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 ${\displaystyle n}$ virus particles or bacteria when inoculated with an MOI of ${\displaystyle m}$ 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.[2]

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

where ${\displaystyle m}$ is the multiplicity of infection or MOI, ${\displaystyle n}$ is the number of infectious agents that enter the infection target, and ${\displaystyle P(n)}$ is the probability that an infection target (a cell) will get infected by ${\displaystyle n}$ 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.[3]

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 ${\displaystyle P(0)=36.79\%}$, and the probability that it be infected by a single particle is ${\displaystyle P(1)=36.79\%}$, by two particles is ${\displaystyle P(2)=18.39\%}$, by three particles is ${\displaystyle P(3)=6.13\%}$, 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 ${\displaystyle P(n>0)=1-P(0)}$. Hence, the average fraction of cells that will become infected following an inoculation with an MOI of ${\displaystyle m}$ is given by:

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

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

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.[4]

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%

• LD₅₀
• Infectious disease