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Infectivity Groups

Module by: Robert G. Whiddon. E-mail the author

Summary: Describes infectivity groups as a method to organize the study of microbiology.

Infectivity Groups


New students of microbiology encounter an array of facts and details that can seem overwhelming. Perhaps the most difficult challenge is trying to grasp the names of organisms, their basic characteristics, and diseases they cause. This can be simplified by the use of Infectivity Groups [1]. This method organizes bacteria by three simple observations or tests and results in a logical collection of 8 groups that describe almost all of clinical microbiology.

Microbiology can take advantage of binary search to learn the basics. A binary search operates by splitting an ordered list in half repeatedly until the sought item is located.

We can arrange bacteria in an ordered list based on three tests or observations. The observations are oxygen requirement, gram stain reaction, and shape.

The oxygen requirement specifies whether the organism is anaerobic or aerobic. Other distinctions such as microaerophilic etc. should be ignored for this purpose. A microaerophilic organism would be classified as aerobic for this purpose. It uses oxygen, but not a lot of oxygen.

Anaerobes are strict anaerobes. Oxygen would harm them.

The Gram stain results in organisms that appear blue-violet (Gram positive) or red (Gram negative). This distinction is made by the structure of the cell wall. You can read about this elsewhere. The only use of this is to declare an organism Gram negative (red) or Gram positive (blue-violet).

The shapes are rods (bacilli) or spheres (cocci). Grouping such as clusters, chains or pairs are not used for this purpose.

The results of each of these tests or observations is a positive or negative result which can be represented by a - or 0 to represent negative(characteristic absent), and a + or 1 to represent positive (characteristic present). Since there are only two possible outcomes for each observation, we can use a binary number system to represent these results.

Figure 1: Microbiology and Computer Science share Binary “thinking”.
Figure 1 (Slide1.png)

How to construct a binary number

To understand binary numbers, review decimal number construction. Most of us encountered the concept of number systems when they were introduced with decimal fractions in grammar school. You may have been required to memorize the value of each column to the left of the decimal. The value of the first columnm is 1, the second column is 10, the third is 100, etc. These values are calculated by raising the base numbr (10 is our common system) by the power of the column's position. The columns are numbered beginning with 0, not 1. Try a few calculations with your pocket calculator. See Table 1.

Table 1: Construction of decimal numbers.
Base Value Col. No. Col. Value Description
10 0 1 read as - 10 raised to the zero equals 1
10 1 10 read as - 10 raised to the one equals 10
10 2 100 read as - 10 raised to the two equals 100
10 3 1000 read as - 10 raised to the three equals 1000
10 4 10000 read as - 10 raised to the 4 equals 10,000

Examine Figure 2. This displays how one “builds” a representation of the number one-hundred sixty five. It requires 1 from the 100's column. Remainder is now 65. This requires 6 from the 10's column. Five remains. This requires 5 from the 1's column. The result is represented as a 3 digit number = 165.

Figure 2: How numbers are built.
Figure 2 (Slide2.png)

Let's build a simple number in binary. Refer to Figure 3. The exponent is displayed above the base number (two in this binary example). The values in the row “Col. Head” are derived by raising the base number (2) to the value of the exponent from the exponent row. The result is the value of the column head. Thus the value of the first three columns reading from right to left are 1,2,4. To represent the number 6 requires 1 from the 4's column. Remainder is now 2. This requires 2 from the 2's column. Nothing remains. The last column is not used and we place a zero there. The result is represented as a 3 digit number = 110.

Figure 3: How to build a binary number.
Figure 3 (Slide3.png)

To create larger numbers, one would require more columns. Refer to Figure 4. In this example we are building the number 165 (decimal) using a binary system. It is customary to use groups of 8 columns to represent binary numbers. Each column or number is called a “bit”. A collection of 8 bits is called a “byte”. This figure displays an 8 bit or one byte representation of the number 165 (decimal). Can you determine how the number was created?

Start at the left column and ask yourself “How many 128s are in 165?” Answer 1. Record a 1 for 128 column. Remainder is 37. Next column. “How many 64s are in 37?” Answer zero. Record a zero for this column. Continue across the table. The sum of all of the column values that have a 1 is 165, our decimal number. The binary representation of 165 decimal is 10100101.

Figure 4: Larger numbers require more columns.
Figure 4 (Slide4.png)

How does this apply to Microbiology?

We can apply this concept to microbiology and index our data based on three initial observations. These are Oxygen requirement, Gram stain reaction, and organism shape. Each of these is binary since the result can only be positive or negative. This binary base with 3 test choices mean that there can only be 8 categories to receive the results of these tests. These groups or categories can be numbered from 0 to 7. Each number represents the pattern of results for these three tests ranging from all negative to all positive and all possible combinations in between. See figures Figure 5 and Figure 6.

Figure 5: The Microbiology application of binary numbers.
Figure 5 (Slide5.png)
Figure 6: This provides a complete matrix by counting in binary numbers. Eight groups equal 0-7 in binary.
Figure 6 (Slide6.png)
Figure 7: Apply terminology to the digital representations.
Figure 7 (Slide7.png)

Next, one can apply descriptive text to each of the rows and develop a description of the group in english language. See Table 2.

Table 2: The eight Infectivity Groups defined.
Oxygen Gram stain Shape Description
0 0 0 Anaerobic, Gram negative, cocci
0 0 1 Anaerobic, Gram negative, rod
0 1 0 Anaerobic, Gram positive, cocci
0 1 1 Anaerobic, Gram positive, rod
1 0 0 Aerobic, Gram negative, cocci
1 0 1 Aerobic, Gram negative, rod
1 1 0 Aerobic, Gram positive, cocci
1 1 1 Aerobic, Gram positive, rod

You now have a framework for organizing your study or identification algorithms.


  1. Rypka, Eugene W. (1983). Infectivity groups: Standardized bacterial ID - fast. Diagnostic Medicine, October, 53-57.

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