DAFTAR PUSTAKA Anderson, Roy dan Robert May. 1992. Infectious Disease of Humans : Dynamics and Control. Inggris: Oxford Unifersity Press. Diekmann, O dan J.A.P Heesterbeek. 2000. Mathematical Epidemiology of Infectious Disease. New York: John Wiley & Son, LTD. Faveir, C, et.al. Early Determination of the Reproductive Number for Vector Born Disease : the Case of Dengue in Brazil. Tropical Medicine and International Health, April 2006. Edwards, Hendry dan David E. Penney.2000. Differential Equations and Boundary Value Problems. USA: Prentice Hall. Heesterbeek, J.A.P. A Brief History of R0 and a Recipe for Its Calculation. Review Article. 2002 Rahayu, Wiwiek dan Rahmi Rusin. Basic Reproduction Number, analisa Dinamika dan Proses Markov dari Model Penyebaran Ebola. Departemen Matematika FMIPA UI. Supriatna, A. K, Soewono Edi dan Van Gils. A Two Age Class Dengue Transmission Model. Marques, C. A, et al. The Basic Reproduction Number for Dengue Fever in Sao Paulo State, Brazil : 1990-1991 epidemic. Transactions of The Royal Society of Tropical Medicine and Hygiene. Hal 54. 1994 Siregar, F. A. Epidemiologi dan Pemberantasan Demam Berdarah Dengue di Indonesia. 2004. Fakultas Kesehatan Masyarakat Universitas Sumatera Utara. Siregar, A. D. Gambaran Pasien Demam Berdarah Dengue di bangsal Anak. Artikel Penelitian hal 67.
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LAMPIRAN Model Tanpa Delay function dy = Dengue(t,y) %nilai-nilai parameter m=2; a=0.45; b=0.15; c=0.0825; lambda=0.5; gamma=1/(60*52); dy = zeros(4,1); % a column vector dy(1) = gamma-m*a*b*y(1)*y(4)- gamma*y(1); dy(2) = m*a*b*y(1)*y(4)- gamma*y(2); dy(3) = lambda-(a*c*y(3)*y(2))- lambda*y(3); dy(4) = (a*c*y(3)*y(2))- lambda*y(4);
y0=[0.9 0.1 0.9 0.1]; waktu=[0 2000]; [T,Y] = ode45(@Dengue,waktu,y0); subplot(2,2,1),plot(T,Y(:,1),'LineWidth', 3),% title('Jumlah Susceptible Host'); ylabel('Hs(t)'), subplot(2,2,2),plot(T,Y(:,2),'LineWidth', 3),% title('Jumlah Infected Host');
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ylabel('Hi(t)'), subplot(2,2,3),plot(T,Y(:,3),'LineWidth', 3),% title('Jumlah Susceptible Host'); ylabel('Vs(t)'), subplot(2,2,4),plot(T,Y(:,4),'LineWidth', 3),% title('Jumlah Infected Host'); ylabel('Vi(t)'),
Model dengan Delay function sol = hoshen03 % Solusi numerik model Hoshen 2003
clear all; clc; % Parameter, satuan waktunya: hari m=2; a=0.45; b=0.15; c=0.0825; lambda=0.5; gamma=1/(60*52); Nv=1; Nh=1; tau1 = 4; tau2 = 6; rO=m*a*a*b*c*exp(-lambda*tau2)/(lambda*gamma) r1=a*a*m*b*c/(lambda*gamma) tunda = [tau1 tau2];
% Membuat data dari Fungsi awal
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% Fungsi awal didefinisikan di bawah titik = 100; tback = linspace(0,titik);
for i = 1 : titik temp = historyhoshen03(tback(i),0,0,0,0,0,0,0); if i == 1 datahis = [temp(1), temp(2), temp(3), temp(4)]; else datahis = [datahis; temp(1), temp(2), temp(3), temp(4)]; end end
% Menghitung PDT tspan = [0 30000]; toleransi = ddeset('RelTol', 1e-5, 'AbsTol', 1e-4);
sol = dde23(@modelnonlinearhoshen03, tunda, @historyhoshen03, tspan, toleransi, m, a, b, c, lambda, gamma, Nh, Nv, tau2);
subplot(2,2,1) semilogy(sol.x, sol.y(1,:), 'LineWidth', 1.5); ylabel('{\fontsize{15} Hs(t)}')
subplot(2,2,2) semilogy(sol.x, sol.y(2,:),'LineWidth', 1.5); ylabel('{\fontsize{15} Hi(t)}')
subplot(2,2,3)
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semilogy(sol.x, sol.y(3,:), 'LineWidth', 1.5); ylabel('{\fontsize{15} Vs(t)}')
subplot(2,2,4) semilogy(sol.x, sol.y(4,:), 'LineWidth', 1.5); ylabel('{\fontsize{15} Vi(t)}')
function his = historyhoshen03(t, m, a, b, c, lambda, gamma, Nh, Nv, tau2) his = [exp(2*t) exp(1-3*t) exp(1+2*t) exp(-t)];
function yp = modelnonlinearhoshen03(t, y, Z, ... m, a, b, c, lambda, gamma, Nh, Nv, tau2)
ylag1 = Z(:,1); ylag2 = Z(:,2);
yp = zeros(4,1);
yp = [ gamma*Nh-m*a*b*y(1)*y(4)/Nv - gamma*y(1) m*a*b*ylag1(1)*ylag1(4)/Nv - gamma*y(2) lambda*Nv-(a*c*y(3)*y(2))/Nh - lambda*y(3) exp(-lambda*tau2)*(a*c*ylag2(3)*ylag2(2))/Nh - lambda*y(4) ];
Titik Kesetimbangan Non Endemik Model 2 restart: with(linalg): hsus:=gamma-(m*a*b*Hs*Vi)-gamma*Hs; hinf := m*a*b*Hs*Vi-gamma*Hi;
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Vsus:=lambda-a*c*Vs*Hi-lambda*Vs; Vinf:=a*c*Vs*Hi-lambda*Vi; solve({hsus,hinf,Vsus,Vinf},{Hs,Hi,Vs,Vi}); A := vector([hsus,hinf,Vsus,Vinf]); Jac:=jacobian(A,[Hs,Hi,Vs,Vi]); jac:=map(rcurry(eval,{'Vi'=0,'Hi'=0,'Vs'=1,'Hs'=1}),Jac); P:=factor(charpoly(jac,s)); denom(P); Pol:=numer(P)/((s+gamma)*(s+lambda)); Pol:=collect(Pol,s):Polneg:=subs(s=-s,Pol); c2:=coeff(Polneg,s,2);c1:=factor(coeff(Polneg,s,1));c0:=coeff(Polneg,s,0); c0:=c0/c2; subs(a^2=Ro*lambda*gamma/(m*b*c),c0);
Titik Kesetimbangan Endemik Model 2 restart: with(linalg): hsus:=gamma-(m*a*b*Hs*Vi)-gamma*Hs; hinf := m*a*b*Hs*Vi-gamma*Hi; Vsus:=lambda-a*c*Vs*Hi-lambda*Vs; Vinf:=a*c*Vs*Hi-lambda*Vi; solve({hsus,hinf,Vsus,Vinf},{Hs,Hi,Vs,Vi}); A := vector([hsus,hinf,Vsus,Vinf]); Jac:=jacobian(A,[Hs,Hi,Vs,Vi]); jac:=map(rcurry(eval,{'Vi'=-(m*a^2*b*c+gamma*lambda)/(m*a*b*(a*c+lambda)),'Hi'=-(-
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m*a^2*b*c+gamma*lambda)/((m*a*b+gamma)*c*a),'Vs'=lambda*(m*a*b+gamma) /(m*a*b*(a*c+lambda)),'Hs'=gamma*(a*c+lambda)/(a*c*(m*a*b+gamma))}),Jac); Polin:=factor(charpoly(Jac,s)); polE1:=Polin/((s+lambda)*(s+gamma)); polE1:=subs({Hs = 1, Vi = 0, Vs = 1, Hi = 0},polE1); coeff(polE1,s,0); polE2:=Polin/((s+lambda)*(s+gamma)); polE2:=subs({Vi = (a^2*c*m*b-lambda*gamma)/((a*c+lambda)*b*m*a), Hs = gamma*(a*c+lambda)/(a*c*(m*a*b+gamma)), Vs = lambda*(m*a*b+gamma)/(a*m*b*(a*c+lambda)), Hi = (a^2*c*m*blambda*gamma)/(a*c*(m*a*b+gamma))},polE2); polE2:=subs(s =-s,polE2); coeff(polE2,s,2);coeff(polE2,s,1);coeff(polE2,s,0);
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