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gen_model_mu.m
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function [ mu] = gen_model_mu(p,tsamp, Ninit, modelcode)
switch modelcode
case 1 % b-d model
b= p(1);
d=p(2);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)= N0.^3;
C_init(4)= N0.^4;
C_init(5) = V0;
C_init(6)= V0;
f = @(t,C) [(b-d)*C(1); % dn/dt
2*C(2)*(b-d) + C(1)*(b+d); % dn2/dt
3*C(3)*(b-d) + 3*C(2)*(b+d) + C(1)*(b-d); %dn3/dt
4*C(4)*(b-d)+ 6*C(3)*(b+d) + 4*C(2)*(b-d) + C(1)*(b+d); % dn4/dt
2*C(5)*(b-d) + (b+d)*C(1); %dV2dt
4*C(4)*(b-d)+ 6*C(3)*(b+d) + 4*C(2)*(b-d) + C(1)*(b+d)-4*(C(1).^3)*(b-d)*C(1)];%dV4dt
%4*C(4)*(b-d)+6*C(3)*(b+d) - 12*C(3)*(b-d)+ 4*C(2)*(b-d) - 12*C(2)*(b+d)-4*C(1)*(b-d)+C(1)*(b+d)]; %dV4dt
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
n3_C = C(:,3);
n4_C = C(:,4);
v2_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 2 % strong Allee model with Allee on birth probability
b= p(1);
d=p(2);
A = p(3);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)=V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)-(b-d)*A); % dn/dt
2*C(2).*(b-d) - (2*C(1).*(b-d)*A) + (C(1).*(b+d))-((b-d)*A); % dn2/dt
(2*C(2).*(b-d) - (2*C(1).*(b-d)*A) + (C(1).*(b+d))-((b-d)*A)-(2*C(1).*((b-d)*C(1)-(b-d)*A))); % dV/dt
(3*C(4).*(b-d)) + (3*C(2).*(b+d)-3*C(2)*(b-d)*A) - (3*C(1).*(b-d)*A)-((b-d)*A);%dn3dt
(4*C(5).*(b-d)) + (6*C(4).*(b+d))-(4*C(4)*(b-d)*A)+(4*C(2).*(b-d))-(6*C(2).*(b-d)*A)+ (C(1).*(b+d))+...
(4*C(1).*(b-d)*A)-((b-d)*A); %dn4dt
(4*C(5).*(b-d)) + (6*C(4).*(b+d))-(4*C(4).*(b-d)*A)+(4*C(2).*(b-d))-(6*C(2).*(b-d)*A)+ (C(1).*(b+d))+...
(4*C(1).*(b-d)*A)-((b-d)*A)-(4.*((C(1)).^3)*(((b-d).*C(1)-(b-d)*A)))];
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 3 % strong Allee model with Allee on death probability
b= p(1);
d=p(2);
A = p(3);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)=V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)-(b-d)*A); % dn/dt
2*C(2).*(b-d) - (2*C(1).*(b-d)*A) + (C(1).*(b+d))+((b-d)*A); % dn2/dt
(2*C(2).*(b-d) - (2*C(1).*(b-d)*A) + (C(1).*(b+d))+((b-d)*A)-(2.*C(1).*((b-d)*C(1)-(b-d)*A))); % dV/dt
(3*C(4).*(b-d)) + (3*C(2).*(b+d))-(3*C(2).*(b-d)*A) + (3*C(1).*(b-d)*A) + ((b-d).*C(1))-((b-d)*A);%dn3dt
(4*C(5).*(b-d)) + (6*C(4).*(b+d))-(4*C(4)*(b-d)*A)+(4*C(2).*(b-d))+(6*C(2).*(b-d)*A)+ (C(1).*(b+d))+...
(4*C(1).*(b-d)*A)+((b-d)*A); %dn4dt
(4*C(5).*(b-d)) + (6*C(4).*(b+d))-(4*C(4).*(b-d)*A)+(4*C(2).*(b-d))+(6*C(2).*(b-d)*A)+ (C(1).*(b+d))+...
(4*C(1).*(b-d)*A)+((b-d)*A)-(4.*((C(1)).^3)*(((b-d).*C(1)-(b-d)*A)))];
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 4 % strong Allee with b-d model
b= p(1);
d=p(2);
A = p(3);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)= V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)-(b-d)*A); % dn/dt
2*C(2).*(b-d)- 2.*C(1)*(b-d)*A + C(1).*(b+d); % dn2/dt
2*C(2).*(b-d)- 2.*C(1)*(b-d)*A + C(1).*(b+d)- 2.*C(1).*((b-d)*C(1)-(b-d)*A); % dV/dt
(3.*C(4).*(b-d)) + (3.*C(2).*(b+d))-(3.*C(2).*(b-d).*A) + (C(1).*(b-d)) - ((b-d)*A);%dn3dt
(4.*C(5).*(b-d)) + (6.*C(4).*(b+d))-(4.*C(4).*(b-d).*A)+(4.*C(2).*(b-d))+ (C(1).*(b+d))+...
(4.*C(1).*(b-d).*A); %dn4dt
(4.*C(5).*(b-d)) + (6.*C(4).*(b+d))-(4.*C(4).*(b-d).*A)+(4.*C(2).*(b-d))+ (C(1).*(b+d))+...
(4.*C(1).*(b-d).*A)- (4.*((C(1)).^3).*(((b-d).*C(1)-(b-d).*A)))];
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 5 % weak Allee with Allee on birth
b= p(1);
d=p(2);
A = p(3);
tau = p(4);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)= V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)*(1-((A+tau)./(C(1)+tau)))); % dN/dt
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*C(2).*(b-d).*((A+tau)./(C(1)+tau))-(b-d).*C(1).*((A+tau)./(C(1)+tau));
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*C(2).*(b-d).*((A+tau)./(C(1)+tau))-(b-d).*C(1).*((A+tau)./(C(1)+tau))+...
-2.*C(1).*((b-d)*C(1)*(1-((A+tau)./(C(1)+tau))));
3.*C(4).*(b-d) - 3.*C(4).*(b-d).*((A+tau)./(C(1)+tau)) + 3.*C(2).*(b+d) - 3.*C(2).*(b-d).*((A+tau))./(C(1)+tau)+...
+ C(1).*(b-d) - C(1).*(b-d).*((A+tau)./(C(1)+tau)); %dn3/dt
4.*C(5).*(b-d) - 4.*C(5).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) - 6.*C(4).*(b-d).*((A+tau)./(C(1)+tau)) + 4.*C(2).*(b-d)+...
-4.*C(2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d) - C(1).*(b-d).*((A+tau)./(C(1)+tau)); %dn4/dt
4.*C(5).*(b-d) - 4.*C(5).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) - 6.*C(4).*(b-d).*((A+tau)./(C(1)+tau)) + 4.*C(2).*(b-d)+...
-4.*C(2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d) - C(1).*(b-d).*((A+tau)./(C(1)+tau))+...
-4.*((C(1)).^3).*((b-d)*C(1)*(1-((A+tau)./(C(1)+tau))))]; %dV4dt
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 6 % weak Allee with Allee on death
b= p(1);
d=p(2);
A = p(3);
tau = p(4);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)= V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)*(1-((A+tau)./(C(1)+tau)))); % dN/dt
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*(C(1).^2).*(b-d).*((A+tau)./(C(1)+tau))+(b-d).*C(1).*((A+tau)./(C(1)+tau));
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*C((2)).*(b-d).*((A+tau)./(C(1)+tau))+(b-d).*C(1).*((A+tau)./(C(1)+tau))+...
-2.*C(1).*((b-d)*C(1)*(1-((A+tau)./(C(1)+tau))));
3.*C(4).*(b-d) - 3.*(C(2).*C(1)).*(b-d).*((A+tau)./(C(1)+tau)) + 3.*C(2).*(b+d) + 3.*(C(1).^2).*(b-d).*((A+tau))./(C(1)+tau)+...
+ C(1).*(b-d) - C(1).*(b-d).*((A+tau)./(C(1)+tau)); %dn3/dt
% fix n4-V4!!!
4.*C(5).*(b-d) - 4.*(C(4).*C(1)).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) + 6.*(C(2).*C(1))*(b-d).*((A+tau)./(C(1)+tau)) + 4.*C(2).*(b-d)+...
-4.*(C(1).^2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d) + C(1).*(b-d).*((A+tau)./(C(1)+tau)); %dn4/dt
4.*C(5).*(b-d) - 4.*C(5).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) + 6.*C(4).*(b-d).*((A+tau)./(C(1)+tau)) + 4.*C(2).*(b-d)+...
-4.*C(2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d) + C(1).*(b-d).*((A+tau)./(C(1)+tau))+...
-4.*((C(1)).^3).*((b-d)*C(1)*(1-((A+tau)./(C(1)+tau))))]; %dV4dt
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
case 7 % weak Allee with Allee on birth & death
b= p(1);
d=p(2);
A = p(3);
tau = p(4);
timesimdatavec = [];
% originally were running simulations-- we don't want to do this.
% instead, take the solved system of ODEs and just use that
for i = 1:length(Ninit)
N0 = Ninit(i);
V0 = 0;
C_init(1)=N0;
C_init(2)=N0.^2;
C_init(3)= V0;
C_init(4)= N0.^3;
C_init(5)= N0.^4;
C_init(6) = V0;
f = @(t,C) [((b-d)*C(1)*(1-((A+tau)./(C(1)+tau)))); % dN/dt
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*(C(1).^2).*(b-d).*((A+tau)./(C(1)+tau)); %dN2/dt
2.*C(2).*(b-d) + (b+d).*C(1) - 2.*C(2).*(b-d).*((A+tau)./(C(1)+tau))-2.*C(1).*((b-d).*C(1).*(1-((A+tau)./(C(1)+tau)))); %dV/dt
3.*C(4).*(b-d) - 3.*(C(2)*C(1)).*(b-d).*((A+tau)./(C(1)+tau)) + 3.*C(2).*(b+d) + C(1).*(b-d)+...
-C(1).*(b-d).*((A+tau)./(C(1)+tau)); %dn3/dt
4.*C(5).*(b-d) - 4.*(C(4)*C(1)).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) + 4.*C(2).*(b-d)+...
-4.*(C(1).^2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d); %dn4/dt
4.*C(5).*(b-d) - 4.*C(5).*(b-d).*((A+tau)./(C(1)+tau)) + 6.*C(4).*(b+d) + 4.*C(2).*(b-d)+...
-4.*C(2).*(b-d).*((A+tau)./(C(1)+tau)) + C(1).*(b+d)+...
-4.*((C(1)).^3).*((b-d)*C(1)*(1-((A+tau)./(C(1)+tau))))]; %dV4/dt
options1 = odeset('Refine',1);
options = odeset(options1,'NonNegative',1:6);
[t,C]=ode45(f, tsamp,C_init, options);
mu_C= C(:,1);
n2_C= C(:,2);
v2_C = C(:,3);
n3_C = C(:,4);
n4_C = C(:,5);
v4_C=C(:,6);
Cstat(:,1,i) = mu_C;
Cstat(:,2,i) = n2_C;
Cstat(:,3,i) = v2_C;
Cstat(:,4,i) = n3_C;
Cstat(:,5,i) = n4_C;
Cstat(:,6,i) = v4_C;
timesimdatavec = vertcat(timesimdatavec, tsamp');
end
mu_exp = Cstat(:,1,:);
mu_exp_long = reshape(mu_exp,size(mu_exp,1)*size(mu_exp,2)*size(mu_exp,3),1);
mu = mu_exp_long;
i0 = find(timesimdatavec==0);
mu(i0)= [];
end
end