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 agent 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 $$m \ll 1$$.