% Equations for the inflammation model
% Marcella Torres 05/2019 
function du = sys_ODEs(t,u,params)

snr=params(1);
smr=params(2);
umr=params(3);
um1=params(4);
um2=params(5);
uan=params(6);
km1m2=params(7);
km1p=params(8);
km1m1=params(9);
km2m2=params(10);
kan=params(11);
knp=params(12);
km1an=params(13);
kpg=params(14);
kpn=params(15);
kpm=params(16);
unr=params(17);
n_inf=params(18);
kanm1=params(19);
kanm2=params(20);
km2m1=params(21);
km1n=params(22);
p_inf=params(23);
kb=params(24);
knan=params(25);
kann=params(26);
kc=params(27);

du = zeros(6,1);

%du(1) is dP/dt: pathogen
du(1)=kpg*u(1)*(1-u(1)/(p_inf+u(6)))-kpn*u(1)*u(4)-kpm*u(1)*u(2)/(1+(u(4)/n_inf)^2)-kpm*u(1)*u(3)/(1+(u(4)/n_inf)^2);
%du(2) is du(2)/dt: u(2) macrophages
du(2)=smr*(km1p*u(1)+km1n*u(4)+km1m1*u(2)+km1an*uan*u(5))/(umr+km1p*u(1)+km1n*u(4)+km1m1*u(2)...
    +km1an*uan*u(5)+ km2m2*u(3)+kc)-um1*u(2)-km1m2*kanm1*u(5)*u(2)/(1+(u(4)/n_inf)^2)+km2m1*u(3);
%du(3) is du(3)/dt: u(3) macrophages
du(3)=smr*(km2m2*u(3)+kc)/(umr+km1p*u(1)+km1n*u(4)+km1m1*u(2)+km1an*uan*u(5)+ km2m2*u(3)+kc)...
    -um2*u(3)+km1m2*kanm1*u(5)*u(2)/(1+(u(4)/n_inf)^2)-km2m1*u(3);
%du(4) is du(4)/dt: neutrophils
du(4)=snr*(knp*u(1)+knan*uan*u(5))/(unr+knp*u(1)+knan*uan*u(5))-kan*u(4);
%du(5) is du(5)/dt: apoptotic neutrophils
du(5)=kan*u(4)-kanm1*u(5)*u(2)/(1+(u(4)/n_inf)^2)-kanm2*u(5)*u(3)/(1+(u(4)/n_inf)^2)-kann*u(4)-uan*u(5);
%du(6) is du(6)/dt: nutrient broth
du(6)=-kb*u(6)*u(1);


end