Mathematical Modeling of Multienzyme Biosensor System

Algorithm 1

function pdex4

m = 0;

x = linspace(0,1);

t=linspace(0,100000);

sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t);

u1 = sol(:,:,1);

u2 = sol(:,:,2);

u3 = sol(:,:,3);

u4 = sol(:,:,4);

u5 = sol(:,:,5);

figure

plot(x,u1(end,:))

title(‘u1(x,t)’)

xlabel(‘Distance x’)

ylabel(‘u1(x,2)’)

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figure

plot(x,u2(end,:))

title(‘u2(x,t)’)

xlabel(‘Distance x’)

ylabel(‘u2(x,2)’)

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figure

plot(x,u3(end,:))

title(‘u3(x,t)’)

xlabel(‘Distance x’)

ylabel(‘u3(x,2)’)

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figure

plot(x,u4(end,:))

title(‘u4(x,t)’)

xlabel(‘Distance x’)

ylabel(‘u4(x,2)’)

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figure

plot(x,u5(end,:))

title(‘u5(x,t)’)

xlabel(‘Distance x’)

ylabel(‘u5(x,2)’)

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function c,f,s = pdex4pde(x,t,u,DuDx)

c = 1; 1; 1; 1; 1;

f = 1; 1; 1; 1; 1.* DuDx;

a=0.01;b=0.01;p=0.01;e=0.01;

rp=0.01;kp=0.01;

rs=0.01;ki=0.01;kc=0.01;kb=5;

F1 =-(rs^∧2*u(1))/(1+a*u(2)+b*u(1));

F2 =-(ki^∧2*b*u(1))/(1+a*u(2)+b*u(1));

F3 =-(kc^∧2)/(1+p/u(4)+e/u(3));

F4 =-(rp^∧2)/(1+p/u(4)+e/u(3))+ (kp^∧2*u(1))/(1+a*u(2)+b*u(1));

F5 =(kb^∧2)/(1+p/u(4)+e/u(3));

s=F1; F2; F3; F4; F5;

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function u0 = pdex4ic(x) %create a initial conditions

u0 = 1; 1; 1; 1; 1;

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function pl,ql,pr,qr=pdex4bc(xl,ul,xr,ur,t) %create a boundary conditions

pl = ul(1)-1; ul(2)-1; ul(3)-1; ul(4)-0.01; ul(5)-0;

ql = 0; 0; 0; 0; 0;

pr = 0; ur(2)-0; ur(3)-0; 0; ur(5)-0;

qr = 1; 0; 0; 1; 0;