In microbiology, the multiplicity of infection or MOI is the ratio of agents (e.g. phage or more generally virus, bacteria) to infection targets (e.g. cell). For example, when referring to a group of cells inoculated with virus particles, the 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 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 {\displaystyle n} virus particles or bacteria when inoculated with an MOI of m {\displaystyle 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.
P ( n ) = m n ⋅ e − m n ! {\displaystyle P(n)={\frac {m^{n}\cdot e^{-m}}{n!}}}
where m {\displaystyle m} is the multiplicity of infection or MOI, n {\displaystyle n} is the number of infectious agents that enter the infection target, and P ( n ) {\displaystyle P(n)} is the probability that an infection target (a cell) will get infected by n {\displaystyle 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. 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 % {\displaystyle P(0)=36.79\%} , and the probability that it be infected by a single particle is P ( 1 ) = 36.79 % {\displaystyle P(1)=36.79\%} , by two particles is P ( 2 ) = 18.39 % {\displaystyle P(2)=18.39\%} , by three particles is P ( 3 ) = 6.13 % {\displaystyle 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 ) {\displaystyle P(n>0)=1-P(0)} . Hence, the average fraction of cells that will become infected following an inoculation with an MOI of m {\displaystyle m} is given by:
P ( n > 0 ) = 1 − P ( n = 0 ) = 1 − m 0 ⋅ e − m 0 ! = 1 − e − m {\displaystyle P(n>0)=1-P(n=0)=1-{\frac {m^{0}\cdot e^{-m}}{0!}}=1-e^{-m}}
which is approximately equal to m {\displaystyle m} for small values of m ≪ 1 {\displaystyle m\ll 1} .
Example
As the MOI increases, the percentages of cells infected with at least one viral particle ( n > 0 {\displaystyle n>0} ) also increases.
See also LD50 Infectious disease
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