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Suppose a single smallpox virus is injected in an human adult's body. Will it cause disease in the host? Is there a minimum microbial load below which it will not cause disease?

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It depends on the pathogen, delivery method, environment, etc. In most cases, a single pathogen is not enough to cause disease -- it may need many millions or billions -- but there are some cases where it does seem that a single pathogen can consistently cause infection. For example

The minimum infectious dose of ASFV in liquid was 100 [i.e 1] 50% tissue culture infectious dose (TCID50), compared with 104 TCID50 in feed. The median infectious dose was 101.0 TCID50 for liquid and 106.8 TCID50 for feed.

--Infectious Dose of African Swine Fever Virus When Consumed Naturally in Liquid or Feed

If you're asking specifically about smallpox, I don't think anyone has done the experiment (the natural and most susceptible host being humans, I think you'd have some trouble finding volunteers to find to lethal dose). A single virus of the related ectromelia (mouse pox) virus can cause death in particularly susceptible mouse strains:

The intranasal lethal mousepox model employing the A/Ncr mouse strain is used to evaluate anti-orthopoxvirus therapies. These infections mimic large droplet transmission and result in 100% mortality within 7-10 days with as little as 1 PFU [plaque-forming unit] of ectromelia virus.

--Mousepox in the C57BL/6 strain provides an improved model for evaluating anti-poxvirus therapies

As a side note, the notion of what a "single virus" actually is, is more fuzzy than you might think, but that's a more complicated question; to a rough approximation a single TCID50 or PFU can be considered to be a single virus.

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According to these sources ( A, B, C, D ), infective dose varies widely among the diseases which are caused by pathogens. It is reported that as few as 10 enterohemorrhagic strains of Escherichia coli cells can cause an infection .

For an infection to occur, the pathogen must overcome and pass the physical, physiological, immunological and environmental barriers. Higher number of cells or viruses increases the possibility of overcoming these barriers. But, you should't forget that a pathogen cell or a virus particle doesn't need another one in order to infect the host, reproduce and cause a disease as a result. One single pathogen has all the necessary properties to do so.

So, in regard to the possibility of an infection, we can't say that one single pathogen can not infect a host and cause a disease. But, it is apparent that as a result of the biological properties of the pathogen and the characteristics of the infection mechanism, a particular pathogen has an observed infective dose that is different from other pathogens.

In addition to this consideration, don't confuse the number of pathogen in the environment (outside the host's body) with the number of pathogen injected into the host's body. Via the injection, the pathogen has already been transported behind some of the barriers.

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