EliI was passing by a health center and I saw a poster having Swahili slogan “Ukimwi unaua” which means “AIDS kills”. Then I thought of HIV and I had questions on how it is multiplying in a human body. Though I am not a medical doctor but I was thinking there might be a mathematical model which describes the behavior of this virus. I came across IEEE journal [1] where by mathematical models were derived but Simulink model was not shared.
Basically, CD4+T Cells are protecting human body from invaders like HIV. Once a person is infected, CD4+T Cells increase rapidly to fight against infection, on the other hand HIV is embedding itself in these cells and destroy them which makes affected CD4+T Cells to rise. However, at a certain period of time there will be an equilibrium in a patient’s body for both Healthy CD4+T Cells, Infected CD4+T Cells and Virus(Viral load).
System parameters
- Parameters.png (21.83 KiB) Viewed 2994 times
- Parameters.png (21.83 KiB) Viewed 2994 times
Then, I presented these equations by building a Simulink model and Matlab code to visualize different scenarios in a patient. This model does not represent a patient who takes antiretro-viral medications.
Initial conditions
Initially, if (Healthy T Cells, Infected T Cells, Virus) = (1000,0,20) per cubic mm, the plots show sudden reduction of healthy cells and rise in Infected T Cells which means there is infection. Furthermore, virus increases at a very rapid rate to ten thousands and then stabilizes. This is a time to eat healthy and do a lot of exercises.
After several days[Time series], a patient will have a massive [ten thousands]increase in viral load as compared to initially which were 20 counts in this example.
A challenge to you
Find that article and build a model when patient is taking medications. Plot phase planes, bode diagrams and transfer functions. You may check as well mathematical models for insulin injection versus glucose levels for patients with diabetes. Take care "AIDS kills", maan this virus multiplies like
Matlab Code
- clc;
- % Death rate of uninfected T Cells per day
- d = 0.02;
- % Rate of free viruses produced per infected T Cell[counts/cell]
- k = 100;
- % Source term for uninfected T cells [per cubic mm per day]
- s = 20;
- % Infectivity rate of free virus particles
- B = 2.4*10^(-5);
- % Death rate of viruses per day
- c = 2.4;
- % Death rate of infected T Cells per day
- u = 0.24;
- sim('HIV_model');
- %days = 50*ones(length(tout),1);
- figure
- subplot(2,2,1)
- plot(tout,T)
- xlabel('Time series[days]')
- text(10,500,'\leftarrow Reduction in T Cells')
- legend("Healthy CD4+T Cells");
- subplot(2,2,2)
- plot(tout,Tstar)
- xlabel('Time series[days]')
- text(15,400,'\leftarrow Rising of infected T Cells')
- legend("Infected CD4+T Cells")
- subplot(2,2,[3 4])
- plot(tout,V)
- xlabel('Time series[days]')
- text(20,15000,'\leftarrow increase in Viral load')
- legend("Viruses[ngoma]")
- saveas(gcf,'hiv.png')
- figure
- plot3(T,Tstar,V)
- xlabel('Healthy T Cells')
- ylabel('Infected T Cells')
- zlabel('Viral load')
[1] Craig, I. K., Xia, X., and Venter, J. W.; Introducing HIV/AIDS Education into the Electrical
Engineering Curriculum at the University of Pretoria. IEEE Transactions on Education,
vol. 47, no. 1, February 2004, pp. 65–73
