Cells that are susceptible to HIV infection are called T- (target) cells. Let T(

Question

Cells that are susceptible to HIV infection are called T- (target) cells. Let T(t) be the population of uninfected T-cells, T (t) that of the infected T-cells, and V (t) the population of the HIV virus. A model for the rate of change of the infected T-cells is dT dt = kV T T where is the rate of clearance of infected cells by the body, and k is the rate constant for the infection of T-cells by the virus. The equation for the virus is dV dt = P cV where P is the rate of production of new HIV virions and c is the “clearance” rate for the virions in the plasma. We model the production of the virus by P(t) = NT (t) where N is the total number of virions produced by an infected T-cell during its lifetime. Since 1/ is the length of its lifetime, NT (t) is the total rate of production of V (t). At least during the initial stages of infection, T can be treated as an approximate constant. The two coupled differential equations above are the equations for T (t) and V (t). (a) A drug therapy using RT (reverse transcriptase) inhibitors blocks infection, leading to k 0. Setting k = 0, solve for T (t). Substitute and solve for V (t). Take V 0 (0) = 0 and leave your final answer in terms of V (0). Show, by hand, that the solution is V (t) = V (0) c [cet ect] for c 6= . What is limt V (t) if c > ? If c < ?

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The question statement is too ambigious. I could not understand what is written and what is asked. kindly upload a picture of question or something.

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