# Science:Math Exam Resources/Courses/MATH102/December 2014/Question A 05

MATH102 December 2014

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### Question A 05

The model given below on the left has been suggested for the spread of HIV within the immune system of an infected person. ${\displaystyle C(t)}$ is the density of healthy immune cells, ${\displaystyle I(t)}$ is the density of HIV-infected immune cells and ${\displaystyle V(t)}$ is the density of virus in the blood of a patient. Which of the options on the right gives a correct interpretation of some part of the model?

{\displaystyle {\begin{aligned}{\frac {dC}{dt}}&=P-\alpha CV-\gamma _{1}C\\{\frac {dI}{dt}}&=\alpha CV-\gamma _{2}I\\{\frac {dV}{dt}}&=\beta I-\gamma _{3}V\end{aligned}}}
1. Healthy cells can become infected when they encounter infected cells.
2. Healthy cells can become infected when they encounter virus.
3. Virus is produced at a rate proportional to the current viral density.
4. Infected cells die at a rate proportional to the viral density.
5. Virus is killed/removed at a rate proportional to the density of healthy immune cells.
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