update

CODE/Faraimunache/HIV_Prototypecode.m

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+function HIV_Prototypecode 
+x0 = [ 1000 0 0.001]; 
+tspan = [0 1000]; 
+options = odeset('Refine',10, 'RelTol',1e-4);
+[t,x] = ode45(@HIV, tspan, x0, options);
+
+%% Plot
+figure(1)
+hold on
+   plot(t,x(:,1),'b','linewidth',2)
+   plot(t,x(:,2),'r','linewidth',2)
+   legend('T','I')
+   title ('CD4^+ populations')
+xlabel('time in days')
+ylabel('Population size')
+
+figure(2)
+   plot(t,x(:,3),'--r','linewidth',2)
+   legend('V')
+   title ('Virus population')
+xlabel('time in days')
+ylabel('Population size')
+
+figure(3)
+   plot(t,x,'linewidth',2)
+   legend('T','I','V')
+   title ('All populations')
+xlabel('time in days')
+ylabel('Population size')
+  end
+
+%initial values for model parameters 
+function dx = HIV(~, x)
+
+lambda= 20;
+mu = 0.02;
+beta = 1.7714e-05;
+delta = 0.1;
+N = 500;
+c=2.4;
+betav = 0.00002;
+%% Thresholds
+R0 = N*beta*delta*lambda/((delta+mu)*(betav*lambda+c*mu));
+betastar = ((c+350*betav)*(delta))/(350*(delta*N));
+%% Model equations 
+dx = zeros(3,1); % 
+%% systems of differential equations
+dx(1) = lambda - mu*x(1) - beta*x(1)*x(3);
+dx(2) = beta*x(1)*x(3) - (mu+delta)*x(2);
+dx(3) = delta*N*x(2) - c*x(3) - betav*x(1)*x(3);
+
+
+
+
+
+end

CODE/Faraimunache/Logistic.m

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+%% Get user input for logistic growth parameters and initial population values
+prompt = {'Enter the value of r:', 'enter the value of K:', 'Initial time t_1:', 'Final time t_f:', 'Initial population N_1:', 'Initial population N_2:', 'Initial population N_3:', 'Initial population N_4:','Initial population N_5:'};
+name = 'Logistic Growth Parameters and Initial Population Values';
+tspan = [1 50];
+defaultinput = {'0.02', '1000', '0', '500', '100', '600', '900','1100','1600'};
+parameters = inputdlg(prompt, name, tspan, defaultinput);
+
+%% Convert input to numeric values
+r = str2double(parameters{1});
+K = str2double(parameters{2});
+t_1 = str2double(parameters{3});
+t_f = str2double(parameters{4});
+N0 = str2double(parameters(5:end));% using multiple initial conditions.
+
+%% Set time range
+t = t_1:0.1:t_f;
+
+% Solve differential equation for each initial population value
+for i = 1:length(N0)
+    [t,N] = ode45(@(t,N) r*N*(1-N/K), t, N0(i));
+    % Plot results for each initial population value on the same graph
+    hold on
+    plot(t,N,'linewidth',2)
+end
+
+% Set plot properties
+%title('Logistic Growth')
+xlabel('Time')
+ylabel('Population Size, N(t)')
+box on
+legend('Population 1', 'Population 2', 'Population 3','Population 4', 'Population 5')

CODE/Faraimunache/ODElogisticmod.m

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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% This code solves the Logistic growth model
+%% 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function ODElogisticmod
+close all;
+clc
+%%%%%%%%%%%%%%%%%% Request parameter values from user %%%%%%%%%%%%%%%%%%%%%
+  prompt={'Enter the value of r ',...
+          'Enter the value of K ',...
+          };
+name='Parameter Values for Logistic Model';
+numlines=1;%specifies the number of lines for each answer in numlines
+
+defaultanswer={'0.02','1000'};
+options.Resize='on';
+options.WindowStyle='normal';
+options.Interpreter='tex';
+% create a dialog box that returns user input for multiple prompts
+%in a cell array
+% inputdlg suspends execution until the user responds.
+parameters=inputdlg(prompt,name,numlines,defaultanswer,options);
+%%%%%%%%%%%%%%%%%%% Request Initial data from user %%%%%%%%%%%%%%%%%
+ prompt1={'Enter the starting time, t_1',...
+          'Enter the final time t_f',...
+          'Enter the initial Population N_1','Enter the initial Population N_2','Enter the initial Population N_3'};
+name1='Initial data';
+numlines=2;
+defaultanswer1={'0','500','100','600','1500'};
+
+options1.Resize='on';
+options1.WindowStyle='normal';
+options1.Interpreter='tex';
+initialDat=inputdlg(prompt1,name1,numlines,defaultanswer1,options1);      
+%%%%%%%%%%%%%%%%%%%%%% Convert cell arrays to numbers %%%%%%%%%%%%%%%%%%%%%
+r     = str2double(parameters{1}); 
+K     = str2double(parameters{2});
+
+t_1    = str2double(initialDat{1});
+t_f    = str2double(initialDat{2});
+N_0    = str2double(initialDat(3:end));
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+tspan = [t_1 t_f];
+for i=1:length(N_0)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Solve system %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+[t,x] = ode45(@Logistic,tspan,N_0(i));
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Plot results %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+figure(1)
+hold on
+plot(t,x,'linewidth',2);
+xlabel('time');
+ylabel('N');
+legend
+%legend('Population N_1','Population N_2','Population N_3');
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function xdot = Logistic(~,x)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+N= x(1);
+
+
+dN = r*N*(1-(N/K));
+
+xdot = dN;
+end
+end

CODE/Faraimunache/ro.m

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+% Created by Farai Chirove
+% 3MC workshop Northwest University
+% Contour plots and surface plots for R_0
+clc
+close all
+
+% step size and time span
+h = 0.0001;
+tspan = 1:h:10;
+
+%parameter values 
+lambda= 20;
+mu = 0.02;
+%beta = 1.7714e-05;
+%delta = 0.1;
+N = 500;
+c=2.4;
+betav = 0.002;
+
+U1 = 1.7714e-05:0.001:0.1;
+U2 = 0.1:0.001:0.2;
+U3 = 0:0.001:1;
+
+for i = 1:length(U1)
+    for j = 1:length(U2)
+
+        u1 = U1(i); u2 = U2(j);
+        R0(i,j) = N*u1*u2*lambda/((u2+mu)*(betav*lambda+c*mu));
+
+         %R0(i,j) = ((1-u1)*(1-u2)*lambda*delta)/(mu*(mu+((1-u2)*gamma*phi*tau)/(ps*T)));
+        %R0(i,j) = ((1-u1)*(1-u2)*lambda*beta)/(mu*(mu+d+(gamma*vartheta*tau)/(pi*T)));
+
+    end
+end
+
+[X,Y] = meshgrid(U1,U2);
+
+Ro = R0; P=X; Q=Y;
+
+figure(1)
+%subplot(1,2,1)
+mesh(P,Q,Ro'), hold on
+[C,h] = contour(P,Q,Ro','color','k'); axis tight
+
+ text_handle1 = clabel(C,h);
+ set(text_handle1,'BackgroundColor',[1 1 .6],...
+     'Edgecolor',[.7 .7 .7])
+% Xlabel('\beta_1'), Ylabel('\beta_2'), Zlabel('R_0')
+% Xlabel('\phi_1'), Ylabel('\phi_2'), Zlabel('R_0')
+title('Change in $\mathcal{R}_{0}$ with $\beta$ and $\delta$', 'Interpreter', 'Latex','FontSize',20)
+xlabel('$\beta$', 'Interpreter', 'Latex','FontSize',20),
+ylabel('$\delta$', 'Interpreter', 'Latex','FontSize',20)
+zlabel('$\mathcal{R}_{0}$', 'Interpreter', 'Latex','FontSize',20)
+set(gcf, 'PaperUnits', 'inches')
+papersize = get(gcf, 'PaperSize');
+width = 6;         % Initialize a variable for width.
+height = 6;          % Initialize a variable for height.
+left = (papersize(1)- width)/2;
+bottom = (papersize(2)- height)/2;
+myfiguresize = [left, bottom, width, height];
+set(gcf, 'PaperPosition', myfiguresize);
+opt = struct('FontSize',20);
+set(get(gcf,'CurrentAxes'), opt)
+ print -depsc FigureR0.eps
+
+figure(2)
+%subplot(1,2,2)
+[C,h] = contourf(P,Q,Ro');
+text_handle = clabel(C,h);
+set(text_handle,'BackgroundColor',[1 1 .6],...
+   'Edgecolor',[.7 .7 .7])
+% Xlabel('\beta_1'), Ylabel('\beta_2')
+% Xlabel('\phi_1'), Ylabel('\phi_2')
+title('Level lines','FontSize',20)
+xlabel('$\beta$', 'Interpreter', 'Latex','FontSize',20) 
+ylabel('$\delta$', 'Interpreter', 'Latex','FontSize',20)
+set(gcf, 'PaperUnits', 'inches')
+papersize = get(gcf, 'PaperSize');
+width = 6;         % Initialize a variable for width.
+height = 6;          % Initialize a variable for height.
+left = (papersize(1)- width)/2;
+bottom = (papersize(2)- height)/2;
+myfiguresize = [left, bottom, width, height];
+set(gcf, 'PaperPosition', myfiguresize);
+opt = struct('FontSize',20);
+set(get(gcf,'CurrentAxes'), opt)
+title('b','FontSize',20)
+ print -depsc FigureRV.eps

CODE/README.md

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+Files here are organised by lecturer, for simplicity.