Use the demographics equation derived in class to make a function which finds the population histories for each of 4 population groups. Migration into group 2 will be defined by a pulse function. SETUP: parameters= [ b2,d1,d2,d3,d4,112,123,t34] where b2, birth rate in group 2 di, death rates in group Pi tij, transition from group Pi to group Pj due to ageing M2effect, rectangular pulse defined by [Mann2,tStartM2,tEndM2] initconds= [ Pinit1, Pinit2, Pinit3,Pinit4] timedata= [tinit,tfinal,delt] RESULTS: P1, P2, P3,P4, group time histories M2, M2 time history Function C Rese 1 function (P1, P2, P3, P4,M2]= Demographics_2_fcn(parameters,M2effect, initconds, timedata) 2 3 4 5 6 7 end 8 Code to call your function C Reset 1 fprintf(" RUN Demographics_2 '); 2 3 % Parameters 4 b2= .02; 5 dl= .004; d2= .0075; d3= .012; d4= .019; 6 t12= .067; t23= .04; t34= .04; 7 8 % Migration effect M2 9 M2 ann= 80; 10 tStartM2= 20; 11 tEndM2= 50; 12 13 % Initial conditions (in 1000's for convenience) 14 Pinit1= 1200; 15 Pinit2= 1000; 16 Pinit3= 800; 17 Pinit4= 600; 18 19 % Solution control data 20 tinit= 0.; 21 tfinal= 100.; 22 delt= 0.5; 24 % SIMULATION SECTION 25 parameters= [b2, di, d2, d3, 04, t12, t23, t34); % bundle for convenience 26 M2effect= [M2ann, tStartM2, tEndM2]; 27 initconds= [Piniti, Pinit2, Pinit3, Pinit4]; 28 timedata= [tinit, tfinal, delt]; 29 30 [P1, P2, P3, P4,M2)= Demographics_2_fcna 31 parameters,M2effect, initconds, timedata); 32 33 % DISPLAY RESULTS SECTION 34 fprintf(' Demographics setup for Case 2: '); 35 fprintf(" b2=%5.4f ', b2); 36 fprintf( d1=%5.4f, d2=%5.4f, d3=%5.4f, d4=%5.4f ',di, d2,d3,04); 37 fprintf( t12=%6.4f, t23=%6.4f, t34=%6.4f ', t12,t23, t34); 38 fprintf(' Mann=%6.0f, tStartM2=84.0f, tEndM2=%4.0f ',... 39 M2ann, tStartM2, tEndM2); 40 fprintf(' initconds: %6.0f,%6.0f,%6.0f,%6.0f ', initconds (1,:)); 41 fprintf(' tinit=%3.1f., tfinal=%6.1f, delt=%6.2f ', tinit,tfinal, delt); 42 43% display starting and ending values in tabular format 44 fprintf(' Demographics results for Case 2: '); 45 nsteps= round((tfinal-tinit)/delt); 46 47 t= tinit: delt:tfinal; 48 fprintf(" Results at start and at finish '); 49 fprintf(" time P1 P2 P3 P4 '); 50 fmt1= '%7.2f %7.0f %7.0f %7.0f %7.0f %8.0f '; 51 for i=1:5 52 fprintf(fmt1, t(i),P1(i),P2(i),P3(i),P4(i)); 53 end 54 fprintf(' '); 55 for i=nsteps-4:nsteps+1 56 fprintf(fmt1, t(i),P1(i), P2(i),P3(i),P4(i)); 57 end 58 59 figure 60 subplot(3,1,1) 61 plot(t,P1(:),'-',t,P2(:),'--', 'LineWidth',2) 62 title( 'Demographics 1: P1, P2 histories, in 1000''s') 63 xlabel('t, years') 64 ylabel('P1, P2') 65 legend ( 'P1','P2') 66 grid on 67 68 subplot(3,1,2) 69 plot(t,P1(:),'-',t,P2(:),'--',t,P3(:),'-,',t,P4(:),':', 'LineWidth',2) 70 title('P1, P2, P3, P4 histories, in 1000''s') 71 %xlabel('t, years') 72 ylabel('P1, P2, P3, P4') 73 legend ( 'P1','P2', 'P3', 'P4') 74 grid on 75 76 subplot(3,1,3) 77 plot(t,M2,'-', 'LineWidth',2) 78 title('Migration effect M2, in 1000''s') 79 %xlabel('t, years') 80 ylabel('M2') 81 grid on 82 83 fprintf(' ') 84 % Assessment: M2 is correct P1 is Correct P2 is Correct P3 is correct P4 is correct Use the demographics equation derived in class to make a function which finds the population histories for each of 4 population groups. Migration into group 2 will be defined by a pulse function. SETUP: parameters= [ b2,d1,d2,d3,d4,112,123,t34] where b2, birth rate in group 2 di, death rates in group Pi tij, transition from group Pi to group Pj due to ageing M2effect, rectangular pulse defined by [Mann2,tStartM2,tEndM2] initconds= [ Pinit1, Pinit2, Pinit3,Pinit4] timedata= [tinit,tfinal,delt] RESULTS: P1, P2, P3,P4, group time histories M2, M2 time history Function C Rese 1 function (P1, P2, P3, P4,M2]= Demographics_2_fcn(parameters,M2effect, initconds, timedata) 2 3 4 5 6 7 end 8 Code to call your function C Reset 1 fprintf(" RUN Demographics_2 '); 2 3 % Parameters 4 b2= .02; 5 dl= .004; d2= .0075; d3= .012; d4= .019; 6 t12= .067; t23= .04; t34= .04; 7 8 % Migration effect M2 9 M2 ann= 80; 10 tStartM2= 20; 11 tEndM2= 50; 12 13 % Initial conditions (in 1000's for convenience) 14 Pinit1= 1200; 15 Pinit2= 1000; 16 Pinit3= 800; 17 Pinit4= 600; 18 19 % Solution control data 20 tinit= 0.; 21 tfinal= 100.; 22 delt= 0.5; 24 % SIMULATION SECTION 25 parameters= [b2, di, d2, d3, 04, t12, t23, t34); % bundle for convenience 26 M2effect= [M2ann, tStartM2, tEndM2]; 27 initconds= [Piniti, Pinit2, Pinit3, Pinit4]; 28 timedata= [tinit, tfinal, delt]; 29 30 [P1, P2, P3, P4,M2)= Demographics_2_fcna 31 parameters,M2effect, initconds, timedata); 32 33 % DISPLAY RESULTS SECTION 34 fprintf(' Demographics setup for Case 2: '); 35 fprintf(" b2=%5.4f ', b2); 36 fprintf( d1=%5.4f, d2=%5.4f, d3=%5.4f, d4=%5.4f ',di, d2,d3,04); 37 fprintf( t12=%6.4f, t23=%6.4f, t34=%6.4f ', t12,t23, t34); 38 fprintf(' Mann=%6.0f, tStartM2=84.0f, tEndM2=%4.0f ',... 39 M2ann, tStartM2, tEndM2); 40 fprintf(' initconds: %6.0f,%6.0f,%6.0f,%6.0f ', initconds (1,:)); 41 fprintf(' tinit=%3.1f., tfinal=%6.1f, delt=%6.2f ', tinit,tfinal, delt); 42 43% display starting and ending values in tabular format 44 fprintf(' Demographics results for Case 2: '); 45 nsteps= round((tfinal-tinit)/delt); 46 47 t= tinit: delt:tfinal; 48 fprintf(" Results at start and at finish '); 49 fprintf(" time P1 P2 P3 P4 '); 50 fmt1= '%7.2f %7.0f %7.0f %7.0f %7.0f %8.0f '; 51 for i=1:5 52 fprintf(fmt1, t(i),P1(i),P2(i),P3(i),P4(i)); 53 end 54 fprintf(' '); 55 for i=nsteps-4:nsteps+1 56 fprintf(fmt1, t(i),P1(i), P2(i),P3(i),P4(i)); 57 end 58 59 figure 60 subplot(3,1,1) 61 plot(t,P1(:),'-',t,P2(:),'--', 'LineWidth',2) 62 title( 'Demographics 1: P1, P2 histories, in 1000''s') 63 xlabel('t, years') 64 ylabel('P1, P2') 65 legend ( 'P1','P2') 66 grid on 67 68 subplot(3,1,2) 69 plot(t,P1(:),'-',t,P2(:),'--',t,P3(:),'-,',t,P4(:),':', 'LineWidth',2) 70 title('P1, P2, P3, P4 histories, in 1000''s') 71 %xlabel('t, years') 72 ylabel('P1, P2, P3, P4') 73 legend ( 'P1','P2', 'P3', 'P4') 74 grid on 75 76 subplot(3,1,3) 77 plot(t,M2,'-', 'LineWidth',2) 78 title('Migration effect M2, in 1000''s') 79 %xlabel('t, years') 80 ylabel('M2') 81 grid on 82 83 fprintf(' ') 84 % Assessment: M2 is correct P1 is Correct P2 is Correct P3 is correct P4 is correct
