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# Multiplicity of infection

The multiplicity of infection or MOI is the ratio of infectious agents (e.g. phage or virus) to infection targets (e.g. cell). For example, when referring to a group of cells inoculated with infectious virus particles, the multiplicity of infection or MOI is the ratio defined by the number of infectious virus particles deposited in a well divided by the number of target cells present in that well.

## 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.

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 $m \ll 1$.