# Multiplicity of infection

In virology, the multiplicity of infection or MOI is the ratio of agents (e.g. phage or virus) to infection targets (e.g. cell). For example, when referring to a group of cells inoculated with virus particles, the multiplicity of infection or MOI is the ratio of the number of virus particles to the number of target cells present in a defined space.

## Interpretation

The actual number of phages or viruses that will enter any given cell is a statistical process: some cells may absorb more than one virus particle while others may not absorb any. The probability that a cell will absorb $n$ virus particles when inoculated with an MOI of $m$ can be calculated for a given population using a Poisson distribution.

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

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

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

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

### MOI Examples

Percentage of cells infected based on MOI.

As the MOI increases, the percentages of cells infected with at least one viral particle also increases.

MOI  % Infected
1.0 63.2%
2.0 86.5%
3.0 95.0%
4.0 98.2%
5.0 99.3%
6.0 99.8%
7.0 99.9%
8.0 ~100.0%

Fields' virology, Part 1 By Bernard N. Fields,David Mahan Knipe,Peter M. Howley,Diane E. Griffin