viral dynamics

{{Use dmy dates|date=December 2018}}

Viral dynamics is a field of applied mathematics concerned with describing the progression of viral infections within a host organism.{{cite book |last1=Nowak |first1=Martin |last2=May |first2=Robert |date=2001 |title=Virus Dynamics: mathematical principles of immunology and virology |publisher=Oxford University Press |url=https://books.google.com/books?id=Kixhc3IiCy4C&q=virus+dynamics |access-date=2015-02-13 |archive-url=https://web.archive.org/web/20150213213133/https://books.google.ca/books?id=Kixhc3IiCy4C&printsec=frontcover&dq=virus+dynamics&hl=en&sa=X&ei=9yXeVIHfH4a8yQTipIGYBA&redir_esc=y#v=onepage&q=virus%20dynamics&f=false#v=onepage&q=virus%20dynamics&f=false |archive-date=2015-02-13 |url-status=live |isbn=9780198504177 }} It employs a family of mathematical models that describe changes over time in the populations of cells targeted by the virus and the viral load. These equations may also track competition between different viral strains and the influence of immune responses. The original viral dynamics models were inspired by compartmental epidemic models (e.g. the SI model), with which they continue to share many common mathematical features, such as the concept of the basic reproductive ratio (R₀). The major distinction between these fields is in the scale at which the models operate: while epidemiological models track the spread of infection between individuals within a population (i.e. "between host"), viral dynamics models track the spread of infection between cells within an individual (i.e. "within host"). Analyses employing viral dynamic models have been used extensively to study HIV,{{cite journal |last1=Perelson |first1=Alan S |last2=Ribeiro |first2=Ruy M |title=Modeling the within-host dynamics of HIV infection |journal=BMC Biology |year=2013 |volume=11 |issue=1 |page=96 |doi=10.1186/1741-7007-11-96 |pmid=24020860 |pmc=3765939 |doi-access=free }} hepatitis B virus,{{cite journal |last1=Nowak |first1=MA |last2=Bonhoeffer |first2=S |last3=Hill |first3=AM |last4=Boehme |first4=R |last5=Thomas |first5=HC |last6=McDade |first6=H |title=Viral dynamics in hepatitis B virus infection |journal=Proceedings of the National Academy of Sciences |year=1996 |volume=93 |issue=9 |pages=4398–4402 |doi=10.1073/pnas.93.9.4398 |pmid=8633078 |pmc=39549 |bibcode=1996PNAS...93.4398N |doi-access=free }}{{cite journal |last1=Ciupe |first1=SM |last2=Ribeiro |first2=RM |last3=Nelson |first3=PW |last4=Perelson |first4=AS |title=Modeling the mechanisms of acute hepatitis B virus infection |journal=Journal of Theoretical Biology |year=2007 |volume=247 |issue=1 |pages=23–35 |doi=10.1016/j.jtbi.2007.02.017 |pmid=17428501 |pmc=1994818|bibcode=2007JThBi.247...23C }} and hepatitis C virus,{{cite journal |last1=Neumann |first1=A |last2=Lam |first2=NP |last3=Dahari |first3=H |last4=Gretch |first4=DR |last5=Wiley |first5=TE |last6=Layden |first6=TJ |last7=Perelson |first7=AS |title=Hepatitis C Viral Dynamics in Vivo and the Antiviral Efficacy of Interferon-α Therapy |journal=Science |year=1998 |volume=282 |issue=5386 |pages=103–107 |doi=10.1126/science.282.5386.103 |pmid=9756471 |bibcode=1998Sci...282..103N }}{{cite journal |last1=Chatterjee |first1=A |last2=Smith |first2=PF |last3=Perelson |first3=AS |title=Hepatitis C Viral Kinetics: The Past, Present, and Future |journal=Clinics in Liver Disease |year=2013 |volume=17 |issue=1 |pages=13–26 |doi=10.1016/j.cld.2012.09.003 |pmid=23177280 |pmc=3584572}} among other infections