme Fgure 7. Grph of ctul populton nd predcted populton vlues gnst tme. Below s the grph of predcted populton vlues gnst tme. Equton (3) ws used to compute the vlues

9 Pure nd Appled Mthemtcs Journl 017; 6(6): Fgure 8. Grph of predcted populton vlues gnst tme Estmton for Future Populton of Nokhl Usng Logstc Growth Model As equton (0) s the generl soluton, we use ths to predct populton of Nokhl from 015 to 040 Tble 5. Predcted populton of Nokhl. Yer Predcted Populton Yer Predcted populton Below s the grph of Predcted Populton from 015 to 040 gnst tme. Equton (0) ws used to the compute the vlues Fgure 9. Grph of predcted populton vlues gnst tme.

10 173 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model 3.6. Estmton for Future Populton of Fen Usng Logstc Growth Model As equton (4) s the generl soluton, we use ths to predct populton of Fen from 015 to 040 Tble 6. Predcted populton of Fen. Yer Predcted Populton Yer Predcted Populton Below s the grph of Predcted Populton from 015 to 040 gnst tme. Equton (4) ws used to the compute the vlues Fgure 10. Grph of predcted populton vlues gnst tme Estmton for Future Populton of Lkhshmpur Usng Logstc Growth Model As equton (8) s the generl soluton, we use ths to predct populton of Lkhshmpur from 015 to 040 Tble 7. Predcted populton of Lkhshmpur. Yer Predcted Populton Yer Predcted Populton

11 Pure nd Appled Mthemtcs Journl 017; 6(6): Below s the grph of Predcted Populton from 015 to 040 gnst tme. Equton (8) ws used to the compute the vlues Fgure 11. Grph of predcted populton vlues gnst tme Estmton for Future Populton of Comll Usng Logstc Growth Model As equton (3) s the generl soluton, we use ths to predct populton of Comll from 015 to 040 Tble 8. Predcted populton of Comll. Yer Predcted Populton Yer Predcted Populton Below s the grph of Predcted Populton from 015 to 040 gnst tme. Equton (3) ws used to the compute the vlues

12 175 Tnjm Akhter et l.: Populton Projecton of the Dstrcts Nokhl, Fen, Lkhshmpur nd Comll, Bngldesh by Usng Logstc Growth Model 4. Dscusson In Fgure 1, 3, 5 & 7 the ctul nd predcted vlues of populton predcted by Logstc Model of the dstrcts Nokh, Fen, Lkhshmpur & Comll re qute close to one nother. Ths ndctes tht errors between them re very smll. We cn lso see n Fgure, 4, 6 & 8 tht grph of predcted populton vlues re ftted well nto the Logstc curve. In cse of Nokhl dstrct populton strts to grow gong through n exponentl growth phse rechng ( hlf of ts crryng cpcty) n the yer 15 fter whch the rte of growth s expected to slow down. As t gets closer to the crryng cpcty, the growth s gn expected to drstclly slow down nd rech stble level. Populton growth rte of Nokhl ccordng to nformton n Bngldesh sttstcl bureu ws round 1.5%, 1.7%n 001, 00 & nd 1.9% n 003, 004, 005 whch corresponds well wth the fndngs n ths reserch work of growth rte of pproxmtely 1.8% per nnum. Populton of Fen tends to grow untl t reches n yer 95 then rte of growth drop off. As t come closer to crryng cpcty, the growth s gn cutely slow down nd become sttc. Fen s populton growth rte corresponds to dt n Bngldesh sttstcl bureu ws closely 1.%, 1.3%, 1.4%, 1.4% n 001, 00, 003 nd 004 whch re dentcl wth the fndngs of growth rte of proxmtely 1.4% per nnum. In Lkhshmpur dstrct populton rse up to exponentlly n yer 75 fter whch growth rte slck off. As the populton pprochng the crryng cpcty, the growth s gn supposed to excessvely slow down nd ctch up to stble stte. The populton growth rte of Lkhshmpur followng to nformton n Bngldesh sttstcl bureu ws pproxmtely 1.3%, 1.6%n 001, 00, nd 1.4% n 003, 004, 005 whch re smlr to the fndngs n ths work of Fgure 1. Grph of predcted populton vlues gnst tme. growth rte of bout 1.5% per nnum. Comll s populton strts to grow through Mlthusn growth when t reches n yer 05 growth rte grdully declne. As t ppers nerer to crryng cpcty, the growth s gn severely slow down nd come up to n nvrble ste. Regrdng to dt of Bngldesh sttstcl bureu Comll s growth rte ws pproxmtely 1.3%, 1.4%, 1.4%, 1.6%, 1.6% n 001, 00, 003, 004, 005 whch re consstent wth the fndngs n ths pper of growth rte of nerly 1.6% per nnum. The Logstc growth model projected Nokhl, Fen, Lkhshmpur & Comll s populton n 040 to be , , & Populton predcted by Logstc model of bove mentoned dstrcts from 015 to 040 re presented n fgure 9, 10, 11 nd 1 respectvely. 5. Conclusons Logstc model predcted crryng cpcty for the populton of Nokhl to be Populton growth of ny country depends lso on the vtl coeffcents. The vtl coeffcents, b re respectvely nd Thus the populton growth rte of Nokhl, ccordng to ths models 1.8% per nnum. Ths pproxmted populton growth rte compres well wth the sttstclly predcted vlues n lterture. Bsed on ths model the populton of Nokhl s expected to be ( hlf of ts crryng cpcty) n the yer 15. Logstc growth model estmted crryng cpcty for the populton of Fen to be Here the vtl coeffcents, b re respectvely nd Thus the populton growth rte of Fen, ccordng to ths model s 1.4% per nnum. Bsed on ths model the populton of Fen s supposed to be (hlf of crryng cpcty) n the yer 95. For Lkhshmpur dstrct crryng cpcty predcted by Logstc growth model s nd the

13 Pure nd Appled Mthemtcs Journl 017; 6(6): vtl coeffcent, b re nd Thus the populton growth rte of Lkhshmpur s 1.5% per nnum. Accordng to ths model, the populton of Lkhshmpur s presumed to be n the yer 75. Logstc growth model clculted crryng cpcty for the Comll s populton to be long wth vtl coeffcents, b re respectvely nd Thus the populton growth rte of Comll, regrdng to ths model, s 1.6% per nnum whch compres well wth the sttstclly predcted vlues n lterture. The populton of Comll wll be n the yer 05. The followng re some recommendtons: t cn be seen tht populton of the bove mentoned dstrcts chnges drmtclly, so the government should work towrds ndustrlzton of these res. Becuse ndustrlzton solves ccommodton problem nd enhnce food resource whch wll rse the crryng cpcty of the envronment by reducng coeffcent b. Vtl coeffcent nd b ought to be re-vlued frequently to estmte the lterton n populton growth rte becuse these coeffcents ply n mportnt role on economc developments, socl trends, emprcl dvncement nd Medcre oblgtons.. Becuse of the rpdly chngng populton vrous nturl dssters my occur s the populton exceeds envronments crryng cpcty. Government should tke precutonry mesures nd fclttes plnnng for worst-cse outcome. Ths study ntroduces n mportnt role for better sustnble development plns wth the lmted resources through the ccurte de of the future populton sze nd relted nformton of resources. Becuse future s ntmtely ted to the pst, projecton bsed on pst trends nd reltonshps rse our understndng of the dynmcs of populton growth nd often provde forecsts of future populton chnge tht re suffcently ccurte to support good decson mkng. The projecton of future populton gves future pcture of populton sze whch s controllble by reducng populton growth wth dfferent possble mesures. In the future to reduce regonl or stte level nequltes comprtve study lke ths wll help the government n formulton the polcy for dentfyng the thrust res to be emphszed to mprove the overll soco-economc development. Hence we hope ths reserch work wll help to buld n evenly developed country. References [1] R. B. Bnks. Growth nd Dffuson Phenomen: Mthemtcl Frme works nd Applctons, Sprnger, Berln, [] B. Mrtn. Dfferentl equtons nd ther pplctons 4th ed. ISBN Sprnger-Verlg, New York, 199. [3] H. Von Foerster. Some remrks on chngng populton, n The Knetcs of Cell Cellulr Prolferton, F. Stohlmn Jr., Ed, Grune nd Strtton, New York, 1959, pp [4] M. J. Hossn, M. R. Hossn, D. Dtt nd M. S. Islm. Mthemtcl Modelng of Bngldesh Populton Growth. Journl of Sttstcs & Mngement Systems Vol. 18(015), No. 3, pp , DOI: / [5] Populton nd Housng Census 011. Zl Report: Nokhl, Bngldesh Sttstcl Bureu, Bngldesh. [6] Populton nd Housng Census 011. Zl Report: Fen, Bngldesh Sttstcl Bureu, Bngldesh. [7] Populton nd Housng Census 011. Zl Report: Lkhshmpur, Bngldesh Sttstcl Bureu, Bngldesh. [8] Populton nd Housng Census 011. Zl Report: Comll, Bngldesh Sttstcl Bureu, Bngldesh. [9] J. D. Murry. Mthemtcl Bology, Thrd Edton, Sprnger. [10] A. Jfr. Dfferentl equtons nd ther pplctons, nd ed. Prentce Hll, New Delh, 004. [11] F. R. Shrpe nd A. J. Lotk. A problem n ge dstrbuton, Phl. Mgzne, 1, 1911, pp [1] A. Wl, D. Ntubbre nd V. Mbonrgr. Mthemtcl Modelng of Rwnd Populton Growth: Journl of Appled Mthemtcl Scences, Vol. 5(53), 011, pp [13] Plckett, R. L. (197). The dscovery of the method of lest squres. Bometrk, 59, [14] Fred Bruer Crols Cstllo-Chvez, Mthemtcl Models n Populton Bology nd Epdemology, Sprnger, 001.