% function to run the ODE model to compute cytokine expression
function [X] = odefn(t, x, p, LPSstim)
global h ssdeg
h = h + 1;
% LPS stimulus
if t > 0
LPS = LPSstim;
else
LPS = 0;
end
%% cytokine expression rates
v1_a = p(1); % activation rate, IL-1b
v1_2 = LPS/(LPS + p(2)); % LPS activates IL-1b
v1_3 = (x(1)^p(5))/(x(1)^p(5) + p(4)^p(5)); % IL-1b activates IL-1b
v1_4 = (x(2)^p(8))/(x(2)^p(8) + p(7)^p(8)); % TNFa activates IL-1b
v1_5 = (p(10)^p(11))/(x(3)^p(11) + p(10)^p(11)); % IL-6 inhibits IL-1b
v1_6 = (p(13)^p(14))/(x(5)^p(14) + p(13)^p(14)); % IL-10 inhibits IL-1b
v1_7 = (p(16)^p(17))/(x(6)^p(17) + p(16)^p(17)); % CCL5 inhibits IL-1b
v1_d = p(19)*x(1); % passive degradation of IL-1b
v2_a = p(20); % activation rate, TNFa
v2_2 = LPS/(LPS + p(21)); % LPS activates TNFa
v2_3 = (x(1)^p(24))/(x(1)^p(24) + p(23)^p(24)); % IL-1b activates TNFa
v2_4 = (x(2)^p(27))/(x(2)^p(27) + p(26)^p(27)); % TNFa activates TNFa
v2_5 = (p(29)^p(30))/(x(3)^p(30) + p(29)^p(30)); % IL-6 inhibits TNFa
v2_6 = (p(32)^p(33))/(x(4)^p(33) + p(32)^p(33)); % TGFb inhibits TNFa
v2_7 = (p(35)^p(36))/(x(5)^p(36) + p(35)^p(36)); % IL-10 inhibits TNFa
v2_8 = (p(38)^p(39))/(x(6)^p(39) + p(38)^p(39)); % CCL5 inhibits TNFa
v2_d = p(41)*x(2); % passive degradation of TNFa
v3_a = p(42); % activation rate, IL-6
v3_2 = LPS/(LPS + p(43)); % LPS activates IL-6
v3_3 = (x(2)^p(46))/(x(2)^p(46) + p(45)^p(46)); % TNFa activates IL-6
v3_4 = (p(48)^p(49))/(x(5)^p(49) + p(48)^p(49)); % IL-10 inhibits IL-6
v3_5 = (p(51)^p(52))/(x(6)^p(52) + p(51)^p(52)); % CCL5 inhibits IL-6
v3_d = p(54)*x(3); % passive degradation of IL-6
v4_a = p(55); % activation rate, TGFb
v4_2 = (x(2)^p(57))/(x(2)^p(57) + p(56)^p(57)); % TNFa activates TGFb
v4_3 = (x(4)^p(60))/(x(4)^p(60) + p(59)^p(60)); % TGFb activates TGFb
v4_d = p(62)*x(4); % passive degradation of TGFb
v5_a = p(63); % activation rate, IL-10
v5_2 = LPS/(LPS + p(64)); % LPS activates IL-10
v5_3 = (x(2)^p(67))/(x(2)^p(67) + p(66)^p(67)); % TNFa activates IL-10
v5_4 = (x(3)^p(70))/(x(3)^p(70) + p(69)^p(70)); % IL-6 activates IL-10
v5_5 = (p(72)^p(73))/(x(6)^p(73) + p(72)^p(73)); % CCL5 inhibits IL-10
v5_d = p(75)*x(5); % passive degradation of IL-10
v6_a = p(76); % activation rate, CCL5
v6_2 = LPS/(LPS + p(77)); % LPS activates CCL5
v6_3 = (x(1)^p(80))/(x(1)^p(80) + p(79)^p(80)); % IL-1b activates CCL5
v6_4 = (x(2)^p(83))/(x(2)^p(83) + p(82)^p(83)); % TNFa activates CCL5
v6_5 = (x(3)^p(86))/(x(3)^p(86) + p(85)^p(86)); % IL-6 activates CCL5
v6_6 = (p(88)^p(89))/(x(4)^p(89) + p(88)^p(89)); % TGFb inhibits CCL5
v6_7 = (p(91)^p(92))/(x(5)^p(92) + p(91)^p(92)); % IL-10 inhibits CCL5
v6_d = p(94)*x(6); % passive degradation of CCL5
%%% set the concentration-independent degradation rate constants
%%% these constants are set at the initial time step
if h == 1
ssdeg = zeros(1,6);
ssdeg(1) = v1_a * v1_2 * v1_3 * v1_4 * v1_5 * v1_6 * v1_7 - v1_d;
ssdeg(2) = v2_a * v2_2 * v2_3 * v2_4 * v2_5 * v2_6 * v2_7 * v2_8 - v2_d;
ssdeg(3) = v3_a * v3_2 * v3_3 * v3_4 * v3_5 - v3_d;
ssdeg(4) = v4_a * v4_2 * v4_3 - v4_d;
ssdeg(5) = v5_a * v5_2 * v5_3 * v5_4 * v5_5 - v5_d;
ssdeg(6) = v6_a * v6_2 * v6_3 * v6_4 * v6_5 * v6_6 * v6_7 - v6_d;
end
%% ODEs to compute cytokine expression
X = zeros(6,1);
X(1) = v1_a * v1_2 * v1_3 * v1_4 * v1_5 * v1_6 * v1_7 - v1_d - ssdeg(1); % IL-1b
X(2) = v2_a * v2_2 * v2_3 * v2_4 * v2_5 * v2_6 * v2_7 * v2_8 - v2_d - ssdeg(2); % TNFa
X(3) = v3_a * v3_2 * v3_3 * v3_4 * v3_5 - v3_d - ssdeg(3); % IL-6
X(4) = v4_a * v4_2 * v4_3 - v4_d - ssdeg(4); % TGFb
X(5) = v5_a * v5_2 * v5_3 * v5_4 * v5_5 - v5_d - ssdeg(5); % IL-10
X(6) = v6_a * v6_2 * v6_3 * v6_4 * v6_5 * v6_6 * v6_7 - v6_d - ssdeg(6); % CCL5
end