N= starting phage density
B= starting bacterial density
p= probability of a single phage particle for infecting a single bacterium
a= number of infecting phage particles
p=a/B
B(0)= bacterial cells not infected
B(1)= bacterial cells infected by one phage particle
B(>1)= bacterial cells infected by several phage particles
n=number of infecting phage particles
Multiplicity of Infection or MOI
m=Multiplicity of Infection or MOI
m=p*N
m= a*N/B
a*N= plaque-forming unit (PFU)
a*N=-B*lnB(0)
Poisson distribution
An estimate of Bacterial cells proportion infected by n phage particles
is:
B(n)= e^-m* m^n/n!
and an estimate of Cellular Classes inside a Bacterial population infected by phages is :
Number of phage particles =0; B(0)=e^-m
Number of phage particles =1; B(1)=e^-m *m
Number of phage particles >1; B(>1)=1-e^-m*(m+1)
Example:
If m= 10 and B=10^7 bacterial cells
B(0)= e^-10= 4,5 *10 ^-5
bacterial cells not infected= 4,5*10^-5*10^7= 450 bacteria
B(1)=e^-10*10=4,5*10^-5*10
bacterial cells infected by one phage particle =4,5*10^-4*10^7=4500 bacteria
B(>1) =1-e^-10*(10+1)
bacterial cells infected by several phage particles=(1-4,5*10^-5(11))*10^7=9,995,050 bacteria
