  Developing antiviral drugs is an exigent task since viruses mutate to
overcome the effect of antiviral drugs. As a result, the efficacy of most
antiviral drugs is short-lived. To include this effect, we modify the Neumann
and Dahari model. Considering the fact that the efficacy of the antiviral drug
varies in time, the differential equations introduced in the previous model
systems are rewritten to study the correlation between the viral load and
antiviral drug. The effect of antiviral drug that either prevents infection or
stops the production of a virus is explored. First, the efficacy of the drug is
considered to decreases monotonously as time progresses. In this case, our
result depicts that when the efficacy of the drug is low, the viral load
decreases and increases back in time revealing the effect of the antiviral
drugs is short-lived. On the other hand, for the antiviral drug with high
efficacy, the viral load, as well as the number of infected cells, monotonously
decreases while the number of uninfected cells increases. The dependence of the
critical drug efficacy on time is also explored. Moreover, the correlation
between viral load, the antiviral drug, and CTL response is also explored. In
this case, not only the dependence for the basic reproduction ratio on the
model parameters is explored but also we analyze the critical drug efficacy as
a function of time. We show that the term related to the basic reproduction
ratio increases when the CTL response step up. A simple analytically solvable
mathematical model is also presented to analyze the correlation between viral
load and antiviral drugs.
