multiplicity of infection

The actual number of viruses or bacteria that will enter any given cell is a stochastic process: some cells may absorb more than one infectious agent, while others may not absorb any. Before determining the multiplicity of infection, it's absolutely necessary to have a well-isolated agent, as crude agents may not produce reliable and reproducible results. The probability that a cell will absorb $n$ virus particles or bacteria when inoculated with an MOI of $m$ can be calculated for a given population using a Poisson distribution. This application of Poisson's distribution was applied and described by Ellis and Delbrück.{{cite journal |last1=Ellis |first1=Emory |last2=Delbruck |first2=Max |date=Jan 20, 1939 |title=The Growth of Bacteriophage |journal=The Journal of General Physiology |volume=22 |issue=3 |pages=365–384 |doi=10.1085/jgp.22.3.365 |pmc=2141994 |pmid=19873108}}

:$P(n)\; =\; \backslash frac\{m^n\; \backslash cdot\; e^\{-m\}\}\{n!\}$

where $m$ is the multiplicity of infection or MOI, $n$ is the number of infectious agents that enter the infection target, and $P(n)$ is the probability that an infection target (a cell) will get infected by $n$ infectious agents.

In fact, the infectivity of the virus or bacteria in question will alter this relationship. One way around this is to use a functional definition of infectious particles rather than a strict count, such as a plaque forming unit for viruses.{{cite web |title=Plaque forming unit |url=https://www.sciencedirect.com/topics/immunology-and-microbiology/plaque-forming-unit |website=Science Direct}}

For example, when an MOI of 1 (1 infectious viral particle per cell) is used to infect a population of cells, the probability that a cell will not get infected is $P(0)\; =\; 36.79\backslash \%$, and the probability that it be infected by a single particle is $P(1)\; =\; 36.79\backslash \%$, by two particles is $P(2)=18.39\backslash \%$, by three particles is $P(3)\; =\; 6.13\backslash \%$, and so on.

The average percentage of cells that will become infected as a result of inoculation with a given MOI can be obtained by realizing that it is simply $P(n>0)\; =\; 1\; -\; P(0)$. Hence, the average fraction of cells that will become infected following an inoculation with an MOI of $m$ is given by:

:$P(n>0)\; =\; 1\; -\; P(n=0)\; =\; 1\; -\; \backslash frac\{m^0\; \backslash cdot\; e^\{-m\}\}\{0!\}\; =\; 1\; -\; e^\{-m\}$

which is approximately equal to $m$ for small values of $m\; \backslash ll\; 1$.

Image:MOIGraph.png

As the MOI increases, the percentages of cells infected with at least one viral particle ($n>0$) also increases.{{cite book| title=Fields virology: Part 1| vauthors=Fields BN, Knipe DM, Howley PM | location=Philadelphia| publisher=Wolters Kluwer Health/Lippincott Williams & Wilkins| date=2007| isbn=9780781760607| oclc=71812790 }}

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• Infectious disease

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Category:Virology

Category:Bacteriology

Category:Bacteriophages

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