Mathematical models to better combat HIV
Prevention and treatment strategies designed by analyzing early viral dynamics
May 31, 2013 - Philadelphia, PA - The first few hours to days following exposure to human immunodeficiency
virus (HIV) can be of critical importance in determining if infection occurs in a patient. But the low numbers of viruses and infected
cells at this stage makes it very difficult to study these events in humans or animal models.
Theoretical mathematical models can help analyze viral dynamics in this early phase, and hence offer insights into
therapeutic and prevention strategies, as evidenced by a paper published last month in the SIAM Journal on Applied Mathematics .
In a paper titled Stochastic Analysis of
Pre- and Postexposure Prophylaxis against HIV Infection , authors Jessica Conway, Bernhard Konrad, and Daniel Coombs present
theoretical models of HIV dynamics immediately following exposure to the virus, thus providing a method to study infection and
treatment at these early stages, as well as come up with preemptive strategies for prevention.
Different classes of HIV drugs target different phases of the viral life cycle. For instance, drugs may prevent the viral
genetic material from being integrated into the host cell or disrupt the formation of new viral particles. "In models of chronic
infection, the different drug mechanisms end up having similar effects in mathematical models," explains author Daniel Coombs.
"But during early infection, every step of the life cycle is critical for the small virus population to persist in the
host, and this leads to interesting differences between the efficacies of different drugs in this phase."
The authors create stochastic models to analyze viral dynamics and to understand how protective or preventative drug treatment
prior to or immediately following exposure can act to reduce risk of infection under various scenarios.
There's a lot of discussion in public health circles about the potential of pre- and post-exposure prophylaxis (PrEP and PEP
respectively) against HIV," says Coombs. "Clinical practices for PEP are based on empirical findings with older, less effective drugs,
while PrEP is very new and still under development." For this reason, clinical trials of PrEP and PEP often show variable success,
making it hard to predict their effectiveness.
"We used stochastic models to investigate different choices of treatment strategies for both PEP and PrEP. Our results
are in good agreement with clinical findings, and also show possible directions for future investigation," says Coombs.
The paper proposes a simple and a more complex model. The simple one-compartment model of HIV infection uses a mathematical
formula that incorporates the dynamics between replication-competent and -incompetent viruses, as well as infected cells in the eclipse
phase (when they do not produce virus) and in the productive phase (when they do). The formula also includes the rate of infection
of new cells, the rate of viral clearance (due to removal or inactivation), as well as the interaction of different types of
drugs. The complex (two-compartment) model is similar, but additionally incorporates different cell types and transport
dynamics-two factors that are also important in the initiation of HIV infection.
While comparing drugs for PrEP, the authors conclude that reverse transcriptase inhibitors, which inhibit the process of
transcription of the virus's RNA into DNA in the host cell, are somewhat more effective than protease inhibitors, which inhibit viral
RNA replication. Protease inhibitors act by inactivating the protease enzyme, a molecule that speeds up breakdown of proteins in
organisms."The differences are small, though, and other practicalities (like toxic side-effects, or drug costs) might well be
more important in making the best choice," says Coombs. For PEP, most models and trials predictably show that fast initiation
of therapy is important. The authors' models indicate that risk reduction falls to below 15% after a three-day delay of
treatment, and a two-week treatment regimen is shown to work essentially as well as the current recommendation of four weeks.
The models presented in the paper deal with HIV infection following blood exposure, hence focusing mainly on occupational
exposure. Mechanisms leading to infection by sexual exposure are more complicated, but the general framework of the model may be
applied to cases of sexual infection. With more experimental data on anatomy, physiology and nature of virus-host interactions,
the current model can be reconstructed to capture the stages of sexual exposure. The concern regarding development of
drug-resistant HIV following PEP and PrEP can also be addressed with more extensive modeling with the help of
additional experimental data from animal models.
"It's tough to study the early events in HIV infection experimentally, so it's very natural to use mathematical modeling
to investigate the possible effects of drug treatment. On the other hand, because experimental work is so difficult, it's not obvious
how to construct a model," says Coombs, explaining the complexities of mathematically modeling HIV. "For this reason, we used the
simplest model we could think of that still captures the essentials of early viral replication. There's a lot of scope to
develop more complex models of early infection, and especially to use information gleaned from experimental infections
of animals. On the other hand, because our models are so simple, they could be adapted to other viral infections such
as HCV or influenza in the future."
Read another nugget article from the SIAM Journal on Applied Mathematics last month that uses mathematical models to help design prevention and treatment strategies against HIV (link to other HIV/viral nugget).
Source Article for above nugget:
Stochastic Analysis of Pre- and Postexposure Prophylaxis
against HIV Infection
Jessica M. Conway, Bernhard P. Konrad, and Daniel Coombs
SIAM Journal on Applied Mathematics , 73(2), 904-928 (Online publish date: April 18, 2013). The source article is available for free access at the link above until August 31, 2013.
About the authors:
Jessica Conway is a postdoctoral researcher in the theoretical biology and biophysics group at Los Alamos National Laboratory in
New Mexico, USA. Bernhard Konrad is a graduate student and Daniel Coombs is a professor of mathematics in the Department of
Mathematics at the University of British Columbia in Vancouver, Canada.
The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society
of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other
scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry,
government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate
institutional members, serves and advances the disciplines of applied mathematics and computational
science by publishing a variety of books and prestigious peer-reviewed research journals, by
conducting conferences, and by hosting activity groups in various areas of mathematics.
SIAM provides many opportunities for students including regional sections and
student chapters. Further information is available at www.siam.org.
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